Their total dinner bill including sales tax rate is 8% and 18% tip will be $156.43 by using the concept of percentages and addition.
What is percent?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement.
What is sales tax?A sales tax is a fee that is paid to the government when certain goods and services are sold. Typically, laws permit the seller to charge the customer the tax at the time of purchase. Use taxes are typically used to describe taxes on goods and services that consumers pay directly to a governing body.
Here,
$122.75 dollars to be paid without tax and tip,
=8% of $122.75
=$9.82.
=122.75+9.82
=$132.57
=18% of 132.57
=$23.86
=132.57+23.86
=$156.43
Using the addition and percentages concepts, they can calculate their total dinner bill, which is $156.43 after adding the 8% sales tax and 18% gratuity.
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how do you work the problem 3k+16=5k?
We have the following:
[tex]3k+16=5k[/tex]solving for k
[tex]\begin{gathered} 5k-3k=16 \\ k=\frac{16}{2} \\ k=8 \end{gathered}[/tex]The value of k is 8
Which choice is equivalent to the quotient shown here for acceptablevalues of x?25(x - 1) = 5(x - 1)?A.5(x - 1)B. 125(x - 1)C. V25(x - 1) -5(x - 1)?D. V5(x - 1)SUBMIT
Given the expression:
[tex]\sqrt[]{28(x-1)}\div\sqrt[]{8x^2}[/tex][tex]\frac{\sqrt[]{28(x-1)}}{\sqrt[]{8x^2}}[/tex]Let's determine the inequality that represents all the values of x.
Here, we are to find the domain.
Let's solve for x.
Set the radicand in the numerator and denominator to be greater or equal to zero.
We have:
[tex]\frac{28(x-1)\ge0}{8x^2\ge0}[/tex]For the numerator, we have:
[tex]\begin{gathered} 28(x-1)\ge0 \\ \text{Divide both sides by 28:} \\ \frac{28(x-1)}{28}\ge\frac{0}{28} \\ \\ x-1\ge0 \\ \text{Add 1 to both sides:} \\ x-1+1\ge0+1 \\ x\ge1 \end{gathered}[/tex]For the denominator, we have:
[tex]\begin{gathered} 8x\ge0 \\ x\ge\frac{0}{8} \\ x\ge0 \end{gathered}[/tex]Therefore, the possible x-values for which the quotient is defined is all positive integers greater or equal to 1.
Thus, we have:
[tex]x\ge1[/tex]ANSWER:
[tex]C.x\ge1[/tex]Timothy ran a lemonade stand for 6 days. on the first day he made $5. Each day after that he made $2 more than the previous day. How much money did Marcus make, , after the 6 days?A) $60B) $15C) $12D) $30
Step `1;
Total number of days = 6
Step 2:
First day = $5
Second day = $5 + $2 = $7
Third day = $7 + $2 = $9
Fourth day + $9 + $2 = $11
Fifth day = $11 + $2 = $13
Sixth day = $13 + $2 = $15
Step 3:
Marcus made = $5 + $7 + $9 + $11 + $13 + $15
= $60
Second method
Use the sum of nth terms of arithmetic progression.
first term a = $5
Common difference = 2
n = 6
[tex]\begin{gathered} S\text{um of the 6 terms = }\frac{n}{2}(\text{ 2a + (n-1)d)} \\ =\text{ }\frac{6}{2}\text{ ( 2}\times5\text{ + (6 -1) }\times\text{ 2)} \\ =\text{ 3( 10 + 5}\times2\text{ )} \\ =\text{ 3( 10 + 10 )} \\ =\text{ 3 }\times\text{ 20} \\ =\text{ \$60} \end{gathered}[/tex]Final answer
Marcus made = $60 Option A
The volume, V, of a cube with edge length s cm is given by the equation V=s3.Is the volume of a cube with edge length s=3 greater or less than the volume of a sphere with radius 3?If a sphere has the same volume as a cube with edge length 5, estimate the radius of the sphere?Compare the outputs of the two volume functions when the inputs are 2?
