The amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.
In the question, we are informed that the triangle KLM, represents a section of a park set aside for picnic tables. We are also informed that the picnic area will take up approximately 400 square yards of the park.
We are asked for the amount of fencing needed to surround the perimeter of the picnic area of the park.
We know the area of a triangle can be found using the trigonometric area formula, Area = (1/2)ab sin C.
Using this in the given triangle KLM, we get:
Area = (1/2)(KL)(KM)(sin K),
or, 400 = (1/2)(KL)(45)(sin 25°),
or, KL = (400*2)/(45*sin 25°) = 800/(45*0.42262) = 800/19.017822 = 42.0658 ≈ 42 yd.
Thus, we get KL = 42 yards.
Now, the perimeter of the picnic area = the perimeter of the triangle KLM = KL + LM + MK = 42 + 20 + 45 yards = 107 yards.
Thus, the amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.
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Answer: b
Step-by-step explanation:
I need help on this Math. You have to find the y-intercept, then put it he y-intercept in coordinate form, and the slope. It was due so long ago. I don't know what to do.
Answer:
Y-Intercept is equal to 100
Y-Intercept in Coordinate for is (0,100)
What is the value of x that would make like a parallel to line b
Answer:
x = 16
Step-by-step explanation:
If the lines were parallel then (12x - 50) and (8x + 14) are alternate angles and are congruent , then
12x - 50 = 8x + 14 ( subtract 8x from both sides )
4x - 50 = 14 ( add 50 to both sides )
4x = 64 ( divide both sides by 4 )
x = 16
For a and b to be parallel then x = 16
Nathan is going to drive from his house to City A without stopping. Let D represent
Nathan's distance from City At hours after leaving his house. A graph of D is shown
below. Write an equation for D then state the slope of the graph and determine its
interpretation in the context of the problem.
The linear function for D is defined as follows:
D(t) = -35t + 280.
The slope of 35 means that Nathan is traveling at a velocity of 35 miles/km per hour.
How to define the linear function?The linear function for this problem is defined in slope-intercept format, as follows:
y = mx + b.
The coefficients of the function are given as follows:
m is the slope, representing the rate of change of the output variable y relative to the input variable x.b is the y-intercept, representing the initial value of the output variable y.From the table, two points are given as follows:
(3, 175) and (5,105).
Given two points, the slope is calculated as the change in y divided by the change in x, hence:
m = (105 - 175)/(5 - 3) = -35.
This slope represents that Nathan is traveling at a velocity of 35 miles/km per hour.
Hence:
D(t) = -35t + b
When x = 3, y = 175, hence the intercept b is obtained as follows:
175 = -35(3) + b
b = 280.
Thus the function is of:
D(t) = -35t + 280.
Missing InformationThe table is given by the image shown at the end of the answer.
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FILL IN THE BLANK. the starting value of an algorithm used to generate a range of numbers is called the _________.
The starting value of an algorithm used to generate a range of numbers is called as Seed .
A pseudo-random number generator (PRNG) is a technique that generates random number sequences using mathematical formulas. A series of numbers that closely resemble the characteristics of random numbers are produced by PRNGs. A Seed state is used by a PRNG to start from any starting state. If the beginning of the series is known, many numbers are created quickly and can also be repeated later. As a result, the numbers are accurate and deterministic.
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one of the most pieces of information with a var is whether each estimated coefficient for the lags are statistically significant (t-tests) true false
False, one of the most pieces of information with a var is whether each estimated coefficient for the lags is statistically significant (t-tests)
Statistical test (t-test)A statistical test called a t-test is employed to compare the means of two groups. It is frequently employed in hypothesis testing to establish whether a procedure or treatment truly affects the population of interest or whether two groups differ from one another.
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Suppose that ΔFAR is similar to ΔSUN. Part A: Identify the corresponding angles.
Angle F is correspond to angle S. Angle A is congruent to angle U
and Angle R is congruent to angle N.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion
Given that ΔFAR is similar to ΔSUN.
