The approximate length of each side of the park is 85m .
Pythagoras Theorem states that the sum square of two sides of triangle is equal to the square of longest side.
According to the question
given that the park is a square
and in square the longest side is it's diagonal and the diagonal is given to be 120m.
In square all sides of square is same .
let the side be x.
By Applying Pythagoras Theorem in the given ΔABC
[tex]AB^{2} +BC^{2} =AC^{2}[/tex]
Substituting the values we get
[tex]x^{2} +x^{2} =120^{2}[/tex]
[tex]2x^{2} =120^{2} \\ \\ 2x^{2} =14400\\ \\ x^{2} =7200[/tex]
[tex]x=\sqrt{7200} =60\sqrt{2}[/tex] = 84.85 ≅ 85
Therefore , the approximate length of each side of the park is 85m .
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Find a₁ for each arithmetic series.Evaluate S₁₅ for the series 3 x+(3 x-2 y)+(3 x-4 y)+ ......
In the given arithmetic series, the first term is a(1) = 3x and the sum of the first 15 terms is S(15) = 45x - 210y
The given series is:
3x + (3 x-2 y) + (3x-4y) + ......
Notice that this is an arithmetic series with:
the first term, a(1) = 3x
the second term, a(2) = 3x - 2y
the 3rd term, a(3) = 3x - 4y
Hence, the common difference is:
d = (3x - 2y) - 3x = -2y
Recall that the nth term of an arithmetic series is given by:
a(n) = a(1) + (n -1) . d
Substitute n = 15, a(1) = 3x, and d = -2y:
a(15) = 3x + (15 - 1) . (-2y)
a(15) = 3x - 28y
The sum of the first n terms in an arithmetic series is given by:
S(n) = n/2 [a(1) + a(n)]
Substitute n = 15
S(15) = 15/2 [a(1) + a(15)]
S(15) = 15/2 . (3x + 3x - 28y)
S(15) = 15 . (3x - 14y) = 45x - 210y
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Every year, the number of birds in a bird sanctuary increases by 3 percent. In 1997, there were 175 birds in the sanctuary. Using this data, predict the number of birds in the sanctuary in 2020.
There are 190 more birds than expected at the refuge.
The information provided in the question indicates that there are 3 percent more birds than there were previously. The sanctuary houses 175 birds, which may be pictured as follows:
There are 175 birds in all.
According to the inquiry, it is rising by 3%.
Number of birds = (175)(3%) = 5.25 at this point.
As a result, given the data, the anticipated enhanced data is as follows:
Added birds is 175 + 5 + 5 + 5 = 190.
190 more birds are therefore expected in the refuge.
How much is a percentage?The final computed numbers should be divided by the total value and then multiplied by 100 to obtain the percentage.
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(3x^5+8x^3-10x^2)-(-12x^5+4x^3+14x^2)
Answer:x
2
(
15
x
3
+
4
x
−
24
)
Step-by-step explanation:
Kate cut a 100-foot rope into two pieces.one piece was 5 feet longer than 4 times the length of the other. Find the length of each piece
Answer:
81 feet & 19 feet
Step-by-step explanation:
Carla puts $625 into a savings account at an annual interest rate of 2.5%. If she does not withdraw or deposit any money, what is the interest that Carla will earn at the end of 6 months?
The formula is I=prt
Given the principal and annual interest rate, the interest that Carla will earn at the end of 6 months is $7.81.
What is the interest that Carla will earn at the end of 6 months?Simple interest is simply a method to determine the amount of interest charged on a sum at a given rate and for a given period of time.
It is expressed as;
I = prt
Given the data in the question;
Principal P = $625Annual interest r = 2.5% = 2.5/100 = 0.025Time period t = 6 months = 6/12 = 0.5 yearsInterest I = ?Plug the given values into the formula above and solve for I.
I = p × r × t
I = $625 × 0.025 × 0.5
I = $7.81
Given the principal and annual interest rate, the interest that Carla will earn at the end of 6 months is $7.81.
