A square acre of land is 5,280 square yards.
Between which two integers is the length of one side?
between 17 and 18 yards
between 72 and 75 yards
between 24 and 243 yards
between 1,320 and 1,321 yards
Answers
By factor decomposition, area of a square and power and root properties, the length of the side is between 72 yards and 76 yards. (Correct choice: B)
What integers are the limits between the length of an equivalent square side of a given area?
The area of a triangle is equal to the square of its side length and the area of land is a composite number, that is, a product of prime numbers. By factor decomposition, the equivalent form of 5,280 square yards is:
5,280 = 2⁵ × 3 × 5 × 11
Then, the equivalent side is equal to the square product of the product:
x = √(2⁵ × 3 × 5 × 11)
x = √(2⁴) × √(2 × 3 × 5 × 11)
x = 2² × √(2 × 3 × 5 × 11)
x = 4√330
As for √330 is between √324 = 18 and √361 = 19, then the length of the side is between 72 yards and 76 yards.
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Related Questions
Try to answer this question for me pleaseee
Answers
Answer:
H
Step-by-step explanation:
180-48=132
answer the number 2 only
Answers
The missing variables on item 2 are given as follows:
\(o = 12\sqrt{3}\)i = 24.What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:
Sine = length of opposite side to the angle/length of hypotenuse of the triangle.Cosine = length of adjacent side to the angle/length of hypotenuse of the triangle.Tangent = length of opposite side to the angle/length of adjacent side to the angle = sine/cosine.For the angle of 60º, we have that:
o is the opposite side.12 is the adjacent side.Hence the length o is given as follows:
tan(60º) = o/12.
\(\sqrt{3} = \frac{o}{12}\)
\(o = 12\sqrt{3}\)
Applying the Pythagorean Theorem, the length i is given as follows:
i² = 12² + \((12\sqrt{3})^2\)
i² = 576
i² = 24²
i = 24.
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Answer:
o = 12√3
i = 24
Step-by-step explanation:
From observation of the given right triangle, we can see that two of its interior angles measure 60° and 90°. As the interior angles of a triangle sum to 180°, this means that the remaining interior angle must be 30°, since 30° + 60° + 90° = 180°. Therefore, the triangle is a special 30-60-90 triangle.
The side lengths in a 30-60-90 triangle have a special relationship, which can be represented by the ratio formula a : a√3 : 2a, where "a" represents a scaling factor that can be any positive real number.
Side a is opposite the 30° angle (shortest leg).Side a√3 is opposite the 60° angle (longest leg).Side 2a is the hypotenuse (longest side).In triangle #2, the shortest leg is 12 units.
As "a" is the shortest leg, the scale factor "a" is 12.
The side labelled "o" is the longest leg opposite the 60° angle. Therefore:
\(o = a\sqrt{3}=12\sqrt{3}\)
The side labelled "i" is the hypotenuse of the triangle. Therefore:
\(i= 2a = 2 \cdot 12=24\)
Therefore:
o = 12√3i = 24please answer asap plz
Answers
4 3/8 + 5 1/2= in fractions
Answers
Answer:
9 7/8
Step-by-step explanation:
1. 4 3/8 can be converted into the improper fraction 35/8, and 5 1/2 can be converted into 11/2.
2. Now that we have 35/8 + 11/2, we have to find a common denominator. Since 2 goes into 8 four times, we can turn 11/2 into 44/8 by multiplying the numerator and denominator (the top and the bottom numbers) by 4.
3. Now we have 35/8 + 44/8. At this point, the all we have to do is add the numerators (the top numbers). 35+44=79, so our answer is 79/8, which we can simplify to 9 7/8.
What kind of graph is this
Answers
4600 people attended a football game. If 10% of the people who attended were teenagers, how many teenagers attended the game?
Answers
Answer:
460 teens
Step-by-step explanation:
10% = 0.1
multiple 0.1 by 4600 to get the amount of teens at the game. You could also do 4600/10 = 460
Convert the following fraction to a decimal.
21/40
Answers
Answer:
21/40=0.525
You basically just divided 21 and 40 and get the answer of 0l525
consider the sequences 31,35,39,43 ,then which of the following is the first terms of the sequences greater than 312
Answers
Answer:
316 ls the next term greater than 312. in the sequence you are adding 4 to the preceding term
A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admitance. Scores on the SAT test are normally distributed with a mean of 999 and a standard deviation of 199. Scores on the ACT test are normally distributed with a mean of 21.6 and a standard deviation of 5.2. It is assumed that the two tests measure the same aptitude, but use different scales.A. If a student gets an SAT score that is the 62-percentile, find the actual SAT score. SAT score = Round answer to a whole number. What would be the equivalent ACT score for this student? ACT score = Round answer to 1 decimal place. B. If a student gets an SAT score of 1563, find the equivalent ACT score. ACT score = Round answer to 1 decimal place.