We have that the volume of sphere is
[tex]\begin{gathered} V_s=\frac{4}{3}\pi\cdot r^3 \\ \end{gathered}[/tex]and the volume of a cube is
[tex]V_c=s^3[/tex]so if s=r=3. The volume of the sphere is greater.
If they have the same volume, we get that
[tex]\begin{gathered} \frac{4}{3}\pi\cdot r^3=125\rightarrow \\ r^3=\frac{3}{4\cdot\pi}\cdot125\approx29.84\approx30 \\ r=\sqrt[3]{30}\approx3.10 \end{gathered}[/tex]when s=r=2 we have that
[tex]\begin{gathered} V_s=\frac{4}{3}\pi\cdot8=\frac{32}{3}\pi \\ V_c=8 \end{gathered}[/tex]so the volume of the sphere is greater
Solve the equation for solutions in the interval [0°, 360°). Round to the nearest degree.
We will have the following:
[tex]\sin (2\theta)=-\frac{1}{2}\Rightarrow2\theta=2\pi n_1+\frac{7\pi}{6}[/tex][tex]\Rightarrow\theta=\pi n_1+\frac{7\pi}{12}[/tex]Now, we will solve for the following:
[tex]\Rightarrow\pi n_1+\frac{7\pi}{12}\le2\pi\Rightarrow\pi n_1\le\frac{17\pi}{12}[/tex][tex]\Rightarrow n_1\le\frac{17}{12}[/tex]This value in degrees is:
[tex]\frac{17}{12}\text{radians}=81.169\text{degrees}[/tex]So, the solution is located in the interval:
[tex]\lbrack0,81\rbrack[/tex]please help me ASAP!!!
substitute x = 5 in the above function
[tex]f(5)=\sqrt[]{2(5)^2-3(5)+1}[/tex][tex]=\sqrt[]{2(25)-15+1}[/tex][tex]=\sqrt[]{50-15+1}[/tex][tex]=\sqrt[]{36}=\text{ 6}[/tex]f(5) = 6
A function can have miltiple x intercepts A function can have multiple y intercepts To find the y intercept you must find the zeros The notation of the Zeros of the function is f(0)
The statements which are true regarding a function among the given answer choices are;
A function can have multiple x-intercepts.The notation of the zeroes of the function is; f(0).Which statements among the answer choices are true for functions?It follows from the complete task content that the statements which are true be identified from the given answer choices.
From the definition of a function; A function is a relation which assigns to every input value one single output value. Hence, it follows that no single input value has more than one output value assigned to it.
It therefore follows from the definition above that; a function can have multiple x-intercepts, but can only have one y-intercept.
Also, the zeroes of the function are represented by the function instance; f(0) at which point the input, x = 0.
Remarks;
The complete task content is such that; The statements which are correct about functions are to.be identified.
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At a point on the ground 35 ft from base of a tree, the distance to the top of the tree is 1 ft more than 3 times the height of the tree. Find the height of the tree. The height of the tree is ___. (ft^3, ft^2, or ft)(Simply your answer. Round to the nearest foot as needed)
At a point on the ground 35 ft from the base of a tree, the distance to the top of the tree is 1 ft more than 3 times the height of the tree. Find the height of the tree
see the attached figure to better understand the problem
Applying the Pythagorean Theorem
(3h+1)^2=h^2+35^2
9h^2+6h+1=h^2+1,225
solve for h
9h^2-h^2+6h+1-1,225=0
8h^2+6h-1,224=0
Solve the quadratic equation
Using a graphing tool
the solution is
h=12 ftPlease help me I need the answer asap.
Therefore the right answer is option D = 1. The values of the variables will be obtained when the system of linear equations is solved; this is referred to as the solution of a linear equation.
