Triangle A and Triangle B are right triangle. Triangle A ha a height of 8 meter and a bae of 6 meter. then The length of one of the legs of the triangle is 10 units.
An isosceles triangle has a base length of 126 units and a height of 16 units. We need to find out the length of one of the legs of the triangle.
First of all, we will consider a perpendicular bisector of the triangle. This divides the given triangle into two equal right-angled triangles. Now, in the smaller triangle, we will use the Pythagorean theorem.
Let the length of the leg be represented by the variable "x". The length of the base of the right-angled triangle is half the length of the base of the original triangle.
x² = (6)² + (8)²
x = sqrt ( 36+64)
x = √100
x = 10
Hence, the length of one of the legs of the triangle is 10 units.
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the difference between the sample statistic and the population parameter when sampling is done correctly is referred to as what?
A sampling error is the difference between a population parameter and a sample statistic.
Parameters are numbers that describe the properties of entire populations. Statistics are numbers that describe the properties of samples. For example, the average income for the United States is a population parameter. Conversely, the average income for a sample drawn from the U.S. is a sample statistic. The difference between a parameter vs a statistic is that a parameter is a fixed measure describing the whole population, while a statistic is a characteristic of a sample, a portion of the target population.
Thus, the difference is defined as sampling error.
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Geometry: 6.7_Law of Cosines: 15 POINTS
The measure of side a is 4.1 unit.
What is law of cosine?Let there is triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:
c² = a² + b² - 2ab cos C
(c is opposite side to angle A)
In the given triangle ABC, we have sides BC = a, AB = b and AC = c
Now we know as per cosine rule for all three sides of the triangle.
c² = a² + b² - 2ab cosC
Where; b = 9 and c = 7 degrees
Angle A = 35 degrees
Plugging these values into the equation, we have;
a² = c² + b² - 2cb cos A
a² = 9² + 7² - 2(9)(7) cos (35)
a² = 81 + 49 - 126 x (-0.9036)
a = 4.1
Therefore, the side a is 4.1 unit.
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One ector of a circle ha an area of 121 quare centimeter and an arc meaure of 36'. What i the area of the circle to the nearet
quare centimeter
The Area of the circle will be = is 144.87 [tex]cm^{2}[/tex]
Given in the question,
The sector of the circle has an area of = 121 [tex]cm^{2}[/tex]
The measure of an arc = is 36 inches.
According to the attached figure,
Let us consider the arc length = L
Let radius = r
As per the question L = 36'
Let the radius be
To calculate the length of the arc we need to use the formula,
L = r x θ
36 = r x θ
θ = [tex]\frac{36}{r}[/tex] degrees ------- equation 1
Now according to the area of the sector of the circle,
A = [tex]r^{2}[/tex] x θ / 2
121 = [tex]r^{2}[/tex] x θ / 2
[tex]r^{2}[/tex] = 2 x 121 / ( [tex]\frac{36}{r}[/tex] )
[tex]r^{2}[/tex] = [tex]\frac{2 * 121 * r}{36}[/tex] ----- equation 2
r = [tex]\frac{2 * 121 }{36}[/tex]
r = 6.72 cm.
Now if the radius is = 6.72 cm
Diameter = 2 x radius
= 2 x 6.72
= 13.44 cm
Area of the circle = [tex]\pi r^{2}[/tex]
= [tex]\pi[/tex] x 6.72 x 6.72
= 144.87 [tex]cm^{2}[/tex]
Therefore, the area of the circle = is 144.87 [tex]cm^{2}[/tex]
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A table of values of a linear function is shown below. Find the output when the input is n Type your answer in the space provided.
Input 1 2 3 4 n
Output -7 -9 -11 -13
Determine the period.
Enter
Answer:
Your answer should be [tex]\frac{\pi }{7}[/tex]
Step-by-step explanation:
Looking at the x-axis we can say that is our b.
Period Formula: 2π/b.
x-axis is from 0 to 20.
b = 14 because of the rise to rise.
2π/14 = π/7
The expression (x + 3)(x + 2) is the product of two binomials. Which expression is also
a product of binomials?
The expression which has product of two binomials is (5-n)(n+7).
What is Expression?An expression is combination of variables, numbers and operators.
Binomials are expressions containing the sum (or difference) of two terms.
The expression (x + 3)(x + 2) is the product of two binomials.
