Answer:
We can use the Pythagorean theorem to find the distance between the transmitter and the second city:
c² = a² + b²
c² = 55² + 51²
c² = 3026
c ≈ 55.01
So the transmitter is about 55.01 miles away from the second city.
To determine how much of the drive will pick up a signal, we can draw a circle with a radius of 40 miles centered at the transmitter, and see which part of the line connecting the two cities is within this circle.
We can see that the line connecting the two cities intersects the circle at two points, forming a right triangle with one leg measuring 40 miles. We can use trigonometry to find the length of the other leg:
sin(theta) = opposite/hypotenuse
sin(theta) = 40/c
csin(theta) = 40
a = csin(theta)
a = 55.01*sin(theta)
Now we need to find the angle theta, which can be found using inverse tangent:
tan(theta) = opposite/adjacent
tan(theta) = 55/51
theta = tan⁻¹(55/51)
theta ≈ 49.72 degrees
So we can substitute this value of theta into the equation we found earlier for a:
a ≈ 43.89
Therefore, the length of the line segment within the circle is approximately 43.89 miles. To find the length of the entire line segment connecting the two cities, we can use the Pythagorean theorem again:
b² = c² - a²
b² = 55.01² - 43.89²
b ≈ 33.6
So the entire length of the line segment connecting the two cities is approximately 33.6 miles. Therefore, the portion of the drive during which you will pick up a signal from the transmitter is 43.89/33.6 = 1.31 hours or about 79 minutes.
sin^2x = (power reducing formula)
[tex]sin^2(x)[/tex] can be expressed as [tex](1 - cos(2x)) / 2[/tex] using the power reducing formula.
To express [tex]sin^2(x)[/tex]using the power reducing formula,
we need to recall the following trigonometric identity:
[tex]sin^2(x) = (1 - cos(2x)) / 2[/tex]
Recognize that the question asks for the power reducing formula for sin^2(x).
Recall the trigonometric identity:[tex]sin^2(x) = (1 - cos(2x)) / 2[/tex]
The power reducing formula for [tex]sin^2(x)[/tex] is:[tex](1 - cos(2x)) / 2.[/tex]
The power reducing formula is a trigonometric identity that allows you to express a trigonometric function of a higher power in terms of a trigonometric function of a lower power.
It is most commonly used for reducing the power of the sine and cosine functions.
The power reducing formula for cosine is:
[tex]cos^2(x) = (1 + cos(2x))/2[/tex]
The power reducing formula for sine is:
[tex]sin^2(x) = (1 - cos(2x))/2[/tex]
These formulas can be derived using the Pythagorean identity, which states that [tex]sin^2(x) + cos^2(x) = 1.[/tex]
By solving for either[tex]sin^2(x) or cos^2(x)[/tex] in terms of the other, and then using the double angle formula for cosine[tex](cos(2x) = cos^2(x) - sin^2(x)),[/tex] we can arrive at the power reducing formulas.
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Question 3(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
5, 5, 6, 8, 10, 15, 18, 20, 20, 20, 20, 20, 20
A graph titled Donations to Charity in Dollars. The x-axis is labeled 1 to 5, 6 to 10, 11 to 15, and 16 to 20. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 1 to 5, up to 3 above 6 to 10, up to 1 above 11 to 15, and up to 7 above 16 to 20.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 13 is the most accurate to use, since the data is skewed.
The range of 20 is the most accurate to use to show that they have plenty of money.
The IQR of 20 is the most accurate to use to show that they need more money.
For the given problem, The correct answer will be option 2: The IQR of 13 is the most accurate to use, since the data is skewed.
How to determine measure of variability?The Interquartile Range (IQR) is a measure of variability that compares the 25th percentile (Q1) to the 75th percentile (Q3) of a dataset (Q3). It is frequently used to describe the distribution or variability of data that may contain outliers or is not regularly distributed.
The data in the histogram is not evenly distributed in this example because there are many donations at the higher end of the scale (16 to 20), resulting in a positively skewed distribution. Using a range of 20, which indicates the difference between the greatest and lowest value in the dataset, may not adequately depict the data's variability since it is significantly impacted by outliers at the extremes.