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Zachary purchased a computer for $1,100 on a payment plan. Two months after he purchased the computer, his balance was $870. Six months after he purchased the computer, his balance was $410. What is an equation that models the balance y after x months?
Answer:
y = 1100 - 115x
Step-by-step explanation:
Let the monthly payment be $p
In two months Zach would have paid 2p dollars
Balance would be 1100 - 2p = y
We know after 2 months, balance y was actually 870
Substituting y = 870 we get
1100 - 2p = 870
Subtract 1100 on both sides
1100 - 1100 - 2p = 870 -1100
==> -2p = - 230
Divide by -2 on both sides
-2p/-2 = -230/-2
p = 115 which represents the monthly payment .
So the balance y after m months is given by the equation
y = 1100 - 115x
We can verify by plugging in the values for the second scenario
For 6 months
y = 1100 - 115 x 6 = 1100 - 690 = $410 which agrees with the given value so our equation is consistent
HELP MEEE!!!! Anna walks 49,879 feet from her house. She rest to get something to eat, then she walked all the way back home. Since Anna walked 49,879 feet from her house, how many miles in total did she walk from her house and walk back?
Answer:24939.5 i think
Step-by-step explanation:
How do i solve this?[tex]2(-15)-\sqrt[3]{18(-15)-1061}[/tex]
- 40.18 is the solution of this function .
What does a math cube root mean?
The factor we multiply by itself three times to obtain a number is its cube root. 3 cube root of, end cubic root is the symbol for the cube root. The opposite of cubing an integer is to get its cube root.Finding a number that, when multiplied twice by itself, equals the original number is necessary in order to compute the square root of any number. Similar to this, we must discover a number that, when multiplied three times by itself, equals the original number in order to find the cube root of any number.[tex]2( -15) - \sqrt[3]{18( -15 ) - 1061}[/tex]
= [tex]2 ( -15 ) - \sqrt[3]{3 - 1061}[/tex]
= [tex]-30 - \sqrt[3]{ - 1058}[/tex]
= - 30 - 10.18
= - 40.18
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What is the simplified answer to 5.3. √2 ? 8√2 2/2 15√2
The simplified answer to 5.3. √2 will be 7.495.
How to calculate the value?It should be noted that we are to find the simplified answer to 5.3. √2 .
This means that we have to multiply them. This will be:
= 5.3 × ✓2
= 5.3 × 1.1414
= 7.495
Note that the options given aren't complete.
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Write two division problems that both have a quotient of -3.
Arrange the numbers Least to Greatest1/2, -1/4, 7.2, 121, 1-41, -1.8, 9.1
The numbers in the order of least to greatest is :
₋1.8 , ₋1/4 , 1/2 , 1.41 , 7.2 , 9.1 , 121
Given, the numbers are in decimal and fraction form.
1/2 , -1/4 , 7.2 , 121 , 1.41 , -1.8 , 9.1
we need to convert the fractions and then arrange the numbers in the ascending order.
Writing the numbers in an ordered list according to their values means arranging them from least to greatest. The smallest number should be put on the left, followed by the next smallest number, which should be written directly to its right.
for 1/2:
1/2 = 0.5
for ₋1/4:
₋1/4 = 0.25
now arrange the numbers according to the least to greatest form.
we have numbers:
0.5 , 0.25 , 7.2 , 121 , 1.41 , ₋1.8 , 9.1
least to greatest form:
₋1.8 , 0.25 , 0.5 , 1.41 , 9.1 , 121
i.e , ₋1.8 , 1/4 , 1/2 , 1.41 , 9.1 , 121
Hence we get the required form.
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How can I solve this?
Answer:
Mean: 160
Median: 150
Mode: none
Range: 105
Standard deviation: 35.3
Step-by-step explanation:
Given:
Mean = 320Median = 300Mode = noneRange = 210Standard deviation = 70.6If each value in the data set is multiplied by a constant value, the mean, median, mode, range, and standard deviation will all be scaled by the same amount.