What are linear equations?An equation with the form Ax+By=C is referred to as a linear equation. It consists of two variables combined with a constant value that exists in each of them. The values of the variables will be obtained when the system of linear equations is solved; this is referred to as the solution of a linear equation. If an equation has the formula y=mx+b, with m representing the slope and b the y-intercept, it is said to be linear.A two-variable linear equation can be thought of as a linear relationship between x and y, or two variables whose values rely on each other (often y and x) (usually x).Hence,
The correct Option is D = 1
Given
[tex]x^2+x-1\\[/tex] = 0
[tex]\frac{1-x}{2x^2} +\frac{ x^2}{2x-2}[/tex] = ?
From [tex]x^2+x-1\\[/tex] = 0
[tex]x^2 = 1-x[/tex]
Therefore,
[tex]\frac{1-x}{2x^2} +\frac{ x^2}{2x-2}[/tex] = [tex]\frac{x^2}{2x^2} + \frac{x^2}{2(x-1)}[/tex]
[tex]\frac{1}{2} + \frac{x^2}{2(x-1)}[/tex]
[tex]\frac{1}{2} + \frac{1}{2}[/tex]
= 1
Therefore the right answer is option D = 1
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Through (1,-2) parallel to y=-2x+5
Answer:
Step-by-step explanation:The line parallel to y = -2x + 5 that passes through the point(1,1)
Has the same slope, m but a different y intercept (0,b)
So lets start by using the given point (1, 1) and the slope intercept form of the line to calculate b
y = mx + b
m = -2
1 = -2(1) + b
1 = -2 + b
Add 2 to both sides of the equation to solve for b
1 + 2 = b
3 = b
The line is
y = -2x + 3
Section 11 - Topic 5Probability and Independence• In your own words, describe what the word independeyou.Now describe dependent..
In probability , there are two events independent events and dependent events.
Independent Events :
Two events A and B are said to be independent if the fact that one event has occurred does not affect the probability that the other event will occur.
Example
. Choosing a marble from a jar AND landing on heads after tossing a coin.
Dependent Events :
If whether or not one event occurs does affect the probability that the other event will occur, then the two events are said to be dependent.
Example
Buying ten lottery tickets and winning the lottery.
50 Points
A rectangle has sides measuring (2x + 5) units and (3x + 7) units.
Part A: What is the expression that represents the area of the rectangle? Show your work.
Part B: What are the degree and classification of the expression obtained in Part A?
Part C: How does Part A demonstrate the closure property for the multiplication of polynomials?
The expression that represents the area of the rectangle is 6x²+29x+35.
Given that, a rectangle has sides measuring (2x + 5) units and (3x + 7) units.
What is the area of a rectangle?The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.
Part A:
Now, area = (2x+5)(3x+7)
= 2x(3x+7)+5(3x+7)
= 6x²+14x+15x+35
= 6x²+29x+35
So, the area of a rectangle is 6x²+29x+35
Part B:
A polynomial's degree is the highest or the greatest power of a variable in a polynomial equation.
Here, the degree of the expression 6x²+29x+35 is 2.
Part C:
Closure property of multiplication states that if any two real numbers a and b are multiplied, the product will be a real number as well.
Here, we obtained product of two binomials is trinomial
Therefore, the expression that represents the area of the rectangle is 6x²+29x+35.
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The probability that John recieves junk mail is 11 percent. If he receives 94 pieces of mail in a week, about how many of them can he expect to be junk mail.a. 5 b. 15 c. 10 d.20
10 (option C)
Explanation:The probability of getting a junk mail = 11%
Number of mails received = 94
Amount that will be junk mail = The probability of getting a junk mail × Number of mails received
Amount that will be junk mail = 11% × 94
= 0.11 × 94 = 10.34
Since we can't have decimal number of mails, we would approximate to the nearest whole number
10.34 to the nearest whole number is 10
Hence, 10 junk mails are expected
Find the 1st term, last term and the sum for the finite arithmetic series.