For the given dataset, IQR can be calculated as:
Arrange the dataset in ascending order:
[tex]5, 5, 6, 8, 10, 15, 18, 20, 20, 20, 20, 20, 20[/tex]
Find the median (Q2), i.e. the middle value of given dataset:
Median (Q2) = 15
Find the lower quartile (Q1), which is the median of the lower half of the dataset:
[tex]Q1 = Median of (5, 5, 6, 8, 10) = 6[/tex]
Find the upper quartile (Q3) i.e. median of the upper half of dataset:
[tex]Q3 = Median \;of (15, 18, 20, 20, 20, 20, 20) = 19[/tex]
[tex]IQR = Q3 - Q1 = 19 - 6 = 13[/tex]
Utilizing the IQR of 13, which represents the range between the 25th percentile (Q1 = 6) and the 75th percentile (Q3 = 19), would provide a more accurate measure of variability that is less impacted by outliers at the higher end of the data. It would also offer a better indication of the organization's typical donations because it captures the middle 50% of the data.
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Can i have help please
Answer:
All new reflected coordinates
T (-3, 6)
S (-2, 4)
U (-4, 4)
R (-3, 2)
Step-by-step explanation:
This is because the are reflected sideways on x = 1. This works like a mirror or opening a page of a book if that helps visualise it.
Javier design a mosaic wall Mural using a 100 tiles in three different colors yellow blue and red if 64 of the tiles are yellow what percent of the tires are either red or blue
The simplified slope of item number 2 is:
a. 1/6
b. 6
c. -6
d. -1/6
The simplified slope of item number 3 is:
a. 4/7
b. 3/4
c. 7/4
d. -4/3
The simplified slope of item number 4 is:
a. 3/5
b. -3/5
c. -5/12
d. -12/5
Answer:
c and a
Step-by-step explanation:
The length of a rectangle is three feet less than two times the width. The perimeter is 27 feet. Find the dimensions.
Answer:
l = 2w - 3
2(2w - 3) + 2w = 27
4w - 6 + 2w = 27
6w - 6 = 27
6w = 33, so w = 5.5 feet and l = 8 feet
Answer:
Width: 5.5 feet
Length: 8 feet
Step-by-step explanation:
Let's begin by assigning variables to stand in for the rectangle's width and length.
Let x represent the rectangle's width.
The length is three feet shorter than double the width, according to the problem. As a result, the length may be written as:
2x - 3
The lengths of all the sides make up a rectangle's perimeter, which in this instance is:
2w + 2l
By substituting the width and length measurements we discovered:
2x + 2(2x - 3)
Simplifying:
2x + 4x - 6 = 27
6x = 33
x = 5.5
The rectangle is 5.5 feet wide as a result.
We may change x into the expression we discovered earlier to figure out the length:
2(5.5) - 3 = 8
The rectangle is 8 feet long as a result.
As a result, the rectangle's measurements are:
Width: 5.5 feet
Length: 8 feet
Not all systems of equations have solutions. Determine which systems below have solutions and which ones don’t.
There is no solution to this system of equations. (option B).
What is equation?
An equation is a mathematical statement which is made by two expressions connected by an equal sign. For example, 3x – 8 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 8.
There is no solution to the given graph of two linear equations or system of linear equations.
From the given graph it is clear that graph of the given two equations shows two lines that are parallel to each other. They don't meet or intersect each other at any point.
Since no point is on both lines, there is no ordered pair that makes both equations true.
Hence, there is no solution to this system of equations.
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Which is colder 32F or -109F
Answer:
Step-by-step explanation:
-109f
From the list of numbers, write down
a. a square number
b. a multiple of 13
c. a factor 186
d. the prime number
Answer:
a) a square number:64
b) a multiple of 13:65
c) a factor of 186:62
d)the prime number:61,67
Three softball players discussed their batting averages after a game.
................Probability
Player 1: four sevenths
Player 2: five eighths
Player 3: three sixths
By comparing the probabilities and interpreting the likelihood, which statement is true?
A. Player 1 is more likely to hit the ball than Player 2 because P(Player 1) > P(Player 2)
B. Player 2 is more likely to hit the ball than Player 1 because P(Player 2) > P(Player 1)
C. Player 3 is more likely to hit the ball than Player 1 because P(Player 3) > P(Player 1)
D. Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2)
The true statement is B. Player 2 is more likely to hit the ball than Player 1 because P(Player 2) > P(Player 1), by comparing the probabilities and interpreting the likelihood.