Therefore, if each value in the data set is multiplied by 0.5:
Mean: 320 × 0.5 = 160Median: 300 × 0.5 = 150Mode: none × 0.5 = noneRange: 210 × 0.5 = 105Standard deviation: 70.6 × 0.5 = 35.3Proof
Data set: {1, 2, 3, 4, 5}
[tex]\sf Mean\:\mu =\dfrac{\sum x_i}{n}= \dfrac{1+2+3+4+5}{5} = 3[/tex]
[tex]\sf Median = 3[/tex]
[tex]\sf Mode = none[/tex]
[tex]\sf Range = 5-1=4[/tex]
[tex]\sf Standard\:deviation\:\sigma=\sqrt{\dfrac{\sum (x_i-\mu)^2}{n}}=\sqrt{\dfrac{10}{5}}=\sqrt{2}[/tex]
If we multiply each value by 0.5, the new data set is:
{0.5, 1, 1.5, 2, 2.5}
[tex]\sf Mean\:\mu =\dfrac{\sum x_i}{n}= \dfrac{0.5+1+1.5+2+2.5}{5} = 1.5[/tex]
[tex]\sf Median = 1.5[/tex]
[tex]\sf Mode = none[/tex]
[tex]\sf Range = 2.5-0.5=2[/tex]
[tex]\sf Standard\:deviation\:\sigma=\sqrt{\dfrac{\sum (x_i-\mu)^2}{n}}=\sqrt{\dfrac{2.5}{5}}=\dfrac{\sqrt{2}}{2}[/tex]
Therefore, if each value in the data set is multiplied by 0.5, the mean, median, mode, range, and standard deviation are all scaled by the same amount.
I can’t seem to figure out how to properly insert (r) and (t) after 2 and 3.
Answer:
7
Step-by-step explanation:
(2t+3r) divide 4
so if r=2 and t=11 the new equation will be :
(2times11 + 3times 2) divide 4
(22+6) divide 4
= 28 divide 4 = 7
Identify the segment bisector of JK
The length of JM is
Given that point M bisects segment JK, the numerical length of segment JK and segment JM are 80 and 40 respectively.
What is the numerical value of JK and JM?Given the data in the question;
Point M bisects segment JK.Segment JM = 7x + 5Segment MK = 8xA bisector divides a line or angle into two equal halves.
Hence
Segment JM = Segment MK
7x + 5 = 8x
Solve for x
8x - 7x = 5
x = 5
Now, numerical value of segment JM will be;
Segment JM = 7x + 5 = 7(5) + 5 = 35 + 5 = 40
Segment JK = (7x + 5) + 8x = 7(5) + 5 + 8(5) = 80
Given that point M bisects segment JK, the numerical length of segment JK and segment JM are 80 and 40 respectively.
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Your friend gave you a free parking pass to a baseball game. Unfortunately, the parking spot number was smudged on the ticket. You know the parking spot was 7 spaces away from your friend's spot. If your friend's parking spot is number 19 in the same row, write and solve and absolute value equation to determine your possible parking spot number(s)? (use \displaystyle xx as the variable to represent the parking spot)
The possible parking spot numbers can be either 12th spot or 26th spot.
What are inequalities ?
When two values are compared , an inequality represents whether one is greater than, less than, or not equal to the other.
It is given that the parking spot was smudged on the ticket.
Let's assume the possible parking spot numbers can be given by x which is represented by an inequality.
Your parking spot is 7 spaces away from your friend's spot which is number 19 in the same row. So , the possible parking spot numbers can be given by ;
19 - 7 ≤ x ≤ 19 + 7
12 ≤ x ≤ 26
Therefore , the possible parking spot numbers can be either 12th spot or 26th spot.
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what is 49/200 equal to explain
Answer:
0.245
Step-by-step explanation:
Divide both the numerator and denominator by 2.