Answer:
Given that,
[tex]\sum ^{30}_{n\mathop=2}(3n-1)[/tex]Simplifying we get,
[tex]\sum ^{30}_{n\mathop{=}2}(3n-1)=\sum ^{30}_{n\mathop{=}2}3n+\sum ^{30}_{n\mathop{=}2}1[/tex][tex]=3\sum ^{30}_{n\mathop{=}2}n+\sum ^{30}_{n\mathop{=}2}1[/tex]we have that,
[tex]\sum ^n_{n\mathop=1}1=n[/tex]If n is from 2 to n we get,
[tex]\sum ^n_{n\mathop{=}2}1=n-1[/tex]Also,
[tex]\sum ^k_{n\mathop=1}n=\frac{k(k+1)}{2}[/tex]If n is from 2 to n we get,
[tex]\sum ^k_{n\mathop=2}n=\frac{k(k+1)}{2}-1[/tex]Using this and substituting in the required expression we get,
[tex]=3\lbrack\frac{30\times31}{2}-1\rbrack+30-1[/tex][tex]=3(464)+29[/tex][tex]=1421[/tex]Answer is: 1421
The graph of f(a) = > has been transformed to create the graph of g(s) =
EXPLANATION
The graph of the parent function: f(x) = 1/x has the following form:
Translating the function two units to the left, give us the Image function:
This function is obtained by adding two units to the denominator.
In conclusion, the solution is -2
Please help. Find value of p
The value of p from the given diagram using the similarity theorem is -13.
Similarity theorem of triangleYou can use three triangle-specific theorems to quickly distinguish similar triangles. These three theorems, known as Angle - Angle (AA), Side - Angle - Side (SAS), and Side - Side - Side (SSS), are proof methods for determining similarity in triangles.
In order to determine the value of p from the given expression, we will use the expression below;
2p-5+3p/14+26 = 3p/26
5p+5/40 = 3p/26
Cross multiply
40 * 3p = 26(5p +5)
120p = 130p + 130
120-130p = 130
-10p = 130
Divide both sides by -10 to have:
-10p/-10 = 130/-10
p = -13
This gives the required value of p from the figure.
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The table gives a set of outcomes and their probabilities. Let A be the event the outcome is divisible by 3". Find P(A). 12 Outcome Probability Tim elaps 1 0.14 PAUS 2 0.02 3 0.19 Smart out of 4 0.01 5 0.04 7 6 0.17 7 0.15 8 0.28
Here, we want to get the probability that a selected outcome is divisible by 3
What we have to do here is ti select numbers that are multiples of 3 and add their probabilities
From the given table, the outcomes that are multiples of 3 are;
3 and 6 only
So, we proceed to add the probabilities of these outcomes
Mathematically, we have this as;
[tex]P(A)\text{ = 0.19 + 0.17 = 0.36}[/tex]Find the interval in the line below. Use correct symbols to indicate in interval notation. If number is no an integer then round to the nearest hundredth.
we can see the interval is between -2 and 1. but the -2 isn't included (you can notice by the white circle) and the 1 is included, so in interval notation you get:
(-2,1]
Anna's room is a rectangle. Its length is 15 feet and its width is 4 yards. What is the perimeter of the room?
Answer:
38
Step-by-step explanation:
Perimeter is basically each side added together. 15 + 15 + 4 + 4 is 38. Therefore, it's 38.
Lesson 6.07: In a random sample of 74 homeowners in a city, 22 homeowners said they wouldsupport a ban on nonnatural lawn fertilizers to protect fish in the local waterways. The samplingmethod had a margin of error of +3.1%. SHOW ALL WORK!A) Find the point estimate.B) Find the lower and upper limits and state the interval.