From the given information,
Probability of the batting average of player 1 = 4/7
Probability of the batting average of player 2 = 5/8
Probability of the batting average of player 3 = 3/6 = 1/2
We have to find the likelihood of each player.
LCM (7, 8, 6) = 56
Probability of player 1 = (4 × 8) / (7 × 8) = 32/56
Probability of player 2 = (5 × 7) / (8 × 7) = 35/56
Probability of player 1 = (1 × 28 ) / (2 × 28) = 28/56
Here the likelihood is greatest for player 2, then player 1 and the least likelihood is for player 3.
Hence the correct option is B.
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In this diagram, AT = 2x + 3, CT = 3x - 1, BT = x + 5,
DT = 4x + 1, and mLATD = 41x + 8. If x = 2,
which segment is the perpendicular bisector of the other? Explain your reasoning.
Neither of the segments is the perpendicular bisector of the other.
Which line is the perpendicular bisector?To determine which segment is the perpendicular bisector of the other, we need to find the equations of the lines containing each segment and then check if one of the lines is perpendicular to the other and passes through the midpoint of the other segment.
Let's start by finding the midpoint of segment AT. The coordinates of A and T are not given, but we don't actually need them to find the midpoint.
So, the midpoint M of segment AT is:
M = ((AT_x1 + AT_x2)/2, (AT_y1 + AT_y2)/2)
We don't know the actual values of AT_x1, AT_x2, AT_y1, and AT_y2, but we can find their expressions in terms of x using the segment lengths and the coordinates of the endpoints. We have:
AT_x2 - AT_x1 = BT_x2 - AT_x1 = (x + 5) - (2x + 3) = -x + 2
AT_y2 - AT_y1 = BT_y2 - AT_y1 = (BT - AT) = (x + 5) - (2x + 3) = x + 2
Therefore,
AT_x1 = AT_x2 + x - 2
AT_y1 = AT_y2 - x - 2
Now, we can substitute x=2 and the expressions for AT_x1 and AT_y1 into the midpoint formula to find the coordinates of M:
M = ((AT_x1 + AT_x2)/2, (AT_y1 + AT_y2)/2) = ((AT_x2 + 2 - AT_x2)/2, (AT_y2 - 2 - AT_y2)/2) = (1, -1)
So, the midpoint of segment AT is M(1, -1).
Next, let's find the equations of the lines containing segments AT and DT. We can use the point-slope form of the equation of a line, which states that the equation of a line passing through a point (x1, y1) with slope m is y - y1 = m(x - x1).
For segment AT, we have:
m_AT = (AT_y2 - AT_y1)/(AT_x2 - AT_x1) = (x + 2)/(x - 1)
Let's substitute x=2 to find the slope of the line containing segment AT:
m_AT = (2 + 2)/(2 - 1) = 4
So, the equation of the line containing segment AT is:
y - AT_y1 = m_AT(x - AT_x1)
y - (22 + 3) = 4(x - 22 - 1)
y - 7 = 4(x - 5)
y = 4x - 13
For segment DT, we have:
m_DT = tan(m∠ATD) = tan(41x + 8)
Let's substitute x=2 and simplify:
m_DT = tan(82 + 8) = tan(90) = undefined
This means that the line containing segment DT is vertical and its equation is x = DT_x1 = 4*2 + 1 = 9.
Now, we need to check if one of these lines is perpendicular to the other and passes through the midpoint of the other segment.
First, let's check if the line containing segment AT is perpendicular to the line containing segment DT. We have:
m_AT * m_DT = 4 * undefined = undefined
Since undefined is not equal to -1, the lines are not perpendicular, and we can rule out the possibility that the line containing segment AT is the perpendicular bisector of segment DT.
Next, let's check if the line containing segment DT is perpendicular to the line containing segment AT. We have:
m_AT = 4
So, the slope of the line perpendicular to the line containing segment AT is -1/4. We can use the point-slope form of the equation of a line again:
y - M_y = -1/4(x - M_x)
y - (-1) = -1/4(x - 1)
y + 1 = -1/4x + 1/4
y = -1/4x + 3/4
Now, we need to check if this line passes through point D, an endpoint of segment DT. We can substitute the coordinates of D into the equation of the line and check if the equation holds true:
DT_y1 = 4*2 + 1 = 9
DT_x1 = 9
9 = -1/4*9 + 3/4
9 = -9/4 + 3/4
9 = -6/4
This is not true, so the line containing segment DT does not pass through point D. Therefore, we can conclude that the line containing segment DT is not the perpendicular bisector of segment AT.