(pq)(qp), (5-n)(n+7), 3x(2x+5), 6x-2y
(pq)(qp) is not the product of binomials because pq and qp are products.
3x(2x+5) is not the product of binomials because 3x is not a sum or difference.
6x-2y is also not because it is one binomial, not two multiplied together.
(5-n)(n+7) is the product of two binomials.
Hence, (5-n)(n+7) is the expression which has product of two binomials.
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Solve the equation by subtracting the appropriate number from both sides and enter the value of x below. x + 2551 = 3105
Answer:
554
Step-by-step explanation:
x + 2551 - 2551 = 3105 - 2551
x = 554
Answer:
[tex]x + 2551 = 3105 \\ x + 2551 - 2551 = 3105 - 2551 \\ x = 554[/tex]
because of different units being used for various data series, which fit statistic can be used across different series that are in fact measured in different units?
The fit statistic that can be used across different series that are in fact measured in different units is; MAPE
What statistic can be used?There are different statistics models in this regards such as;
Mean Absolute Error (MAE)
Mean Absolute Scaled Error (MASE)
Accuracy Percent (Accuracy %)
Mean Squared Error (MSE)
Root Mean Squared Error (RMSE)
Mean Absolute Percent Error (MAPE)
Now, we are told that we need the fit statistic that can be used across different series that are in fact measured in different units.
The correct one will be Mean Absolute Percent Error (MAPE) because the average absolute percent difference between the values that are fitted by the model and the observed data values.
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Which equation represents twenty-nine is one-third of the number n?
Answer:
29=n/3
Step-by-step explanation:
Answer:
29 = n/3
Step-by-step explanation:
[tex]29 = \frac{1}{3} of \: n \\ 29 = \frac{1}{3} \times n \\ 29 = \frac{n}{3} [/tex]
PLLEAASSEEE HELPP MEEEE DONT ANSWER IF U NOT GOING TO HELP PLS
On solving the provided question by slope intercept form, equation formed id=s 3x + 4y - 14= 0 .
What is Slope Intercept Form?One of the most popular ways to express a line's equation is in the slope intercept form of a straight line. Given the slope of the straight line and the y-intercept, the slope intercept formula may be used to get the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). A line's equation is the equation that each point on the line fulfills. There are several ways to solve the equation for a straight line given as, - Slope-intercept form, Point slope form Two-point form and Intercept the form
slope = -3/4
points ( -2,5 )
equation,
(y - y1) = m(x - x1)
( y - 5) = -3/4(x+2)
4y - 20 = -3x - -6
3x + 4y - 14= 0
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Will give brainliestttt PLEASE I NEED HELP :((((
Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.
The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 4)(2, 8)(3, 16)(4, 32)
Part A: Is this data modeling a linear function or an exponential function? Explain your answer.
Part B: Write a function to represent the data. Show your work. (4 points)Part C: Determine the average rate of change between station 2 and station 4. Show your work. (4 points)
Step-by-step explanation:
A
for a linear function the slope ratio has to be the same between every pair of data points.
between (1, 4) and (2, 8) we have
x changes by +1 (from 1 to 2).
y changes by +4 (from 4 to 8).
the slope is
+4/+1 = 4
between e.g. (2, 8) and (3, 16) we have
x changes by +1 (from 2 to 3).
y changes by +8 (from 8 to 16).
the slope here is +8/+1 = 8.
which is not the same as 4.
so, it is not a linear function.
it is an exponential function.
B.
the function is actually
f(x) = y = 2^(x+1)
an exponential function is of the form
y = a^x
in our case we have
4 = a¹ = 2²
8 = a² = a¹×2 = 2² × 2 = 2^(2+1)
16 = a³ = a²×2 = a¹×2×2 = 2²×2×2
we see
f(n) = a1×2^(n-1) = 2²×2^(n-1) = 2^(n+1)
C.
the average rate of change is
(the difference of the function results at the interval ends) / (the difference of the interval ends).
so, in our case
(f(4) - f(2))/(4 - 2) = (32 - 8)/2 = 24/2 = 12
the average rate of change between stations 2 and 4 is 12 (or 12/1).
Answer:
Um in an old question of mine you said "its been forever". That was my elijahmiraclechild account. I don't really remember you but I would like to
Step-by-step explanation:
A radioactive isotope has a half life of 1 month. It begins with 500 grams. After 8 months, how many grams would it have. Round to the nearest two decimal places.