Confidence interval is written in the form,
(point estimate +/- margin of error)
The given scenario involves population proportion
The formula for the point estimate is
p' = x/n
where
p' = estimated proportion of success. p' is a point estimate for p which is the true proportion
x represents the number of success
n represents the number of samples
From the information given,
n = 74
x = 22
p' = 22/74 = 0.297
The formula for finding margin of error is expressed as
[tex]\begin{gathered} \text{margin of error = z}_{\frac{\alpha}{2}}(\sqrt[]{\frac{p^{\prime}q^{\prime}}{n}} \\ q^{\prime}\text{ = 1 - p'} \\ q^{\prime}\text{ = 1 - 0.297 = 0.703} \end{gathered}[/tex]A) The point estimate is 0.297
B) margin of error = +/-3.1% = 3.1/100 = +/- 0.031
Thus,
the lower limit would be 0.297 - 0.031 = 0.266
Expressing in percentage, it is 0.266 x 100 = 26.6%
the upper limit would be 0.297 + 0.031 = 0.328
Expressing in percentage, it is 0.328 x 100 = 32.8%
Thus, the confidence interval is between 26.6% and 32.8%
Ali borrowed Php22,000 for 3months at the discount rate of 5 ¼ % from a bank. Find the (a) bank’s discount and (b) proceeds.
If an M amount is borrowed for a time t at a discount rate of r per year, then the discount D is calculated as
[tex]\begin{gathered} D=M\cdot r\cdot t \\ \\ \text{where} \\ r\text{ is expressed in decimals} \end{gathered}[/tex][tex]\begin{gathered} \text{Given} \\ M=22000 \\ r=5\frac{1}{4}\%\rightarrow5.25\%\rightarrow0.0525 \\ t=\mleft(\frac{3}{12}\mright)\text{or }0.25\text{ (3 months out of 1 year or 12 months} \end{gathered}[/tex]Substitute the following values to get the bank's discount.
[tex]\begin{gathered} D=Mrt \\ D=(22000)(0.0525)(\frac{3}{12}) \\ D=288.75 \end{gathered}[/tex]Therefore, the bank's discount is Php 288.75.
To calculate for proceeds, subtract the amount borrowed by the bank's discount.
[tex]\begin{gathered} P=M-D \\ P=22000-288.75 \\ P=21711.25 \end{gathered}[/tex]The proceeds given to Ali is Php 21,711.25.
Determine a third pair of congruent parts to establish congruence between the triangles. Give the congruence postulate involved
In this problem, we have that
mYO ≅ XO
The third pair of congruent parts is
m by vertical angles
therefore
triangle YOT ≅ triangle XOB ----> by ASA congruence postulate
Identify the range of the function shown in the graph. 10 8 4 -10-8-4-2 8 10 O A. -2< y < 2 O B. {-2, 2) O C. y is all real numbers OD. Y > 0
Answer
Option B is correct.
Range: y is all real numbers.
Explanation
The range of a function refers to the region of values where the function can exist. It refers to the values that the dependent variable [y or f(x)] can take on. It is the region around the y-axis that the graph of the function spans.
For this question, we can see that the graph spans over the entire y-axis.
Hence, the range of this function shown in the graph is all real number.
Hope this Helps!!!
11 gallons Blue Car 2 of gas 35.4 miles A gallons 27 miles Silver Car 5 14. You are running a fuel economy study. You want to find out which car can travel a greater distance on 1'gallon of gas. a. What is the gas mileage, in miles per gallon, for the blue car? b. What is the gas mileage, in miles per gallon, for the silver car? c. Which car could travel the greater distance on 1 gallon of gas?
Answer:
a) 23.67 miles per gallon
b) 34 miles per gallon
c) The silver car could travel a greater distance.
Step-by-step explanation:
a)
Conversion of the mixed numbers to fractions:
[tex]1\frac{1}{2}=\frac{1\ast2+1}{2}=\frac{2+1}{2}=\frac{3}{2}[/tex][tex]35\frac{1}{2}=\frac{35\ast2+1}{2}=\frac{70+1}{2}=\frac{71}{2}[/tex]Gas mileage:
3/2 gallons - 71/2 miles
1 gallons - x miles
Simplifying the top line by 2.