Answers
Answer:
A.
SAT score = 1060
ACT score = 23.2
B.
ACT score = 36.3
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
SAT:
\(\mu = 999, \sigma = 199\)
If a student gets an SAT score that is the 62-percentile, find the actual SAT score.
This is X when Z has a pvalue of 0.62. So X when Z = 0.305.
\(Z = \frac{X - \mu}{\sigma}\)
\(0.305 = \frac{X - 999}{199}\)
\(X - 999 = 0.305*199\)
\(X = 1059.7\)
Rounding to the nearest whole number.
SAT score = 1060
ACT:
\(\mu = 21.6, \sigma = 5.2\)
The equivalent score is X when Z = 0.305.
\(Z = \frac{X - \mu}{\sigma}\)
\(0.305 = \frac{X - 21.6}{5.2}\)
\(X - 21.6 = 0.305*5.2\)
\(X = 23.19\)
So
ACT score = 23.2
B. If a student gets an SAT score of 1563, find the equivalent ACT score
Z-score for the SAT score.
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{1563 - 999}{199}\)
\(Z = 2.83\)
Equivalent ACT:
\(Z = \frac{X - \mu}{\sigma}\)
\(2.83 = \frac{X - 21.6}{5.2}\)
\(X - 21.6 = 2.83*5.2\)
\(X = 36.3\)
ACT score = 36.3
Find the perimeter of the rectangle 2A+ 4
a
Answers
L = length
W = Width
Given C is the midpoint of BD.
Prove: AACB AACD
Reasons
Statements
1. C is the midpoint of BD
1. given
A
2. BC e CD
2.
3. AC e AC
3. reflexive property
4. given
B
С
4.2BCA and 2DCA
are right 25
5.
D
5. all rights are
Complete the two-column proof.
6. AACB = AACD
6. SAS
Answers
Answer:definition of midpoint, angle BCA is congruent to angle DCA
The triangles ΔABC and ΔADC are congruent triangles by
a) definition of mid-point
b) measure of ∠ACB = measure of ∠ACD = 90°
What are Congruent Triangles?Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape
The three sides are equal (SSS: side, side, side)
Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)
Given data ,
Let the first triangle be represented as ΔABC
Let the second triangle be represented as ΔADC
Now , the side AC is the common bisector of both the triangles such that
C is the midpoint of BD
So , the measure of side BC = measure of side CD
And , the perpendicular bisector is right angle
So , the measure of ∠ACB = measure of ∠ACD = 90°
And , the measure of AC = measure of AC ( reflexive property )
Therefore , the triangles are congruent by SAS theorem
Hence , the triangles are congruent
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Classifg each angle as acute , right , obtuse , or straight
1) 10°
2) 98°
3) 180°
4) 90°
Answers
Answer:
1) acute
2) obtuse
3) straight
4) right
Step-by-step explanation:
acute angle=less than 90
right angle=90 exactly
obtuse=greater than 90
straight=exactly 180
hope this helps
At Burnt Mesa Pueblo, archaeological studies have used the method of tree-ring dating in an effort to determine when prehistoric people lived in the pueblo. Wood from several excavations gave a mean of (year) 1246 with a standard deviation of 42 years. The distribution of dates was more or less mound-shaped and symmetric about the mean. Use the empirical rule to estimate the following:
a. a range of years centered about the mean in which about 68% of the data (tree-ring dates) will be found between _______and _____ A.D.
b. a range of years centered about the mean in Which about Of the data (tree-ring dates) will be found between______ and ________ A.D.
c. a range of years centered about the mean in Which almost all the data (tree-ring dates) Will be found between_____ and A.D.
Answers
Answer:
(1204 ; 1288) ;
(1162 ; 1330) ;
(1120 ; 1372)
Step-by-step explanation:
Given that:
Mean, m = 1246 years
Standard deviation, s = 42 years
68% is within one standard deviation the mean ;
Therefore 68% equals ;
mean ± 1(standard deviation)
(1246 - 1(42)) ; (1246 + 1(42))
1204 ; 1288
B) b. a range of years centered 95% about the mean in Which about Of the data (tree-ring dates) will be found between______ and ________ A.D.
95% is within two standard deviation of the mean ;
Therefore 95% equals ;
mean ± 2(standard deviation)
(1246 - 2(42)) ; (1246 + 2(42)
(1246 - 84) ; (1246 + 84)
(1162 ; 1330)
c. a range of years centered about the mean in Which almost all the data (tree-ring dates) Will be found between_____ and A.D.