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Please help!!!!!!!!
The following data shows the grades that an 8th grade mathematics class received on a recent exam.
{99, 94, 91, 79, 88, 94, 92, 93, 90, 89, 77, 75, 65, 90, 87, 93, 92, 82, 65, 60, 78}
Part A: Determine the best graphical representation to display the data. Explain why the type of graph you chose is an appropriate display for the data. (6 points)
Part B: Explain, in words, how to create the graphical display you chose in Part A. Be sure to include a title, axis label(s), scale for axis if needed, and a clear process of how to graph the data. (6 points)
The line plot of the data points is added as an attachment
The best representation and whyPart A:
A line plot or dot plot would be an appropriate graphical representation for this data set. A line plot would show each data point on a number line with an X above the value,
This graph would be appropriate for displaying this data because the data set is relatively small and the values are discrete (whole numbers), making it easy to see the frequency and distribution of the data points.
Part B:
To create a line plot or dot plot for this data set, you would first need to create a number line that spans the range of values in the data set.
In this case, the range of values is from 91 to 125, so the number line would include all values between these two numbers.
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Amazon's "Smile" logo is a parabola and is modeled by h(x) =-0.03x + 0.4x, where h(x) is the height of
the Smile (in feet) at a distance of x (in feet) from one side. Find the Axis of Symmetry. How high is the Smile
at the Axis of Symmetry?
The axis of symmetry is located at a distance of 6.67 feet from one side of the smile and the height of the smile at the axis of symmetry is 0.891 feet.
The equation of the Amazon Smile logo is given by:
h(x) = -0.03x² + 0.4x
To find the axis of symmetry, we need to use the formula:
x = -b / 2a
where a and b are the coefficients of the quadratic equation ax² + bx + c = 0.
a = -0.03 and b = 0.4.
x = -0.4 / 2(-0.03) = 6.67 feet
Therefore, the axis of symmetry is located at a distance of 6.67 feet from one side of the smile.
To find the height of the smile at the axis of symmetry, we need to substitute x = 6.67 into the given equation:
h(6.67) = -0.03(6.67)² + 0.4(6.67) = 0.891 feet
Therefore, the axis of symmetry is located at a distance of 6.67 feet from one side of the smile and the height of the smile at the axis of symmetry is 0.891 feet.
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Do you want to use a Square section of your yard for a garden. Do you have a most 52 feet of fencing to surround the garden. Right and solve inequality to represent the possible length of each side of the garden
The possible lengths of each side of the garden is given by the inequality relation 0 ≤ x ≤ 12
Given data ,
Let's assume that the square garden has sides of length x.
To surround the garden, we will need fencing of length equal to the perimeter of the square, which is 4x
The total amount of fencing is at most 52 feet
So , the inequality is
4x ≤ 52
Dividing both sides by 4, we get:
x ≤ 13
Therefore, the possible length of each side of the garden is less than or equal to 13 feet
And , each side of garden should be more than 0 , so
x > 0
Hence , the full inequality representing the possible length of each side of the garden would be 0 < x ≤ 13
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is 3- greater than 5-
No, 3 is not greater than 5. This is because 5 is larger than 3.
Is 3- greater than the number 5?From the question, we have the following parameters that can be used in our computation:
3 and 5
No, 3 is not greater than 5. This is because 5 is larger than 3.
In other words, 5 is further to the right on the number line than 3.
We can also say that 5 is the greater number and 3 is the lesser number.
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Which of the following are examples of rational numbers? Select all that apply.
√4+√16
√5 +√36
√9+√24
2* √4
√49 • √81
3√12
The rational numbers in the list of options are √4+√16, 2* √4 and √49 • √81
The examples of rational numbers among the given options are:
2√4: √4 is equal to 2, so 2√4 = 2*2 = 4, which is a rational number.√49 • √81: √49 is equal to 7 and √81 is equal to 9, so √49 • √81 = 7 • 9 = 63, which is a rational number.√4+√16: √4 is equal to 2 and √16 is equal to 4, so √4+√16 = 2 + 4 = 6, which is a rational number.The other options are not rational numbers:
√5+√36: √5 is an irrational number, so √5+√36 is not a rational number.√9+√24: √24 is an irrational number, so √9+√24 is not a rational number.3√12: √12 is equal to 2√3, so 3√12 = 3 • 2√3 = 6√3, which is not a rational number.Read more about rational numbers at
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What is the volume of a right circular cylinder with diameter 6 cm and height 16 cm? Leave your answer in terms of π
If diameter 6 cm and height 16 cm, the volume of the right circular cylinder is 144π cubic cm.