3 gallons - 71 miles
1 gallon - x miles
3x = 71
x = 71/3
x = 23.67 miles per gallon
b)
Conversion of the mixed number to fraction:
[tex]27\frac{1}{5}=\frac{27\ast5+1}{5}=\frac{135+1}{5}=\frac{136}{5}[/tex]Mileage:
4/5 gallons - 136/5 miles
1 gallon - x miles
Simplifying the top line by 5
4 gallons - 136 miles
1 gallon - x miles
4x = 136
x = 136/4
x = 34 miles per gallon
c)
Blue car: 23.67 miles per gallon
Silver car: 34 miles per gallon
Silver car could travel a greater distance.
All changes saved16. Suppose you invest $7500 at an annual Interest rate of 4.2% compounded continuously. How much will you have in the account after 2 years? Round the solution to the nearest dollar.$8158$17,372$17,373$8157
We have to use the continuous compound interest formula
[tex]A=P\cdot e^{rt}[/tex]Where P = 7500, r = 0.042, t = 2. Let's replace and solve
[tex]\begin{gathered} A=7500\cdot e^{0.042\cdot2} \\ A\approx8,157 \end{gathered}[/tex]Hence, the answer is $8,157.Find conditions on k that will make the matrix A invertible. To enter your answer, first select 'always', 'never', or whether k should be equal or not equal to specific values, then enter a value or a list of values separated by commas.
To be a matrix to be invertible the determinant of the matrix must be non zero thus for k ≠ 2 the matrix will be invertible.
What is a matrix?matrix, a collection of numbers lined up in rows and columns to produce a rectangular array.
In computer graphics, where they have been used to describe picture transformations and other alterations.
The elements of the matrix, also known as the entry, are the numerals.
A matrix will be invertible only and only if the determinant is non-zero.
Given the matrix A.
The determinant of A is that |A| will be,
|A| = -3(8 - 8) - 0(-k + 2) - 3(-4k + 8) ≠ 0
0 + 0 + -3(-4k + 8) |A| ≠ 0
-4k + 8 ≠ 0
-4k ≠ -8
k ≠ 2
Hence "To be a matrix to be invertible the determinant of the matrix must be non zero thus for k ≠ 2 the matrix will be invertible".
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l show how the distributive property can make the arithmetic simpler in the following problems5(108)
Firstly Example of Distributive property can be shown below.
GIiven: 6(9 - 4)
6 x 9 - 6 x 4
54 - 24 = 30
a) 3(50.15)
3(50 + 0.15)
3x50 + 3 x0.15
150 + 0.45 = 150.45
(b) 5(108)
5(100 + 8)
5x100 + 5x8
500 + 40 = 540
find the intercepts and graph the equation by plotting points. 13^2 + 4y = 52
ANSWER
[tex]y-intercept:(0,-\frac{117}{4})[/tex]Graph:
EXPLANATION
Given:
[tex]13^2+4y=52[/tex]Desired Results:
Intercepts and graph the equation
Solve for y
[tex][/tex]9. A researcher gathered data on hours of video games played by school-aged children and young adults. She collected the following data:601241215171711409914110131015163915121698131016651717129(a) Complete the frequency distribution for the data.HoursFrequencyRelative Frequency0-23-56-89-1112-1415-17(b) Which of the following is the correct histogram for this data?246810Hours0369121518Frequency[Graphs generated by this script: