Interquartile range of the scores is 7.
What is interquartile range?When values are ranked from lowest to highest, the IQR designates the middle 50% of those values. Find the median (middle value) of the bottom half and upper half of the data before calculating the interquartile range (IQR). Quartile 1 (Q1) and Quartile 3 are these values (Q3). The IQR represents the variation between Q3 and Q1. The strongest indicator of variability in data sets with outliers or skewed distributions is the interquartile range. It's unlikely to be impacted by outliers because it's based on numbers that come from the center half of the distribution.
Given Set
16, 12, 20,35,21,17,19,20,13,12,15
12, 12, 13, 15, 16, 17, 19, 20, 20, 21, 35
25 percentile(Q₁) = 13
50 percentile(Q₂) = 17
75 percentile(Q₃) = 20
Interquartile range = Q₃ - Q₁
Interquartile range = 20-13
Interquartile range = 7
Interquartile range of the scores is 7.
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Thursday
Each 4th grade class at Garza Elementary collected plastic water bottles to recycle.
Each number on the stem and leaf plot represents how many bottles each class
brought in. Record each answer in the blank box next to each question.
Help fill the table please.
1. how many fourth grade classes brought in between 90 and 100 bottles
2. How many classes brought in more than 100 water bottles
3. how many classes brought in less than 99 water bottles
4. How many fourth grade glasses are represented on the stem and leaf plot
The number of students that collected between 90 and 100 bottles is 3.
The number of students that collected more than 100 bottles are 7.
The number of students that collected less than 90 students are 2
The total number of classes represented is 10.
Here is the completed frequency table
Number of bottles collected Classes
90 - 100 3
101 - 110 6
111 - 120 1
What is a stem and leaf plot?A stem-and-leaf plot is a table that splits a number into a stem and leaf. The stem is the first number in the digit while the leaf is the last number. For example the stem in 45 is 4 and the leaf is 5.
An advantage of the stem-and-leaf plot is that it provides an easy way to present and interpret a dataset. A disadvantage of the stem-and-leaf plot is that it cannot be used for a large dataset.
Bottles collected that are between 90 and 100 are 94, 98, 99
Bottles that are greater than 100 are 105, 107, 107, 113, 114, 119, 120
Bottles that are less than 99 are 94, 98
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IXL Transversals of parallel lines: prove angle relationships 6QF for geometry, please help
4) [tex]m\angle XWY=m\angle HGY[/tex] (definition of congruent angles)
5) [tex]\angle HGY \cong \angle GTU[/tex] (corresponding angles theorem)
6) [tex]m\angle HGY=m\angle GTU[/tex] (definition of congruent angles)
7) [tex]\angle GTU[/tex] and [tex]\angle UTR[/tex] are supplementary (linear pair)
8) [tex]m\angle GTU+m\angle UTR=180^{\circ}[/tex] (definition of supplementary angles)
9) [tex]m\angle HGY+m\angle UTR=180^{\circ}[/tex] (substitution)
10) [tex]m\angle RTU+m\angle XWY=180^{\circ}[/tex] (substitution)
it takes 126 cubes that have edge lengths of 1/3feet to completely fill this plastic bin what is the area of the base of bin
Answer: 1) Each of the 126 cubes has a volume = (1/3)3 = 1/3 × 1/3 × 1/3 = 1/27 cubic feet.
2) It takes 126 cubes to fill the bin, so the bin has a volume of 126 × 1/27 = 126/27 cubic feet. (Don't do this division yet - leave it as an improper fraction)
3) The volume of the bin is also given by the formula Volume = Area of Base × Height. Plus we know the volume is 126/27 cubic feet and the height is 2 1/3 = 7/3 of a foot, so:
Step-by-step explanation: Volume = Area of Base × Height
126/27 = Area of Base × 7/3
126/27 × 3/7 = Area of Base
The area of the base of bin is 2 feet².
What is Volume of Cube?The formula of volume of the cube is given by: Volume = a³, where a is the length of its sides or edges.