The volume of a right circular cylinder is given by the formula V = πr^2h, where r is the radius of the base and h is the height. In this case, the diameter is given as 6 cm, so the radius is half of the diameter, which is 3 cm. The height is given as 16 cm.
Substituting these values into the formula, we get:
V = π(3 cm)^2(16 cm)
V = π(9 cm^2)(16 cm)
V = 144π cubic cm
A right circular cylinder is a three-dimensional object with a circular base and straight sides that are perpendicular to the base. The volume of a cylinder is the amount of space that it occupies and is calculated by multiplying the area of the base by the height.
In this case, the base of the cylinder is a circle with radius 3 cm, so its area is π(3 cm)^2 = 9π square cm. The height of the cylinder is 16 cm, so the volume is 9π x 16 = 144π cubic cm.
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Suppose a continuous random variable X is uniformly distributed on the interval [4,9]. able Y distributed? That is, determine the probability density function fy(y) 1. None of these. 2. for 4-y-9 = 10, 0 otherwise
For a continuous random variable X, which is uniformly distributed on an interval [4,9], the probability density function of [tex]f_Y( y)[/tex] is equals to
[tex]f_Y( y) =\begin{cases} \frac{2y}{5},\quad 2≤ x ≤ 3 \\ 0, \quad \: otherwise\ \ \end{cases}[/tex]. So, option(5) is correct.
We have a continuous random variable X is uniformly distributed on the interval [4,9]. The PDF is a probability that a random variable acquire a value exactly same or equal to the random variable but in case of CDF, this probability values is less than or equal to the random variable. The probability density function for X is defined as [tex]f_X(x) = \frac{1}{b - a} [/tex] so, we can write it as [tex]f_X ( x) =\begin{cases} \frac{1}{5},\quad 4≤ x ≤ 9 \\ 0, \quad otherwise \\ \end{cases}[/tex].
We have to determine the probability density function [tex]f_Y(y)[/tex]. For this first we have to calculate the cumulative distribution function for f(x) is written as [tex]F_X(x) = \int_{4}^{x} f(x) dx [/tex]
[tex]= \int_{4}^{x} \frac{1}{5} dx [/tex]
[tex]= \frac{1}{5} [ x]_{4}^{x} [/tex]
[tex]F_X(x) = \frac{x - 4}{5}[/tex]
Now, we have, [tex] Y = \sqrt{X}[/tex]
when X = 4 => Y = 2 and X = 9 => Y = 3
Also, X = Y²
Differentiating X = Y² with respect to Y
=> dX = 2Y dY
=> dX/dY = 2Y
Now, pdf of Y is written as [tex]f_Y(y) = f_X(x)|\frac{dX}{dY}| [/tex]
[tex] = \frac{ 1}{5} × 2y[/tex]
[tex]= \frac{ 2y}{5}[/tex]
So, [tex]f_Y( y) =\begin{cases} \frac{2y}{5},\quad 2≤ x ≤ 3 \\ 0, \quad \: otherwise \ \ \end{cases}[/tex]. Hence, required value is [tex]f_Y( y) =\begin{cases} \frac{2y}{5},\quad 2≤ x ≤ 3 \\ 0, \quad \: otherwise \ \ \end{cases}[/tex].
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Complete question:
The above figure complete the question.
Show that the four points (2,1), (-1,-5), (1,5) and (-2,-1) are the vertices of a parallelogram
They form a parallelogram because opposite sides of the given points have an equal slope.
What is the slope?The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).
According to the given information:To prove that the four points (2,1), (-1,-5), (1,5), and (-2,-1) are the vertices of a parallelogram, we need to show that opposite sides are parallel.
First, we can find the slope of the line connecting (2,1) and (-1,-5):
m1 = (1 - (-5)) / (2 - (-1)) = 6/3 = 2
Next, we can find the slope of the line connecting (1,5) and (-2,-1):
m2 = (5 - (-1)) / (1 - (-2)) = 6/3 = 2
Since the slopes are the same, the line segments connecting these points are parallel.