About 99.7% which is within 3 standard deviations of the mean
99.7% is within 3 standard deviations of the mean ;
Therefore ;
mean ± 3(standard deviation)
(1246 - 3(42)) ; (1246 + 3(42))
(1120 ; 1372)
solve the equation for z
5z-8=32
A. z=4
B. z=4.8
C. z=6
D. z=8
Answers
Answer:
Z=8 is the answer
Step-by-step explanation:
first, you add 8 to both sides which leaves you with 5z=40. then after that you divide both sides by 5 which leaves you with 5/5z = 40/5. then buy dividing 5 by 5 its leaves you with 1 which is equal to z because blank variables equal 1. On the other side if the equation 40 by 5 is 8 so that leaves you with z=8
Step-by-step explanation:
\( \tt{5z - 8 = 32}\)
We want to remove the 8 first.
Step 1 : Since the original equation is minus 8 , we are going to use the opposite operation and add 8 to both sides.
⟶ \( \tt{5z - 8 + 8 = 32 + 8}\)
Simplify -8 + 8 = 0 on the left. 32 + 8 = 40 on the right. Then we need to think about how to remove the coefficient 5.
⟶ \( \tt{5z = 40}\)
Step 2 : Since the opposite of multiplication is division , we are going to divide both sides by 5.
⟶ \( \tt{ \frac{5z}{5} = \frac{40}{5}} \)
Simplify. 5 / 5 = 1 on the left. 40/5 = 8 on the right. So , our answer is z = 8.
⟶ \( \tt{z = 8}\)
\( \pink{ \boxed{ \boxed{ \text{Our \: final \: answer : \boxed{ \underline{ \tt{z = 8}}}}}}}\)
Hope I helped ! ♡
Have a wonderful day / night ! ツ
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Find the average of
8,11,14,13,14, 9,15
Answers
Answer:
12
Step-by-step explanation:
(8+11+14+13+14+9+15)/7 = 12
Answer:
MedianTotal obs. = 7
if odd —Average = (n + 1 )/2
n = no. of obs.Average = 7 + 1 /2
= 8/2 = 4th obs.
=> 13Mean= Sum of obs./ Total obs.
= 8,11,14,13,14,9,15/7
= 84/7
=> 12Figure A is similar to Figure B. What must always be true?
a.
The corresponding side lengths of A and B are proportional.
c.
The corresponding side lengths of A and B are equal.
b.
The corresponding side lengths of A are twice the corresponding side lengths of B.
d.
The corresponding side lengths of A are half the corresponding side lengths of B.
Answers
Option (a) is the correct answer. When two figures are similar, it means they have the same shape but different sizes.
How to solve the question?
In other words, their corresponding angles are congruent, and their corresponding side lengths are proportional.
Option (b) and (d) suggest that the corresponding side lengths of A and B are related by a constant factor (either 2 or 1/2). However, this is not necessarily true for all similar figures. The constant of proportionality can be any positive real number.
Option (c) suggests that the corresponding side lengths of A and B are equal, which means that A and B are not just similar but congruent. This is not necessarily true for all similar figures, as similar figures can differ in size.
Therefore, option (a) is the only answer that must always be true for similar figures. The corresponding side lengths of similar figures are proportional, which means that if one side of figure A is twice as long as a corresponding side of figure B, then all other corresponding sides will also be in the same ratio of 2:1. Similarly, if one side of figure A is three times as long as a corresponding side of figure B, then all other corresponding sides will also be in the same ratio of 3:1. This proportional relationship holds true for all pairs of corresponding sides in similar figures
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Option (a) is the correct answer. The corresponding side lengths of A and B are proportional, must always be true if Figure A is similar to Figure B.
How to find if the figure is similar?When two figures are similar, their corresponding angles are congruent, and their corresponding side lengths are proportional. This means that if we take any two corresponding sides of the figures, the ratio of their lengths will be the same for all pairs of corresponding sides.
Option b and d cannot be true, as they both suggest a specific ratio of corresponding side lengths, which is not necessarily true for all similar figures.
Option c is not necessarily true, as two similar figures can have corresponding side lengths that are not equal but still have the same ratio.
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SOMONE HELPPPPPP
Its HRW
Answers
Answer:
0.48
Step-by-step explanation:
the eight is in the hundredths place, which is how you represent a percentage. (correct me if i'm wrong)
What is the domain of the relation?