Given:
Edge = 1/3 feet
Volume of 1 cube= l³= (1/3)³ = 1/27
Totals cubes= 126
So, Volume of 126 cube= 126 x 1/27 = 126/ 27
Then, Volume of Plastic Bin= Area of base x height
126 / 27 = Area of base x 7/3
Area of base = 126 /27 x 3 /7
Area of base = 2 ft²
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Find a_10 5, 12, 19, 26, 33...
Given,
The progression is 5, 12, 19, 26, 33...
The first term of the series is, a = 5.
The common difference of the series is,
d = 12 - 5 = 7
The 10th term of the series is,
[tex]\begin{gathered} a_{10}=a+(10-1)\times d \\ =5+9\times7 \\ =5+63 \\ =68 \end{gathered}[/tex]Hence, the 10th term of the series is 68.
You are about to enter an elevator with a weight capacity of 500 pounds. There are three people already in the elevator. The weights of the passengers are 107 pounds, 172 pounds and 129 pounds. Assuming that you weigh 136 pounds, is it safe for you to enter the elevator?
Given
capacity of 500 pounds.
weights of the passengers are 107 pounds, 172 pounds and 129 pounds.
you weigh 136 pounds
Find
is it safe for you to enter the elevator?
Explanation
as total pounds in the elevator = 107 + 172 + 129 = 408 pounds
total pounds included my weight = 408 + 136 = 544 pounds
capacity = 500 pounds
so , extra pounds = 544 - 500 = 44 pounds
so , no it is not safe for you to enter the elevator.
Final Answer
Therefore , No the weigh capacity would be exceeded by 44 pounds
Simplify 2(x+8)+6x Write your answer in factored form
Answer:
8x + 16 is your answer
Step-by-step explanation:
22. A 250W carrier is to be modulated at an 85% modulation level. What is the total transmitted power? a. 340.3 W b. 25.32 dB c. 0.340 kW d. 55.32 dBm e. All of the above.
The total transmitted power is a. 340.3 W.
The transmitted and carrier power is related with modulation through the formula -
[tex] P_{t} = P_{c}(1 + \frac{ {m}^{2} }{2} )[/tex]
where [tex]P_{t}[/tex] is transmitted power, [tex]P_{t}[/tex] is carrier power and m is modulation.
Keep the values in formula to find the value of total transmitted power.
[tex]P_{t}[/tex] = 250 (1 + 85%²/2)
Taking square of percentage
[tex]P_{t}[/tex] = 250 (1 + 0.7225/2)
Performing division in the bracket
[tex]P_{t}[/tex] = 250 (1 + 0.36125)
Performing addition in the bracket
[tex]P_{t}[/tex] = 250×1.36125
Performing multiplication
[tex]P_{t}[/tex] = 340.3125
Thus, the total transmitted power when carrier power is 250 W and modulation is 85% is a. 340.3 W.
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find the lateral area and surface area the lateral area of the prism is __in squared. the surface area of the prism is __ in squared
Answer
The lateral area of the prism is 900 in squared
The surface area of the prism is 960 in squared
Explanation
Given:
The first side of the triangular base, a = 12 in
The second side of the triangular base, b = 13 in
The height of the prism, h = 30 in
What to find:
The lateral area and surface area of the prism.
Step-by-step solution:
The first step is to find the third side, c of the triangular base using Pythagoras rule.
[tex]\begin{gathered} b^2=c^2+a^2 \\ \\ 13^2=c^2+12^2 \\ \\ c^2=13^2-12^2 \\ \\ c^2=169-144 \\ \\ c^2=25 \\ \\ c=\sqrt{25} \\ \\ c=5\text{ }in \end{gathered}[/tex]Now, the next step is to calculate the lateral area of the prism using the formula below.
[tex]\begin{gathered} L.A=ha+hb+hc \\ \\ L.A=30\times12+30\times13+30\times5 \\ \\ L.A=360+390+150 \\ \\ L.A=900\text{ }in^2 \end{gathered}[/tex]The lateral area of the prism is 900 in squared
The final step is to calculate the surface area of the prism using the formula below.
[tex]S.A=Lateral\text{ }Area+Base\text{ }Area[/tex]The base area is
[tex]=2(\frac{1}{2}cb)=2(\frac{1}{2}\times5\times12)=2(\frac{60}{2})=60\text{ }in^2[/tex]Therefore, the Surface Area = (900 + 60) = 960 in squared
Melissa brought 6 apples for $1.20 .if each apple cost the same amount, how much would 20 apples cost
The cost of 20 apples is such that the ratio of apples to cost maintained or each apple costs the same amount is $4.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
As per the given,
Melissa brought 6 apples for $1.20.