Now, we can find the slope of the line connecting (2,1) and (1,5):
m3 = (5 - 1) / (1 - 2) = -4
Next, we can find the slope of the line connecting (-1,-5) and (-2,-1):
m4 = (-1 - (-5)) / (-2 - (-1)) = 4/3
Since the slopes are different, the line segments connecting these points are not parallel.
However, we can also see that the line connecting (1,5) and (-1,-5) has the same slope as the line connecting (-2,-1) and (2,1), which is:
m5 = (5 - (-5)) / (1 - (-1)) = 10/2 = 5
Therefore, the line segments connecting (1,5) and (-1,-5), and (-2,-1) and (2,1) are parallel.
Since opposite sides are parallel, the four points (2,1), (-1,-5), (1,5), and (-2,-1) form a parallelogram.
Therefore, they form a parallelogram because opposite sides of the given points have an equal slope.
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Ima be giving brainliest plus help!!!!!!!
Answer:
32 degrees
Step-by-step explanation:
Recall the three main trig functions: sine, cosine, and tangent.
When using sine, we divide the opposite side from the angle by the hypothenuse.
When using cosine, we divide the adjacent side of the angle by the hypothenuse.
When using tangent, we divide the opposite side from the angle by the adjacent side to the angle.
Since we are given the opposite and adjacent sides, we'll use tangent.
We set up the equation like normal:
tan x [tex]= \frac{13}{21}[/tex]
Now, when finding the angle measurement using trig, we must use the opposing trig function, arcsine, arccosine, and arctangent. The opposing trig function is arctangent. We have to move arctangent to the other side, so that it can be used with the fraction, so:
[tex]x = arctan(\frac{13}{21} )[/tex]
(You would also write arctan, as tan with an exponent of -1) Now, just punch the right side of the equation into a calculator. The nearest degree is 32.
Therefore, the answer is 32 degrees. If you got something different, make sure your calculator is in degrees, not radians! (They are usually abbreviated as DEG and RAD.)
Help I don't understand.
Using the given percentage we can see that the minimum and maximum numbers are:
N- = 967
N+ = 1,150
How to get the minimum and maximum amounts?The total number of students is 3,650, and we know that the average percentage is 29% ± 2.5%
The minimum value is what we get when we use the minus sign:
29% - 2.5% = 26.5%
The 26.5% of 3,650 is:
N- = (0.265)* 3,650 = 967
The maximum value is what we get when we use the plus sign:
29% + 2.5% = 31.5%
The 31.5% of 3,650 is:
N+ = (0.315)*3,650 = 1,150
These are the two values.
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Which type of government structure would be threatened by debate over public policy?
A government structure that is authoritarian or dictatorial in nature would be threatened by debate over public policy.
In such a system, the government exercises complete control over decision-making and any opposition or dissent is not tolerated.
Open debate and discussion over public policy would challenge the authority of the government and its ability to maintain control over the population.
Democracies, on the other hand, thrive on healthy debate and discussion over public policy, as it allows for diverse perspectives and ideas to be heard and considered.
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find the value of H for the parallellogram to the right
Answer:
h = 10 13/14 units
Step-by-step explanation:
You want the height from the side of length 14 of a parallelogram with side length 17 and height 9.
AreaThe area of a parallelogram is the same, no matter which side is used as the "base". This means ...
A = bh = 17(9) = 14(h)
h = 17·9/14 = 10 13/14 . . . . units
A jar contains marbles that are green, red or blue,
1/6 of the marbles are red
1/3 of the marbles are blue
Given that there are 18 green marbles in the jar,
work out how many are blue,
Answer:
36
Step-by-step explanation:
Given:
1/6 of the marbles are red
1/3 of the marbles are blue
There are 18 green marbles in the jar
We can set up the following equations based on the given information:
Number of red marbles = 1/6 * x
Number of blue marbles = 1/3 * x
Number of green marbles = 18
Since the total number of marbles in the jar is "x", we can write the equation for the sum of all the marbles as:
(Number of red marbles) + (Number of blue marbles) + (Number of green marbles) = x
Substituting the values from the given information:
1/6 * x + 1/3 * x + 18 = x
Multiplying through by 6 to eliminate the fraction:
x/6 + 2x/6 + 18 = 6x/6
x + 2x + 108 = 6x
Combining like terms:
3x + 108 = 6x
Subtracting 3x from both sides of the equation:
3x + 108 - 3x = 6x - 3x
108 = 3x
Dividing both sides by 3 to solve for x:
108/3 = 3x/3
36 = x
what are the points that are contained in the graph of the equation?