Answer:
t1/2=1m => 30days
A0=500g =0.5kg
t=8m = 240days
A=?
λ=ln2÷t1/2
λ=0.6931÷30
λ=0.0231033333
A=A0×e^-λ×t
A=0.5×e^-0.0231033333×240
A=1.953125grams
A rocket will launch in 3. 75 hour and the launch time i 11:20 am. What time i it now??
The time presently is 8:15 a.m, and the rocket will launch in 3.75 hours, at 11:20 a.m.
What is subtraction?Subtraction (represented by the minus sign) is one of four mathematical operations, the others being addition, multiplication, and division. Subtraction is the procedure of removing items from a collection. Subtraction may be thought of as the inverse of addition. Counting forwards helps children learn to add. To subtract, they just count backwards.
Here,
launch time=11:20 am
time left to launch=3.75 hour
=0.75*60
=45 minutes
= 3 hours 45 minutes
=11 hours 20 minutes-3 hours 45 minutes
=8 hours 15 minutes
=8:15 AM
The time right now is 8:15 AM when rocket will launch in 3. 75 hour and the launch time is 11:20 am.
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The domain of a certain exponential function is all real numbers. The range of the function is all real
numbers greater than -3. The graph of the function has a horizontal asymptote at y = -3.
Select a graph or graphs to fit the description of the function.
One exponential function with the given features is y = 2^x - 3, and is graphed at the end of the answer.
How to define the exponential function?An exponential function is defined as follows:
y = a(b)^x + c.
In which:
a is the initial value.b is the rate of change.c is the horizontal asymptote.The graph of the function has a horizontal asymptote at y = -3, hence:
c = -3.
For a and b, they can assume any non-negative values, hence we attribute these following values:
a = 1, b = 2.
The graph is given at the end of the answer.
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use the side-by-side boxplots shown to complete parts (a) through (e).
(a) The median of variable x is 70.
(b) The third quarterly of variable y is 94.
(c) Variable y has more dispersion.
(d) Shape of variable x is Symmetric.
(e) The shape of y variable is Skewed left.
a) The median of the variable x, which sits in the middle of the provided box plot, is 70 (roughly).
b) Variable Y's third quarterly value is 94. (approximately).
c) Because Q1 is farther away from the median than Q2, variable y has a higher inter quarterly range than variable x.
d) The shape of the variable x is symmetrical because both the left and right whiskers are roughly the same length and the median is located in the center of the box.
e) The left whisker of the y variable is longer than the right whisker, and the median is located outside the box's center.
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The complete question is given below:
find the value of x.
6.0 percent of a population are infected with a certain disease. there is a test for the disease, however the test is not completely accurate. 90.0 percent of those who have the disease test positive. however 3.1 percent of those who do not have the disease also test positive (false positives). a person is randomly selected and tested for the disease. what is the probability that the person has the disease given that the test result is positive?
Probability of the person has the diseases and the test result is positive = 1/90 = 0.011
What is probability?Probability refers to the possibility of occurring a certain event. It is expressed by the ratio of the number of favorable outcome to the total possible outcome.
How can we calculate probability?Given, percentage of people who have disease and test result positive =90
percentage of people who has not disease but test result positive =3.1
Suppose 6.0 percent of population are infected
Now, probability of a randomly selected person who has diseases and test positive
= 1/90
= 0.011
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The fraction 5/6 * i is equivalent to what percent ? Round your percent to the nearest tenth. 5/6 is approximately 96
It is approximately equal to 83.3%
What are percentages?In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”
Given here, 5/6 thus in percentage terms it will be = 5/6 × 100
= 83.3%
Hence the answer is 83.3%
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A shape has 7 non-congruent sides. If 6 of the exterior angles measure 310
degrees, and the remaining angle measures (6x + 2) degrees, what is the value
of x ?
The last remaining non - congruent side measure = 48°
what is non- congruent sides?Non congruent means "not congruent," i.e., not the same shape, and the sides. Congruent shapes are those that are copies of one another that have been rotated, reflected, and translated.
given
the sum of 6 exterior angles = 310°
remaining angle = ([tex]6x+2[/tex])
All sides of exterior angles sum= 360°
so , remaining angle + sum of all exterior angles=360°
[tex](6x+2)[/tex] + 310° = 360°
[tex](6x+2)[/tex] = 360° - 310C
[tex](6x+2)[/tex] = 50°
[tex]x[/tex] = 48°
The last remaining non - congruent side measure = 48°
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The function f(x) = 5one-fifth is reflected over the y-axis. which equations represent the reflected function? select two options.