49/200 will be 24.5/100
If you divide a number by 100, you move the decimal place 2 digits to the left. 24.5/100 will become 0.245
Please help on geometry step by step im trying to learn
Answer:
m∠FQR = 23°
Step-by-step explanation:
Since m∠KQF = 90°, it's a complementary angle and is equal to 90°
Step 1: Write the equation. Since The whole angle equals 90° add everything together to equal 90°
(3x - 23)° + (2/3x + 3)° = 90
3x - 23 + (2/3)x + 3 = 90
Combine like terms
multiply the denominator by 3. (3 × 3) = 9 + 2 = 11
(11/3)x - 20 = 90
+ 20 +20
(11/3)x = 110
÷(11/3) ÷(11/3)
x = 30°
Step 2: Find m∠FQR
m∠FQR = ((2/3)x + 3))
(2/3)(30) + 3
20 + 3 = 23
m∠FQR = 23°
I hope this helps!
Answer:
Step-by-step explanation:
(2/3x+3) + (3x-23)=90
(2/3+3)x -20 =90
11/3x =90 + 20
x= 110 * 3/11 =30
FQR = 2/3x+3= 2/3 (30) +3 = 20 +3 =23
h(x) = -4x - 3, find h(2).
Answer:
-11.
Step-by-step explanation:
h(x) = -4x - 3, find h(2).
Replace the x by 2:
h(2) = -4(2) - 3
= -8 - 3
= -11.
Find the next term in each sequence. 2,4,8,16, . . . . . .
Answer:2,4,8,16,32,64,128,256,512,1024,2048,4096
Step-by-step explanation:
You just mutiply the number with 2
3/4 h -12= 8 5/8 pls answer with a detailed explanation
The value of h based on the information illustrated is 24 1/2.
How to calculate the value?It should be noted that the fraction given is illustrated as:
3/4h - 12 = 8 5/8
Add 12 to both sides
3/4h - 12 + 12 = 8 5/8 + 12
3/4h = 20 5/8
Multiply both side by 4/3
3/4h × 4/3 = 20 5/8 × 4/3
h = 165/8 × 4/3
h = 27 1/2
Therefore, the value of h is 24 1/2.
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samantha is using a wooden strip 7/8 yard long to make a picture frame.If she cuts off a piece that is 3/4 long, which fraction best represents the porportion that is left lf the original strip?
The portion of wooden strip that is left from the original strip is 1/4
How to calculate the amount of the original strip left ?Samantha is using a wooden strip that measures 7/8 yard
Samantha cuts off a piece of the wood that is 3/4 long
The fraction that represents the proportion of the original strip that is left can be calculated as follows
7/8 - 3/4
The LCM of both fractions is 8
7 - 6/8
= 2/8
convert to the lowest term
1/4
Hence the proportion of the original wooden strip that remains is 1/4
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Which number line model shows the subtraction −3−6?
Answer:
C.
-3-6=-9
Step-by-step explanation:
-3-6=-9
C. The blue arrow goes to negative 3. Then the red arrow goes from negative 3 to negative 9.
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PLEASE HELP!!! Given the function defined by f(x)=6x-3, find f(-4.6). Simplify.
Write an explicit formula for each sequence. Then generate the first five terms. a₁ =1024, r=0.5
The formula of the given geometric sequence is: a(n) = 1024 . (0.5)ⁿ⁻¹ and the first five terms are: 1024, 512, 256, 128, and 64.
The formula of the n-th term of a geometric sequence is:
a(n) = a₁ . r^(n-1)
Where:
a₁ is the first term
r is the ratio = a(n)/a(n-1)
Parameters given in the problem:
a₁ =1024, r=0.5
Plug these parameters into the formula, then we get the explicit formula of the n-th term:
a(n) = 1024 . (0.5)ⁿ⁻¹
The first 5 terms:
a₁ = 1024
a(2) = 1024 . (0.5)²⁻¹
= 1024 . (0.5)¹ = 512
a(3) = 1024 . (0.5)³⁻¹
= 1024 . (0.5)² = 256
a(4) = 1024 . (0.5)⁴⁻¹
= 11024 . (0.5)³ = 128
a(5) = 1024 . (0.5)⁵⁻¹
= 1024 . (0.5)⁴ = 64
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A die is rolled. If the number rolled is greater than 2 , find the probability that it is a 6 .
According to the question, when die is rolled check the number is greater than two and it should be [tex]6[/tex].