Answer:
(0, [tex]\frac{1}{2}[/tex] ) , (1, [tex]\frac{5}{4}[/tex] ) , (2, 2 )
Step-by-step explanation:
to determine which points are contained in the graph.
substitute the x- coordinate of each point into the equation and if the value obtained is equal to the y- coordinate of the point then it is contained in the graph.
(0, [tex]\frac{1}{2}[/tex] )
y = [tex]\frac{3}{4}[/tex] (0) + [tex]\frac{1}{2}[/tex] = 0 + [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{2}[/tex] = y- coordinate ← contained in graph
(1, [tex]\frac{5}{4}[/tex] )
y = [tex]\frac{3}{4}[/tex] ( 1) + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{4}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{4}[/tex] + [tex]\frac{2}{4}[/tex] = [tex]\frac{5}{4}[/tex] = y- coordinate ← contained in graph
([tex]\frac{1}{2}[/tex], 0 )
y = [tex]\frac{3}{4}[/tex] ([tex]\frac{1}{2}[/tex] ) + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{8}[/tex] + [tex]\frac{4}{8}[/tex] = [tex]\frac{7}{8}[/tex] ≠ y- coordinate ← not contained in graph
(2, 2 )
y = [tex]\frac{3}{4}[/tex] (2) + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{2}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2 = y- coordinate ← contained in graph
If three squares have sides that make an acute triangle, then the sum of the areas of the two small squares...
If three squares have sides that make an obtuse triangle, then the sum of the areas of the two small squares...
If three squares have sides that make a right triangle, then the sum of the areas of the two small squares...
The Pythagorean Theorem can be utilized in any situation to establish a connection between the side lengths of the squares and the sort of triangle that results.
What is the Pythagorean Theorem?Let's use the notation "a, b, and c" to indicate the three squares' side lengths, where "a" stands for the shortest side, "b" for the midpoint, and "c" for the longest side.
The area of the largest square (c), which is created by the hypotenuse of the triangle, is equal to the sum of the areas of the two smaller squares when three squares' sides form an acute triangle.
The areas of the two smaller squares (a and b) formed by the two larger squares (a and b) are equal when three squares have sides that form an obtuse triangle.
If three squares have sides that make a right triangle, then the sum of the areas of the two small squares is equal to the area of the largest square (c) formed by the hypotenuse of the right triangle.
In all cases, the Pythagorean Theorem can be used to determine the relationship between the side lengths of the squares and the type of triangle formed.
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I need help solving this
The values using trigonometric ratios are sinR = 15/17; cosR = 8/17, tanR = 15/8
How to solve an equation?An equation is an expression that uses mathematical operations to show how numbers and variables are related to each other.
Pythagoras ratio is an equation that shows the relationship between the sides of a right triangle.
To find TR, using Pythagoras:
TR² = TY² + YR²
TR² = 15² + 8²
TR = 17
Trigonometric ratios show the relationship between sides and angles of right triangle.
Hence:
sinR = 15/17; cosR = 8/17, tanR = 15/8
The values are sinR = 15/17; cosR = 8/17, tanR = 15/8
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PLEASE HELP!!!
A principal of $4200 is invested at %8 interest, compounded annually. How much will the investment be worth after 12 years?
Answer:
$10,244.14 after 12 years
Step-by-step explanation:
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
A = the final amount of the investment
P = the principal amount ($4200 in this case)
r = the annual interest rate (8% or 0.08 as a decimal)
n = the number of times the interest is compounded per year (once annually in this case)
t = the number of years the money is invested (12 years in this case)
Substituting the given values into the formula, we get:
A = 4200(1 + 0.08/1)^(1*12)
A = 4200(1.08)^12
A = 4200(2.44140625)
A = $10,244.14 (rounded to the nearest cent)
EFGH is a square. If FG= 9, what is FJ? Round your answer to the nearest tenth, if necessary.
~a.) 4.5
~b.) 6.4
~c.) 9
~d.) 12.7
Answer:
6.4
Step-by-step explanation:
I need help on this question
Answer:
Step-by-step explanation:
I think it’s b