We need to find the corresponding sides.
Corresponding angles are the angles that are in the same position in any different 2-dimensional shapes.
For any two polygons to be congruent, they must have exactly the same shape and size.
This means that all their interior angles and their corresponding sides must be the same measure.
Angle F is correspond to angle S.
Angle A is congruent to angle U.
Angle R is correspond to angle N.
Hence, Angle F is congruent to angle S. Angle A is congruent to angle U
and Angle R is congruent to angle N.
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Solve the equation for z.
6 = 8x
Answer:
Step-by-step explanation:
A city wide soccer club has a phone tree to keep members informed of cancellations due to bad weather. At the first stage of the calling process, 2 leaders are informed. In stage 2, each person who was informed in stage 1 calls 3 players who are not informed. In stage 3, each person who was informed in stage 2 calls 3 players who are not informed. This pattern repeats and ends after stage 5. The number of players informed at each stage, P, is a function of the stage number X
The evaluation of the function with which the number of players leading and informed can be found, is prevented as follows;
(a) The stage of the information
(d) The number of leaders and players informed
(c) The function using function notation is P(x) = 2 × 3⁽ˣ⁻¹⁾
(d) We can say that the number of players and leaders depend on the stage of the information
(e) The statement P(4) = 54 indicates that in stage 4, 54 people are informed
(f) Domain; [1 , ∞)
Range; [2, ∞)
(g) The shape of the graph is the curved shape of an exponential function un which the asymptote is an horizontal line
What is an exponential function?An exponential function is a function in which the argument is an index of a constant of the form f(x) = a·bˣ
(a) The independent variable is the input variable, which is the stage of the calling process
(b) Dependent variable is the output variable, which is the number of leaders and players who are informed
(c) The specified function that represents the number of players who are informed, is presented as follows;
P = 2 × 3ˣ⁻¹
Where;
P = The number of players informed
x = The of information of the players
Expressing the above function using function notation, we get;
P(x) = 2 × 3ˣ⁻¹
(d) We can say that the number of players and leaders informed is a function of the stage of the information
(e) The meaning of the equation P(4) = 54 is that at stage 4, the number of layers and leaders informed is 54
(f) The domain of the function P(x) = 2 × 3ˣ⁻¹ is the set of all positive integers equal to or larger than 1 or Z⁺ {1, 2, 3, ...}
The range of the function is the set of integers, such that 2 ≤ x ≤ ∞
(g) Please find attached the graph of the function created with MS Excel
The attached graph of the function indicates that the shape of the graph is the graph of an exponential function, which is non linear and has a horizontal asymptote , but does not have a vertical asymptote.
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Please help me respond this question
The price that is the Second standard above the mean, if the mean is $10000 and the standard deviation is $500 is $18000.
What is mean?The central tendency along the median and mode of a probability distribution is measured by the mean. It is also known as "expected value."
Given:
The mean, m = $17000,
The standard deviation, σ = $500
Calculate the second standard deviation as shown below,
Second standard deviation = mean + 2 × standard deviation
Second standard deviation = 17000 + 2 × 500
Second standard deviation = 17000 + 1000
Second standard deviation = $18000
Therefore, the price that is the Second standard above the mean, if the mean is $10000 and the standard deviation is $500 is $18000.
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write an equation that can be used to determine the length
A. The equation that can be used to represent the side a of the cube is a³ = 343.
B. The value of a is 7 units.
How to represent the volume of a cube?The diagram above is a cube . A cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.
Therefore, the cube has a volume of 343 cm³.
Hence, the equation that can be used to represent the side a of the cube is as follows:
volume of a cube = l³
where
l = side lengthTherefore,
volume of the cube = a³
343 = a³
Let's solve the equation.
343 = a³
a³ = 343
cube root both sides
a = ∛343
a = 7 units
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help please, show steps to the question
The interest rate for Rebeka's account is 5%.