The ratio of cost to apple ⇒
1.20/6
Now let's suppose the cost of 20 apples is x dollars.
The ratio of cost to apple ⇒
x/20
Since the cost of each apple is the same, therefore, both ratios must be the same.
x/20 = 1.20/6
x = 20(1.20/6)
x = 4
Hence "The cost of 20 apples is such that the ratio of apples to cost maintained or each apple costs the same amount is $4".
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Which of the following equations represents a line that is perpendicular toy=-3x+6 and passes through the point, (3, 2)?A. y=-3x+1B. y=(1/3x)+3C. y=(-1/3x)+1OD. y=(1/3x)+1
Step 1
For perpendicular lines
[tex]m_1=-\frac{1}{m_2}[/tex][tex]m_1=-3[/tex][tex]\begin{gathered} -3=-\frac{1}{m_2} \\ m_2=-\frac{1}{-3} \\ m_2=\frac{1}{3} \end{gathered}[/tex]Step 2
[tex]\begin{gathered} Given\text{ points \lparen3,2\rparen} \\ y=mx+b---\text{ Standard equation of a line} \\ y=\frac{1}{3}x+b \end{gathered}[/tex][tex]2=\frac{1}{3}(3)+b[/tex]Find b, the y-intercept
[tex]\begin{gathered} 2=1+b \\ b=2-1=1 \end{gathered}[/tex]Answer; Option D
[tex]y=\frac{1}{3}x+1[/tex]
(-8.8)(-9) =
(0.5)(-0.5)=
(-0.2)(-5)
Answer:
(-8.8)(-9)= 79.2
(0.5)(-0.5)= -0.25
(-0.2)(-5)= 1
If P is the centroid of the triangle JKL, JK = 22, KN = 13, and OL = 18, find each measure.
Given
JK = 22
KN = 13
OL = 18
Procedure
Centroid formulation
KM = JK/2 = 22/2 = 11
KM = 11
NL = KN
NL = 13
KL = 2KN = 2(13) = 26
KL = 26
JO = OL = 18
JO = 18
JL = 2OL = 2(18)
JL = 36
2. A new car dealership invites 500 people to a promotional event. Only 330 people attend the event. What percentage of the people attend the event?
since
[tex]550X=330[/tex]then
[tex]X=\frac{330}{500}=0.66[/tex]then it is the 100x0.66= 66%
find the value of x and y that make the quadrilateral
The quadrilateral have equal opposite sides, for example:
Then, (4x + 6) must be equal to (7x - 3), and (4y - 3) is equal to (3y + 1), therefore
[tex]4x+6=7x-3[/tex]We can solve that equation for x
[tex]\begin{gathered} 4x+6=7x-3 \\ \\ 3x=9 \\ \\ x=\frac{9}{3}=3 \end{gathered}[/tex]Hence, x = 3. Now let's solve the other equation
[tex]\begin{gathered} 4y-3=3y+1 \\ \\ y=4 \end{gathered}[/tex]Then the value of y is 4.
Final answers:
x = 3
y = 4
A manufacturer of ski clothing makes ski pants and ski jackets. The profit on a pair of ski pants is $3 and on a jacket is $2. Both pants and jackets require the work of sewing operators and cutters. There are 60 minutes of sewing operator time and 48 minutes of cutter time available. It takes 8 minutes to sew one pair of ski pants and 4 minutes to sew one jacket. Cutters take 4 minutes on pants and 8 minutes on a jacket. The manufacturer wants to make a minimum of 4 ski pants and 2 ski jackets, Let x represent the number of ski pants. Let y represent the number of ski jackets.