The total number of outcomes : [tex]n(E)= {1,2,3,4,5,6}[/tex]
And getting a number greater than [tex]2[/tex] [tex]= {3,4,5,6}[/tex]
Finally, getting a number as [tex]6 = {6}[/tex]
Therefore, the probability can be written as:
[tex]P(E) = \frac{1}{6}[/tex]
Hence, the calculated probability is [tex]\frac{1}{6} .[/tex]
What is Probability?
The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.
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Evaluate. Remember Order of
Operations! (PEMDAS)
-8 × 2² - (-40+ 6) = [?]
Answer:
The answer is 2
Step-by-step explanation:
Write these propositions using p and q and logical connectives (including negations). (a) you do not drive over 65 miles per hour. (b) you drive over 65 miles per hour, but you do not get a speeding ticket. (c) you will get a speeding ticket if you drive over 65 miles per hour
Writing the propositions using p and q with logical connectives, including negations, in each of the statement will give;
(a) you do not drive over 65 miles per hour-
¬ p
(b) you drive over 65 miles per hour, but you do not get a speeding ticket
p ∨ ¬ q
(c) you will get a speeding ticket if you drive over 65 miles per hour-
p → q
We are to represent each statement using letters; p and q
The letters p and q are then connected with the logical connectives symbols; example negation, conjunction, disjunction and implication symbols.
Thus, each statement given in the question is logically written as;
(a) ¬ p
(b) p ∨ ¬ q
(c) p → q
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Lo5(x2-9)=0 pls help me my assignments is too hard so i learned that you can help me thanks
The final answer is the combination of both solutions x = 3,− 3.
What are quadratic in math?
A quadratic in mathematics is a particular kind of problem that involves squaring, or multiplying a variable by itself. This terminology comes from the fact that a square's area equals the product of its side length and itself. Quadratum, the Latin word meaning square, is where the word "quadratic" originates.Use the quadratic formula to find the solutions
x = - b + √b² - 4ac / 2a
Substitute the values
a = 1, b = 0, and c = − 9 into the quadratic formula and solve for x.
x = 0 + √ 0² - 4 . ( 1 . 9 ) / 2. 1
Simplify
The final answer is the combination of both solutions.
x = 3,− 3
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Determine whether each sequence is arithmetic. If so, identify the common difference and find the 32 nd term of the sequence. 2,4,7,10, . . . . .
The given sequence 2, 4, 7, 10, … is not an Arithmetic sequence.
The sequence we are provided is 2, 4, 7, 10, …
Here, [tex] a_{1}[/tex] = 2, [tex] a_{2}[/tex] = 4 and [tex] a_{3}[/tex] = 7.
A sequence is considered as an Arithmetic sequence if their difference is equal. Represented as -
[tex] a_{2}[/tex] - [tex] a_{1}[/tex] = [tex] a_{3}[/tex] - [tex] a_{2}[/tex] = [tex] a_{4}[/tex] - [tex] a_{3}[/tex] and so on
Now, in the given sequence
⇒[tex] a_{2}[/tex] - [tex] a_{1}[/tex] = 4 - 2
[tex] a_{2}[/tex] - [tex] a_{1}[/tex] = 2
⇒ [tex] a_{3}[/tex] - [tex] a_{2}[/tex] = 7 - 4
[tex] a_{3}[/tex] - [tex] a_{2}[/tex] = 3
⇒ [tex] a_{4}[/tex] - [tex] a_{3}[/tex] = 10 - 7
[tex] a_{4}[/tex] - [tex] a_{3}[/tex] = 3
Since, the difference between the given sequence of terms are not same.
∴ The given sequence 2, 4, 7, 10, … is not an Arithmetic sequence.
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PLEASE ANSWER FAST Estimate 4001 + 283 + 97 =
Answer:
4400
Step-by-step explanation:
4001→4000 (you need to round the number to the nearest thousand)
283→300 (you need to round the number to the nearest hundred)
97→100 (you need to round the number to the nearest ten, in this case 100)
4000+300+100= 4400
Hope this helps! :)