What is the meaning of interest rate?
The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.
Given that, Rebeka deposits $1500. She earn $131.25 as interest after 21 months.
The formula of simple interest is
I = PRT
I = interest
P = Principal
R = Rate of interest
T = time
In the given question,
P = $1500
I = $131.25
T = 21 months = 21/12 years.
Putting P = $1500, I = $131.25, T = 21/12 years in I = PRT:
131.25 = 1500 × R × (21/12)
Divide both sides by 1500 × (21/12):
R = 131.25 /[1500 × (21/12)]
R = [131.25 × 12] /[1500 × 21]
R = 0.05
R = 5%
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If AC is 15, what is BC?
A
O A. 15
OB. 13
O C. 3
OD. 2
4x+1
2x-4
Option D is correct that is BC = 2
What is a line?A line is a perfectly straight, one-dimensional shape that is endlessly long and thin in both directions.
She tells us that AC is 15, and we may deduce that AC equals AB plus BC from the figure.
AC Equals AB plus BC.
AB=4X+1, BC=2X-4, and AC=15
15 = 4X +1 + 2X- 4
15 = 6X - 3
18 = 6X
X = 3
We now know that 2X - 4
2(3) - 4 = 2 since we have X = 3.
BC = 2.
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Simplify the expression. 14+(-4)-6/7j-3/7j+7
Answer: 17 - 9/7j
Step-by-step explanation:
Look, simplifying is really easy! Just go along and learn!
14 + (-4) - 6/7j - 3/7j + 7
The (+,-) rule, remember the minus always overides the plus no matter what.
6 + 3 = 9 So, -6 - 3 = -9
14 - 4 -9/7j + 7
14 - 4 = 10
10 + 7 - 9/7j
10 + 7 = 17
17 - 9/7j
This would be your simplified answer.
The point N lies on the segment MP.
Find the coordinates of N so that the ratio of MN to NP is 5 to 4.
The coordinate of the point N that divides the line segment MP will be (9, -5).
What is the section of the line?Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have
x = (mx₂ + nx₁) / (m + n)
y = (my₂ + ny₁) / (m + n)
The coordinates of the endpoint are (-6, 5) and (21, -13). And the ratio is 5:4. Then the coordinate of the point N is given as,
x = (21 × 5 + (-6) × 4) / (5 + 4)
x = 81 / 9
x = 9
y = ((-13) × 5 + 5 × 4) / (5 + 4)
y = - 45 / 9
y = - 5
The coordinate of the point N that divides the line segment MP will be (9, -5).
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If B is the midpoint of AC, which of the following choices is the value of x?
44
5
10
None of these choices are correct.
Math
-
Because point B is midpoint of AC , so AB = BC . Therefore :
8x + 4 = 10x - 6
10x - 8x = 4 + 6
2x = 10
x = 5 ✓
_____
Select the graph for the solution of the open sentence. Click until the correct graph appears.
|x| + 1 < 3
Answer:
The third one
Step-by-step explanation:
Answer:
The 2nd one
Step-by-step explanation:
So the absolute value of x is either -x or x, saying that we don't know if x is positive or negative,
so |x|+1<3 means that |x|<2, so I would say its the 2nd one.
Please help meeeee asap !!!!!!!!?!??
The number of boxes Anica need to pack all the stuffed animals is 3.
Given that, Anica has 13 stuffed animals, and each box holds 5 animals.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Here,
Number of boxes completely filled =13/5
5|13|2
10
_____
3
3 animals are left
Therefore, the number of boxes Anica need to pack all the stuffed animals is 3.
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3) A man works x hours per weekday
except Saturday when he works y hours. If
he works z hours on sunday how many
hours does he work per week?