The correct option D. f(x) = 5(5)ˣ and E. f(x) = 5(1/5)⁻ˣ, for the reflected function over the y-axis.
Explain the term reflected over the y-axis?The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be an additive inverse.We are aware of:
f(x) = 5(1/5)ˣ
Positive x-values and negative x-values are switched by a reflection over the y-axis, which also swaps the values of x and x.
Therefore:
f(ax) = f(x)
The following will be the value of the supplied function's y-axis reflection:
(Remember to swap out positive and negative x-values.)
f(x) = 5(1/5)⁻ˣ
A comparable form will be:
f(x) = 5(1/5)⁻ˣ
f(x) = 5(1/5)⁽⁻¹⁾⁽ˣ⁾
f(x) = 5[(1/5)⁻¹]ˣ
f(x) = 5(5)ˣ
Therefore
The following equations depict the reflected function:
f(x) = 5(5)ˣf(x) = 5(1/5)⁻ˣTo know more about the reflected over the y-axis, here
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The complete question is-
The function f(x) = 5(1/5)ˣ h is reflected over the y-axis. Which equations represent the reflected function? Select two options.
A. f(x) = One-fifth
B. f(x) = One-fifth.One-fifth.One-fifth
C. f(x) = 5One-fifth
D. f(x) = 5(5)ˣ
E. f(x) = 5(1/5)⁻ˣ
A city has a 5% sales tax. What is the constant of proportionality?
Answer: 0.05
Step-by-step explanation:
The equation is k = y/x, which is a constant change rate
Take 5 divided by 100 = 0.05
5% = 0.05
So the constant of proportionality is 0.05
Select the correct answer from each drop-down menu.
The endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5).
The center of the circle is at the point
O and its radius is
units. The equation of this circle in standard form is
The equation of this circle in standard form is x² + y² - 8x - 16y + 73.75 = 0
How to determine the equation of this circle in standard formFrom the question, we have the following parameters that can be used in our computation:
Endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5)
These endpoints represent endpoints of the diameter
So, we have the diameter to be
diameter = √[(x₂ - x₁)² + (y₂ - y₁)²]
Substitute the known values in the above equation, so, we have the following representation
diameter = √[(4 - 4)² + (5.5 - 10.5)²]
Evaluate
diameter = 5
So, we have
radius, r = 5/2
The midpoint is
(a, b)= 1/2[(4 + 4, 5.5 + 10.5)]
So, we have
(a, b)= (4, 8)
The circle equation is calculated as
(x - a)² +(y - b)² = r²
Substitute the known values in the above equation, so, we have the following representation
(x - 4)² +(y - 8)² = 2.5²
This gives
x² - 8x + 16 + y² - 16y + 64 = 6.25
Evaluate the like terms
x² + y² - 8x - 16y + 73.75 = 0
Hence, the equation is x² + y² - 8x - 16y + 73.75 = 0
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The diagram below is used to sort out numbers.
Type each number in the correct location on the diagram.
3
30
333
3001
two-digit
numbers
multiples
of 3
three-digit
numbers
The solution is given as,
Two-digit numbers Multiples of 3 Three-digit numbers
30 3,30, 333, 333
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Place the given number in the appropriate place.
Numbers are 3, 30, 333, 3001,
Two digit number among the numbers = 30
Multiples of 3 among numbers = 30, 333, 3
Three-digit numbers among the numbers = 333
Thus, It is shown that the numbers are placed in their appropriate positions.
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How would I solve this? I need steps..
Option 2 and option 4 are the respective answers.
what is a discriminant of a quadratic equation?The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac. The discriminant tells us whether there are two solutions, one solution, or no solutions.
Given here -3x²+6x+2 = 0
therefore the discriminant is (6)² - ( -3×4×2) = 60
Thus the parabola formed by the curve would intersect the x-axis twice
Now for the second part of the answer, the equation is given as
3(2x-1) (x-4) = 3( 2x² - 9x + 4)
=6x² - 27x + 12
Applying the direct formula for root we get x = 27 + √(27² − 4×6×12)/12
Hence, option 2 is the correct answer for part 1, and option 4 is the correct answer for the latter question.