setBorder(54,40,20,15); initPicture(0,18,0,10);axes(34,2,1,null,2); fill="blue"; textabs([165,0],"Hours","above");line([0,-0.2],[0,0.2]); text([0,0],"0","below");line([3,-0.2],[3,0.2]); text([3,0],"3","below");line([6,-0.2],[6,0.2]); text([6,0],"6","below");line([9,-0.2],[9,0.2]); text([9,0],"9","below");line([12,-0.2],[12,0.2]); text([12,0],"12","below");line([15,-0.2],[15,0.2]); text([15,0],"15","below");line([18,-0.2],[18,0.2]); text([18,0],"18","below");textabs([0,115],"Frequency","right",90);rect([0,0],[3,6]);rect([3,0],[6,4]);rect([6,0],[9,5]);rect([9,0],[12,7]);rect([12,0],[15,6]);rect([15,0],[18,10]);]246810121416Hours061218Frequency[Graphs generated by this script: setBorder(54,40,20,15); initPicture(0,18,0,16);axes(34,2,1,null,2); fill="blue"; textabs([165,0],"Hours","above");line([0,-0.32],[0,0.32]); text([0,0],"0","below");line([6,-0.32],[6,0.32]); text([6,0],"6","below");line([12,-0.32],[12,0.32]); text([12,0],"12","below");line([18,-0.32],[18,0.32]); text([18,0],"18","below");textabs([0,115],"Frequency","right",90);rect([0,0],[6,10]);rect([6,0],[12,12]);rect([12,0],[18,16]);]2468101214Hours061218Frequency[Graphs generated by this script: setBorder(54,40,20,15); initPicture(0,18,0,14);axes(34,2,1,null,2); fill="blue"; textabs([165,0],"Hours","above");line([0,-0.28],[0,0.28]); text([0,0],"0","below");line([6,-0.28],[6,0.28]); text([6,0],"6","below");line([12,-0.28],[12,0.28]); text([12,0],"12","below");line([18,-0.28],[18,0.28]); text([18,0],"18","below");textabs([0,115],"Frequency","right",90);rect([0,0],[6,12]);rect([6,0],[12,14]);rect([12,0],[18,12]);]2468Hours0369121518
Remember that the frequency refers to the number of times a data shows up. In this case, the frequency is the number of data that falls into each interval.la
To find the relative frequency is calculated by dividing each frequency by 38 (the total number of data).
[tex]\begin{gathered} \frac{6}{38}=0.1579 \\ \frac{4}{38}=0.1053 \\ \frac{4}{38}=0.1053 \\ \frac{8}{38}=0.2105 \\ \frac{7}{38}=0.1842 \\ \frac{9}{38}=0.2368 \end{gathered}[/tex]Let's include the relative frequencies in the table.
On the other hand, the correct histogram has to show the frequencies in the same order. The following histogram shows the correct frequency distribution.
If sin A = 3/5 and cos B = 20/29 and angles A and B are in Quadrant 1, find the valueof tan(A + B).
Our approach is to use SOHCAHTOA to derive values for sine and cosines of both A and B.
[tex]\begin{gathered} \sin A=\frac{3}{5},\text{ cosA=}\frac{\sqrt[]{5^2-3^2}}{5}=\frac{4}{5} \\ \cos B=\frac{20}{29},\text{ sinB=}\frac{\sqrt[]{29^2-20^2}}{29}=\frac{21}{29} \end{gathered}[/tex][tex]\begin{gathered} \tan (A+B)=\frac{\tan A+\tan B}{1-\text{tanAtanB}}\text{ WHERE} \\ \tan A=\frac{\sin A}{\cos A},\tan B=\frac{\sin B}{\cos B} \end{gathered}[/tex][tex]\begin{gathered} \tan (A+B)=\frac{\frac{\frac{3}{5}}{\frac{4}{5}}+\frac{\frac{21}{29}}{\frac{20}{29}}}{1-\frac{\frac{3}{5}}{\frac{4}{5}}\times\frac{\frac{21}{29}}{\frac{20}{29}}}=\frac{\frac{3}{4}+\frac{21}{20}}{1-\frac{3}{4}\times\frac{21}{20}}=\frac{\frac{9}{5}}{1-\frac{63}{80}}=\frac{\frac{9}{5}}{\frac{17}{80}} \\ \tan (A+B)=8.47 \end{gathered}[/tex]tan (A+B) = 8.47