For the sewing operator:
[tex]8x\text{ + 4y }\leq\text{ 60}[/tex]For cutter:
[tex]4x\text{ + 8y }\leq48[/tex]The two above equation is solve to obtain the graph
The solution of the graph is where the two lines meet
The coordinate is (10, 4), at the this point the maximum profit is made
So 10 ski pants and 4 ski jackets is made to get maximum profit
The profit made is given by
P = 3x + 2y
x =10 , y = 4
P = 3(10) + 2(4)
P = 30 + 8 = $38
Factories 6ax2-3ay-8bx2+4by
=[2[tex]x^{2}[/tex]-y][3a-4b] This is the factorized form of 6a[tex]x^{2}[/tex]-3ay - 8 b[tex]x^{2}[/tex] + 4by
What is factorization ?To factorize a number, use the factorization formula. Factorization is the process of dividing a whole into components that, when multiplied together, equal the original number. The factorization approach simplifies any algebraic or quadratic equation by using the basic factorization formula, which represents the equations as the product of factors rather than expanding the brackets. Any equation may have an integer, a variable, or the algebraic expression itself as a factor.
6a[tex]x^{2}[/tex]-3ay - 8 b[tex]x^{2}[/tex] + 4by
Rearrange the expression
6a[tex]x^{2}[/tex] -8bx² -3ay +4by
2[tex]x^{2}[/tex][3a-4b] - y[3a-4b]
=[2[tex]x^{2}[/tex]-y][3a-4b]
This is the factorized form of 6a[tex]x^{2}[/tex]-3ay - 8 b[tex]x^{2}[/tex] + 4by
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Gravel is being dumped from a conveyor belt at a rate of 30 ft^3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 10 ft high?
The height of the pile increasing at the rate of 4.56 inches per minute when the pile is 10 ft high.
In given situation, the rate of change of height is equal to the rate of change of volume, divided by the base area.
First we find the base area.
base area = (π/4)d²
base area = (π/4)10²
base area = 25π ft²
base area ≈ 78.5 ft²
Then the rate of change of height would be,
(30 ft³/min)/(78.5 ft²)
≈ 0.38 ft/min
= 4.56 inches / minute
Therefore, the height of the pile increasing at the rate of 4.56 inches per minute when the pile is 10 ft high.
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Which of the following statements best describe the branches of the hyperbola?Select one:a.It is not possible to determine how the branches of the hyperbola open.b.The branches of the hyperbola are positioned at a 30⁰ angle.c.The branches of the hyperbola open up and down.d.The branches of the hyperbola open side to side.
Answer:
Explanation:
The first step is to plot the graph of the parabola. It is shown below
Looking at the graph, the branches open up and down. Thus, the correct option is
c. The branches of the hyperbola open up and down.
For j(x) = 3x − 1, find j of the quantity x plus h end quantity minus j of x all over h period a 3 to the power of the quantity x minus 1 end quantity times the quantity 3 to the power of h end quantity all over h b 3 to the power of the quantity x minus 1 end quantity times the quantity 3 to the power of h minus 1 end quantity all over h c 3 to the power of the quantity x minus 1 end quantity times the quantity 3 to the power of h plus 1 end quantity all over h d the quantity x minus 1 end quantity times the quantity 3 to the power of h plus 1 end quantity all over h
The resulting value of the function [j(x+h)-j(x)/h] is 3⁽ˣ⁻¹⁾ ([tex]3^{h}[/tex]-1)/h
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = aˣ in mathematics, where x is the independent variable
Given the function expressed as;
j(x) = 3⁽ˣ⁻¹⁾
Required value of the function [j(x+h)-j(x)]/h
We have to determine the function j(x+h) and j(x)
j(x+h) = [tex]3^{(x+h) -1}[/tex]
Substitute the values,
[j(x+h)-j(x)]/h = [ [tex]3^{(x+h) -1}[/tex] - 3⁽ˣ⁻¹⁾ ]/h
⇒ [ [tex]3^{(x-1) +h}[/tex] - 3⁽ˣ⁻¹⁾ ]/h
⇒ [ [tex]3^{(x-1)} \times3^{h}[/tex] - 3⁽ˣ⁻¹⁾ ]/h
⇒ 3⁽ˣ⁻¹⁾ ([tex]3^{h}[/tex]-1)/h
Hence, the equivalent value of the function is 3⁽ˣ⁻¹⁾ ([tex]3^{h}[/tex]-1)/h
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Given that f(x) = x sqaured - 10x + 16 and g(x) = x - 8, find f (x) · g(x) andexpress the result in standard form.