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when the spring is stretched and the distance from point a to point b is 5.3 feet, what is the value of θ to the nearest tenth of a degree?
a. 60.0
b. 35.2
c. 45.1
d. 55.5
When the spring is stretched and the distance from point a to point b is 5.3 feet, the value of θ is 53.13 degrees
The distance between point a to point b = 5.3 feet
The length of the top side = 3 feet
Therefore, it will form a right triangle
Here we have to use trigonometric function
Here adjacent side and the hypotenuse of the triangle is given
The trigonometric function that suitable for the given conditions is
cos θ = Adjacent side / Hypotenuse
Substitute the values in the equation
cos θ = 3 / 5
θ = cos^-1(3 / 5)
θ = cos^-1(0.6)
θ = 53.13 degrees
Therefore, the value of θ is 53.13 degrees
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g there are 10 clubs on campus. how many ways are there if you want to choose 3 student clubs out of 10 to join?
there are 10 clubs on campus. how many ways are there if you want to choose 3 student clubs out of 10 to join is 120
A fractional factorial experiment utilizes subset of combinations that are gotten from the full factorial experiment. They are applicable when there are too many inputs to screen practically or cost or time would be excessive.
Also, using the fractional factorial experiment makes running the experiments faster and cheaper.
10C3 = 10! / (7!*3!)
= 10*9*8/6
= 120
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sqrt{ 45 Multiplyed bysqrt 10
Answer:
Step-by-step explanation:
If C is ¼ of the distance from A to D if A is (3,7) and D is (11,11) where is C?
Answer:
(8.25, 9.75)
Step-by-step explanation:
To find the point that is ¼ of the distance from A to D, we first need to find the coordinates of D. Since A is located at the point (3, 7) and D is located at the point (11, 11), we can use the distance formula to find the distance between these two points. The distance formula is given by:
distance = √((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, we have x1 = 3, y1 = 7, x2 = 11, and y2 = 11, so the distance between A and D is:
distance = √((11 - 3)^2 + (11 - 7)^2) = √(8^2 + 4^2) = √(64 + 16) = √80 = 8.944
Now that we know the distance between A and D, we can use this information to find the point that is ¼ of the distance from A to D. Since C is ¼ of the distance from A to D, it is located ¼ of the way along the line between A and D. This means that we can find the coordinates of C by taking the average of the coordinates of A and D, weighted by ¼ and ¾, respectively. In other words, the coordinates of C are given by:
C = ¼ * A + ¾ * D
where A and D are the coordinates of points A and D, respectively. Plugging in the coordinates of A and D, we get:
C = ¼ * (3, 7) + ¾ * (11, 11) = (0.75 * 3 + 2.25 * 11, 0.75 * 7 + 2.25 * 11) = (8.25, 9.75)
Therefore, the point C is located at the coordinates (8.25, 9.75).
True
False
ܘ ܗ
10
15-
f(x)
0
3
The range of the given function in the figure is R - {0, 1, 2, 3}.
What is the range of a function?The range of a function is represented by the set of output values for the given input values.A range for a function depends on the domain of the function. Where the domain is nothing but the set of input values to the function.If a function is given by y = f(x), then the range is given by R = {y: x ∈ D of f}D - the domain of the function; R - the range of the functionCalculation:The given mapping shows a function f(x).
There are 4 inputs to the function and 5 outputs.
So, the domain set for the given function is written as D = {0, 5, 10, 15}
And the range set for the given function is written as R = {0, 1, 2, 3}
(Since the 5th output is repeating, in the range it is considered only once).
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help plss and if u could plot the point as well thats better
TY
The linear functions defined in this problem are given as follows:
1. y = -x + 3.
2. y = x - 3.
3. y = 3x + 1.
4. y = -2x - 2.
How to define the linear functions?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
The coefficients and their meaning 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 value of y when the graph of the function touches or crosses the y-axis.From the second bullet point above, the intercepts for each function in this problem are given as follows:
1. b = 3.2. b = -3.3. b = 1.4. b = -2.The slopes are given as follows:
1: m = -1, when x increases by 1, y decays by 1.2: m = 1, when x increases by 1, y increases by 1.3. m = 3, when x increases by 1, y increases by 3.4: m = -2, when x increases by 1, y decays by 2.Missing Information
The problem is incomplete, hence we just define the linear functions.
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