Answers
(X+3)/6=5/4 what is x
Answers
Answer:
x = 9/2
Step-by-step explanation:
(x+3)/6=5/4
(x+3)/6*6=5/4*6
x+3=30/4
x+3-3=30/4-3
x=9/2
How many centigrams are in 1 gram? Use the metric table to help answer the question.
Answers
Answer:
100 cg
Step-by-step explanation:
Answer:
100 centigrams
Step-by-step explanation:
How many solutions does this system have? no solutions one unique solution O O two solutions O or an infinite number of solutions
Answers
Answer:
no solutions
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
equation of blue line is y = x + 2 , in slope- intercept form
with slope m = 1
equation of red line is y = x - 3 , in slope- intercept form
with slope m = 1
• Parallel lines have equal slopes
then the blue and red lines are parallel.
the solution to the system is at the point of intersection of the 2 lines
since the lines are parallel then they do not intersect each other.
thus the system shown has no solution.
Can someone PLEASE help me on A 3
Answers
Answer:
20.5, 23, 25.5
Step-by-step explanation:
+2.5
hope this helps branliest plzz
In triangle ABC, AP is an angle bisector of angle BAC. What is the length of PC? Round you answer to the nearest whole number.
A) 6 B) 7 C) 8 D) 9
Answers
Answer:
D) 9
Step-by-step explanation:
x = ½ × 13 = 6.5
y = ½ × 5 = 2.5
6.5 + 2.5 = 9
So the length of PC is 9
HOPE THIS HELPS AND HAVE A NICE DAY <3
what is 83.1 divided by 5
Answers
Answer: The answer is 16.62
Estimate the total amount of time Jessie practices by rounding to the nearest 100 minutes
Answers
Using simple mathematical operations, we know that Jessie's total time of practice is 410 minutes.
What are mathematical operations?A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.
There are predefined rules associated with the math operator's symbol that must be applied to the supplied operands or numbers.
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition Subtraction (from left to right).
So, the total time Jessie practices:
We must include the time spent practicing during the first week and the second week in order to determine the overall amount of time Jesse practices.
Total time:
165 + 245
410 minutes
Rounding off: 410 minutes
Therefore, using simple mathematical operations, we know that Jessie's total time of practice is 410 minutes.
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Complete question:
Jesse practices the trumpet for a total of 165 minutes during the first week of school. He practices for 245 minutes during the second week. A. Estimate the total amount of time Jesse practices by rounding to the nearest 10 minutes.
find the selling price for the item flash drive: $12 markup:35%
Answers
Answer:
16.2
Step-by-step explanation:
12*1.35=16.2
(can I get brainliest pls)
use the function f(x) = 3x+8. evaluate the function for f(1). 8, 11, 3
Answers
Answer: 11
Step-by-step explanation:
F(1) = 3(1) + 8
F(1) = 3 + 8
F(1) = 11
You just substitute the x in for 1 and solve from there.
The triangle shown below has an area of 25 units?
Find the missing side.
Length is 10
Answers
Missing side in the triangle is equal to \(\boldsymbol{5}\) units.
Define triangle.A triangle is a polygon that consists of three sides.
A right angled triangle in which one angle is equal to \(\boldsymbol{90^{\circ}}\)
Area of a triangle \(=\boldsymbol{\frac{1}{2}bh}\) where \(b,h\) denote base and height of a triangle respectively.
So,
\(25=\frac{1}{2}(10)h\)
\(h=\frac{50}{10}\)
\(=\boldsymbol{5}\) units
So, missing side is equal to \(\boldsymbol{5}\) units.
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When factoring a polynomial in the form ax2 + bx + c, where a, b, and c are positive real numbers, should the signs in the binomials be both positive, negative, or one of each? Create an example to verify your claim.
Answers
When factoring a polynomial in the form ax2 + bx + c, where a, b, and c are positive real numbers, the signs in the binomials should be both positive
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the true statement?The form of the polynomial is given as:
ax2 + bx + c
Where a, b, and c are positive real numbers.
Since a, b, and c are positive real numbers. then the form of the expansion would be:
ax2 + bx + c = (dx + e)(fx + g)
Example to verify the claimTake for instance, we have the following quadratic equation
x^2 + 6x + 8
Expand the equation
x^2 + 6x + 8 = x^2 + 4x + 2x + 8
Factorize the equation
x^2 + 6x + 8 = (x + 2)(x + 4)
Hence, the signs in the binomials should be both positive
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Your new computer cost $1500 but it depreciates in value by about 18% each year. About how long will it take before your computer is worth close to zero dollars, according to your equation?
Answers
Answer:
5.5 years
Step-by-step explanation:
100/18 = roughly 5.5 years (5.55555556 to be exact)
Hope this makes sense.