Given the functions
[tex]f(x)=x^2-10x+16[/tex][tex]g(x)=x-8[/tex]You have to calculate
[tex]f(x)\cdot g(x)[/tex][tex](x^2-10x+16)\cdot(x-8)[/tex]To solve this you have to apply the distributive property of multiplications, that is, you have to multiply each term of the first parenthesis with each term of the second parenthesis.
As follows:
[tex]\begin{gathered} (x^2-10x+16)\cdot(x-8) \\ (x^2\cdot x)+(x^2)\cdot(-8)+(-10x\cdot x)+(-10x)\cdot(-8)+(16\cdot x)+(16\cdot(-8)) \\ x^3-8x^2-10x^2+80x+16x-128 \end{gathered}[/tex]Now simplify the like terms
[tex]\begin{gathered} x^3+(-8x^2-10x^2)+(80x+16x)-128 \\ x^3-18x^2+96x-128 \end{gathered}[/tex]The result in standard form is
[tex]f(x)\cdot g(x)=x^3-18x^2+96x-128[/tex]answers pleaseeee
im struggling
Answer:
y=3/4x-2
Step-by-step explanation:
slope=3/4x
y-intercept=-2
As part of a charity drive, 50 fourth grade students each donated an equal number of dimes and 30 third grade students each donated the same number of nickels. Let d represent the number of dimes and n represent the number of nickels. Determine which of the expressions shows the total amount (in cents) donated by the 3rd and 4th grade students. A.) 10(50d)+5(30n)B.) 80cC.) 10d+5nD.) 50d+30n
The average amount of time spent grocery shopping is 45 minutes with a standard deviation of 12 minutes. Using the Empirical Rule, what percent should spend less than 33 minutes?
You have:
mean = 45
standard deviation = 12
Use the following formula:
Find the standard form for the equation of a circle ( x − h )^2 + ( y − k )^2 = r^2 with a diameter that has endpoints ( − 4 , − 8 ) and ( 6 , − 4 ) .h=k=r=
Answer:
[tex](x-1)^2+(y+6)^2=29[/tex][tex]\begin{gathered} h=1 \\ k=-6 \\ r=\sqrt{29} \end{gathered}[/tex]Explanation:
Given:
Endpoints of the diameter of a circle as (-4, -8) and (6, -4)
To find:
Equation of a circle in standard form
The equation of a circle in standard form is generally given as;
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h, k) is the coordinate of the center of the circle and r is the radius of the circle.
We'll go ahead and determine the coordinates of the midpoint of the endpoints of the diameter which will be the coordinates of the center of the circle as seen below wi;
[tex]h=\frac{x_1+x_2}{2}=\frac{-4+6}{2}=\frac{2}{2}=1[/tex][tex]k=\frac{-8+(-4)}{2}=\frac{-12}{2}=-6[/tex]So the center of the circle has coordinates (1, -6)
Since h = 1, and k = -6 and we have that x1 = -4 and y1 = -8, we can go ahead and solve for r as seen below;
[tex]\begin{gathered} (-4-1)^2+(-8-(-6))^2=r^2 \\ (-5)^2+(-2)^2=r^2 \\ 25+4=r^2 \\ 29=r^2 \\ \therefore r=\sqrt{29} \end{gathered}[/tex]We can now write the equation of the circle in standard form as;
[tex]\begin{gathered} (x-1)^2+(y-(-6))^2=29 \\ (x-1)^2+(y+6))^2=29 \end{gathered}[/tex]Last year, 49% of business owners gave a holiday gift to their employees. A survey of business owners conducted this year indicates that 40% planned to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 85 business owners.
b. Suppose the business owners in the sample do as they plan. Conduct a hypothesis test that can be used to determine whether the proportion of business owners providing holiday gifts had decreased from last year.
State the hypotheses.
Compute the test statistic and p-value.
c. Using a 0.01 level of significance, would you conclude that the proportion of business owners providing gifts decreased?