Step-by-step explanation:
Monday to Friday = 5x
Saturday = y
Sunday = z
Per week, he works 5x + y + z hours.
solve g/4 + 11 = 28 g =
Answer:
g = 68
Step-by-step explanation:
g/4 + 11 = 28
subtract 11 from both sides:
g/4 + 11 - 11 = 28 - 11
g/4 = 28 - 11
g/4 = 17
multiply both sides by 4:
4(g/4) = 4(17)
g = 68
Give the values of b, h, and k for the function
The value of b = 5 , h = -4 and k = -1 for the function f(x) = [tex]log_{5}[/tex](x - 4) - 1
What is a function ?
An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable).
A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function.
An input is connected to an output by a function. It resembles a device with an input and an output. In addition, the output is somehow connected to the input. The standard way to write a function is f(x) "f(x) =... "
Translated of logarithmic function:
f(x) = [tex]log_{b}[/tex] (x + h) + k
where b is base, h - horizontal shift, k - vertical shift
According to given function the values are:
b = 5, h = - 4, k = - 1
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Graph the points (0.5,4.5) and (-0.5,-4.5)
Answer:
Step-by-step explanation:
To graph the points (0.5, 4.5) and (-0.5, -4.5) on a coordinate plane, you can use a ruler or a graph paper to plot the points.
To plot the point (0.5, 4.5), start by drawing the horizontal and vertical axes of the coordinate plane. The horizontal axis, or the x-axis, is the line that runs horizontally across the plane, and the vertical axis, or the y-axis, is the line that runs vertically. The intersection of the two axes is called the origin.
Next, locate the point (0.5, 4.5) on the coordinate plane. To do this, find the point that is 0.5 units to the right of the y-axis and 4.5 units above the x-axis. This point is the point (0.5, 4.5).
To plot the point (-0.5, -4.5), locate the point that is 0.5 units to the left of the y-axis and 4.5 units below the x-axis. This point is the point (-0.5, -4.5).
The resulting graph should look like this:
|
4.5| * (0.5, 4.5)
|
|
|
|
0.5| * (-0.5, -4.5)
|
|
|
-4.5
-4.5 -2.5 -0.5 0.5 2.5 4.5
-0.5
find the lengths of the hypotenuses (x) of the triangle whose legs are given
1) 3cm,4cm
a = 3 cm
b = 4 cm
c = ?
c = √{ a² + b² }
c = √{ 9 + 16 }
c = 5 cm
_____
Answer:
5cm
Step-by-step explanation:
You use the Pythagoras theorem
[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ {3}^{2} + {4}^{2} = {c}^{2} \\ 9 + 16 = {c}^{2} \\ 25 = {c}^{2} \\ \sqrt{25} = \sqrt{ {c}^{2} } \\ 5 = c \\ c = 5[/tex]
You buy the following from Amazon:
25 flash drives for $10 each
What is the Subtotal: $
Today only they are 25% off, how much do you save: $
What is the new Subtotal: $
Sales tax is 4%: $
What is the total: $
(For all numbers, put in the change. If there is no change, make sure you put .00. For example, if the amount was 27, make sure you put 27.00.
If there is no number in the pennies place, make sure you put a 0. For example, if your amount was 5.4, make sure you put 5.40)
The Subtotal for 25 flash drives is $250.00. You can save $62.50. The new Subtotal becomes $187.50. Sales tax of 4% will equal $7.50. The Total for the 25 flash drives will be $187.50 + $7.50 which gives $195.00
To find the solution, we must solve for the questions individually;
The Subtotal is 25 x $10 = $250.00
You save = 25% of $250
which is 25/100 x 250 = $62.50
The new Subtotal = $187.50
Sales tax of 4% = 4% of $187.50
which gives 4/100 x 187.5 = $7.50
The Total for the 25 flash drives will be $187.50 + $7.50 = $195.00
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Use the order of operations to find the value of the following expression.
10 2 - 2 (8) + 11
1: 95
2: 15
3: 155
4: 795
Answer:
Step-by-step explanation:
Using PEMDAS order of operations:
ParnthesesExponentMultiplyDivideAddSubtract:
10 2 - 2 (8) + 11
(I am assuming that you mean 10 * 2):
10 * 2 - 2 (8) + 11
= 20 - 16 + 11
= 4 + 11
= 15.