Using the z-distribution, it is found that:
b)
The hypotheses are: null [tex]H_0: p \geq 0.49[/tex], alternative [tex]H_1: p > 0.49[/tex]The test statistic is of z = -1.69.The p-value is of 0.0455.c) There is not enough evidence to conclude that the proportion of business owners providing gifts decreased using a 0.01 significance level.
What are the hypotheses tested?At the null hypotheses, it is tested if there is no evidence that the proportion decreased from 49%, that is:
[tex]H_0: p \geq 0.49[/tex]
At the alternative hypotheses, it is tested if there is evidence that the proportion decreased from 49%, that is:
[tex]H_1: p > 0.49[/tex]
What is the value of the test statistic?The test statistic is given according to the following rule:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which the parameters are described as follows:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.Considering that 40% of the sample of 85 planned to provide a gift, and the proportion tested is of 49%, the values of the parameters are given as follows:
[tex]\overline{p} = 0.4, p = 0.49, n = 85[/tex]
Hence the test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.4 - 0.49}{\sqrt{\frac{0.4(0.6)}{85}}}[/tex]
z = -1.69.
What is the p-value of the test and what is the conclusion?Considering a left-tailed test, as we are testing if the proportion is less than a value, with z = -1.69, using a z-distribution calculator, the p-value is of 0.0455.
Since the p-value of the test is greater than 0.01, there is not enough evidence to conclude that the proportion of business owners providing gifts decreased using a 0.01 significance level.
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Does the graph represent a function? 4 5 6 7 -3+ no O yes
To prove:
The given graph is a function.
The given graph is a function if and only if no x value has more than one value of y, or we can say that a graph is a function iff no vertical line intersects the graph in more than one point.
Thus, by the given graph it is clear that for x = 7 their are two values for y that is y = -6 , -7
So, the given graph is not a function
6.4 The ratio of length and breadth of a rectagular field is 4:3. If perimeter of the field is 700m, find (i) length and breadth of the field (ii) area of the field.
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Question: how do I figure out if a number is rational or irrational
A number is said to be rational if it can be written or transformed into the p/q form, where p and q are integers and q is a non-zero number; if it cannot be written in this form, it is said to be irrational.
Any number that can be written or stated in the p/q form, where p and q are integers and q is a non-zero number, is said to be rational.
A number that is irrational, on the other hand, cannot be stated in p/q form, and its decimal expansion is non-repeating and non-terminating.
Example: √2, √7, √11
Hence we get the required answer.
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A trendline is given to depict the enrollment at a local college where x is the year and y represents enrollment. y=178.09x−353194Use the trendline to estimate the enrollment for 2009. Round to the nearest whole number.
To determine the enrollment in 2009 we need to plug x=2009 in the equation given to determine the value of y:
[tex]\begin{gathered} y=178.09(2009)-353194 \\ y=357782.81-353194 \\ y=4588.81 \end{gathered}[/tex]Therefore, in the year 2009, there were 4589 students enrolled
Select the correct answer from each drop-down menu.
A triangle FGH, right angle at H is shown. Base GH has length labeled 3 units. Height FH has length labeled 4 units, and hypotenuse FG has length 5 units.
Use the figure to complete the following statements.
sin(F) =
cos(F) =
sin(G) =
cos(G) =
The value of given expressions will be sin(F) = 3/5, cos(F) = 4/5, sin(G) = 4/5 and cos(G) = 3/5.
A triangle may be defined as a closed figure having three sides and three angle, the sum of which is equal to 180°. A right-angled triangle is the one which has one angle as 90°. We consider a right-angled triangle FGH which is right-angled at H. The sine of any angle is given by the division of Perpendicular to its Hypotenuse. The cosine of any angle is given by the division of Base to its Hypotenuse. Now, we need to find
sin(F) = Perpendicular/Hypotenuse, for angle at F perpendicular will be GH and Hypotenuse will be FG. So, sin(F) = 3/5
cos(F) = Base/Hypotenuse, for angle at F Base will be FH and Hypotenuse will be FG. So, cos(F) = 4/5
sin(G) = Perpendicular/Hypotenuse, for angle at G perpendicular will be FH and Hypotenuse will be FG. So, sin(F) = 4/5
cos(G) = Base/Hypotenuse, for angle at G Base will be GH and Hypotenuse will be FG. So, cos(F) = 3/5
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