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answer:
x=25
Step-by-step explanation:
Haley B. Workin did eight chores in the morning. She did 40% of her daily
chores in the morning. How many daily chores does she have?
Answer:
20
Step-by-step explanation:
You want to know how many daily chores Haley has if 40% of them are 8 chores.
ChoresLet c represent the number of daily chores. The number of chores accomplished in the morning was ...
0.40c = 8
Dividing by 0.40, we find ...
c = 20
Haley has 20 daily chores.
What i the dicontinuity of f(x) = the quantity of 4x quared minu 16, all over 2 x minu 4
At x = 4, the function f(x) = (x2 - 16)/(6x - 24) discontinues.
Where is a break in the line?When a number is 0 in the numerator as well as the denominator, a point of discontinuous is reached. There's an point of disconnection there since both the exponent and the denominator are zeros. Plug into the last simplified equation to obtain the value, where is the region of discontinuous.
Briefing :We are given the function as;
f(x) = (x² - 16)/(6x - 24)
We must find the function's discontinuities.
Now, when x = 4, the fraction 6x - 24 equals 0.
This means that the function is now incomplete when x = 4.
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you buy 1 shirt and 3 pairs of pants for $44. your friend buys 3 shirts and 1 pair of pants for $44. what is the cost of each shirt? of each pair of pants?
The cost of each shirt and pair of pants is $11 each.
Let us represent the shirt by x and pair of pants by y. So forming the equation based on the information. Equation for items bought by me -
x + 3y = 44 : Equation 1
Equation for items bought by my friend -
3x + y = 44 : Equation 2
Performing multiplication of equation 1 with 3
3x + 9y = 132 : Equation 3
Performing subtraction of equation 2 from equation 3
3x + 9y = 132
3x + y = 44
We get -
9y - y = 132 - 44
8y = 88
y = 88/8
Performing division
y = 11
Keep the value of y in equation 1
x + 3×11 = 44
x + 33 = 44
x = 44 - 33
x = 11
Hence, both of these items cost $11.
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Show that the function f(x) = x + 5x + 1 has exactly one zero in the interval (-1,0). Which theorem can be used to determine whether a function f(x) has any zeros in a given interval?
The function f(x) = x + 5x + 1 has exactly one zero in the interval (-1, 0). To prove this, we can use the Intermediate Value Theorem.
This theorem states that if a function f(x) is continuous on an interval [a, b] and if its values at a and b have opposite signs, then there exists at least one root (zero) of the function in the interval (a, b). Therefore, since f(-1) = -6 and f(0) = 1, both of which have opposite signs, the Intermediate Value Theorem can be used to conclude that there exists at least one root of the function in the interval (-1, 0).
Furthermore, since the function is a quadratic function of the form f(x) = ax2 + bx + c, it is known that a quadratic equation can have at most two roots (zeros) (in a given interval). Therefore, since the Intermediate Value Theorem implies that the function f(x) has at least one zero in the interval (-1, 0), it follows that the function has exactly one zero in the interval (-1, 0).
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write the expression as a single logarithm with coefficient 1. assume all variables represent positive real numbers. 1/4logbx^5y^7-4/7logbx^4y
the formula as one logarithm with a coefficient of 1 with a expression. assume all variables represent positive real numbers. 1/4logbx^5y^7-4/7logbx^4y is logbx^4y^11/28
Since the coefficients of the expression of two logs are not the same, we need to adjust the exponents in order to combine them into one logarithm. Since the first logarithm has a coefficient of 1/4, we multiply the exponent of the second logarithm by 4/7 to get 4/7*4 which is equal to 4. We then add 4 to the exponent of the first logarithm to get 11. This gives us a combined logarithm of logbx^4y^11/28.
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