Answers
The angles in the picture are calculated and their values are as follows:
< ABC = 37.63 degrees < BCA = 72.55 degrees< CAB = 69.82 degreesHow to solve for the angles <ABC, <BCA and < CABGiven data
a = 3
b = 3.2
c = 5
using cosine rule for <ABC
b^2 = a^2 + c^2 - 2ac cos B
2ac cos B = a^2 + c^2 - b^2
cos B = (a^2 + c^2 - b^2) / 2ac
cos B = (3^2 + 5^2 - 3.2^2) / 2*3*5
cos B = 23.76/30
B = arc cos (0.792)
B = 37.63 degrees
using sine rule for <BCA
sine B / b = sin C / c
sin 37.63/ 3.2 = sim C / 5
C = arc sin (0.954)
C = 72.55
solving for <CAB
< CAB = 180 - 72.55 - 37.63
< CAB = 69.82 degrees
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Related Questions
You are writing up plans for a table from a 4 foot by 8 foot rectangular sheet of plywood. The table top will be square and the top face must be sanded. Which of the following is closest to the side length in feet of largest square you can cut from the sheet of plywood
Answers
4 foot.
Given that
a rectangular sheet of plywood with dimension 4 foot × 8 foot
Area of rectangle = length × breadth
length of the rectangle = 4 foot
breadth = 8 foot.
A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.
Since we have to cut the plywood.
And, form a square from it.
we know that all sides of square are same.
The largest square you can cut from a rectangle will have a side length equal to the smallest dimension of the rectangle.
Therefore both are squares of sides 4 foot.
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answer quickly but only if you are sure
or else you are getting reported :D
Answers
Answer:
0.0092
Step-by-step explanation:
Rewrite the denominator out of its scientific notation. The numerator will always be 1 when you are working with whole numbers turning into fractions.
[tex]=9.2\cdot \frac{1}{10^3}\\=\frac{1\cdot \:9.2}{10^3}\\=\frac{9.2}{10^3}\\=\frac{9.2}{1000}\\=0.0092[/tex]
Is the situation an example of a continuous or discrete relation?
a. Bag of Apples
b. Distance from here to the moon
c. Area of a circle
d. Number of telephones calls made each day
e. The height of a ball as it is thrown into the air.
f. The balance in an account over a week.
Answers
The variables are:
a) discrete.
b) continuous.
c) continuous.
d) discrete.
e) continuous.
f) discrete.
Is the situation an example of a continuous or discrete relation?A continuos variable can take any value in a dense set, while a discrete variable can only take some selected values.
a) "Bag of apples"
Here the variable is the number of apples in the bag, we can only have whole numbers of apples, then this variable is discrete.
b) "Distance from here to the moon"
This is a distance, so the value is continuous.
c) "Area of a circle"
Exactly like in the case above, the area is continuous.
d) "Number of telephone calls made each day"
Like in the first example, here the variable can only take whole numbers thus, it is discrete.
e) "The height of a ball as it is thrown into the air."
Similar than case b, a height can take any value on a given range, thus, this is continuous.
f) "The balance in an account over a week."
Here the balance can only be a number followed by 2 digits after the decimal point, so from:
$23.50
We can only go up to:
$23.51
Then all the values in between are not allowed, this means that the variable is discrete.
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1 teaspoon of 3. Natasha made a sauce in cooking class. She used 2 cups of cream, salt, cup of chives and 1 cups of butter. Approximately how many cups of 4 A ingredients did she use?,
Answers
We need to know about mixed fraction to solve this problem. Natasha used approximately 4 cups of ingredients.
A mixed fraction is a fraction that is represented with its quotient and remainder. For example there is a mixed fraction [tex]5\frac{2}{3}[/tex] where 5 is the quotient and 2 is the remainder. To convert a mixed fraction to a simple fraction we multiply the denominator by the quotient and add the remainder to it to get the numerator of the simple fraction, the denominator remains the same. In this question we have to find the cups of ingredients that Natasha uses to make the sauce, we have to simplify all the mixed fractions and then add the fraction together to get the number of cups.
cups of cream=[tex]2\frac{3}{4}[/tex]=11/4
teaspoon of salt =1/2
cups of chive=3/8
cups pf butter=[tex]1\frac{1}{4}[/tex]=5/4
total cups of ingredients used= 11/4+3/8+5/4=(22+3+10)/8=35/8≈4 cups
Therefore we found out that the total number of cups natasha uses to make the sauce is 4.
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
Answers
Answer:
x² + (y – 3)² = 36
and
x²+ (y + 8)²= 36
Step-by-step explanation:
The equation of circle that has a center (a, b) is given by the formula
(x - a)² + (x - b)² = r²
where r is the radius of the circle
If the circle lies on the y axis, its x-coordinate must be 0.
The radius of the circle = 1/2 x diameter = 1/2 x 12 = 6 units
So the equation must be of the form
(x - 0)² + (y - b)² = 36
We can eliminate x² + (y – 5)² = 6
We can also eliminate (x + 6)² + y² = 144
That leaves us with the two possible equations
x² + (y – 3)² = 36 (center at 0, 3)
and
x²+ (y + 8)²= 36 (center at (0, -8) )
Simplify to a single power of 3:
Answers
Answer:
5
Step-by-step explanation:
[tex]\frac{3^8}{3^3}=3^{8-3}=3^{\boxed{5}}[/tex]
What are the zeros of the polynomial y = 3x(x - 2) (2x + 7)?
Answers
Answer:
the second answer option
Step-by-step explanation:
come on, that is really easy, now that the polynomial is already written that way.
when is the product of several factors 0 ?
when at least one of the factors is 0.
so let's go through, when are the factors 0 :
3 : can never be 0. 3 is 3.
x : yes, when x = 0.
(x - 2) : yes, when x = 2
(2x + 7) : ok, that requires a little bit of thinking
2x + 7 = 0
2x = -7
x = -7/2
and that's it.
at, the correct answer is
0, 2, -7/2
25 students in class A did a science exam. 30 students in class B did the same science exam.
The mean mark for the 25 students in class A is 67.8 The mean mark for all the 55 students is 72.0
Work out the mean mark for the students in class B.
Answers
Step-by-step explanation: All you have to do is 72.0 - 67.8
need help getting Mathematical Applications for the Management, Life, and Social Sciences, 12th Edition, Multi-Term i have a test due in a couple days and i don’t got money for a textbook
Answers
a) Basic mathematical expression
b)completely factorized polynomial
a) Algebra is a subject that is based on the principles of mathematics. Understanding basic mathematical expressions like addition, subtraction, multiplication, and division is essential to learning algebra and solving equations.
The basic mathematical expression = +, -, x, /
b)A polynomial can be called a fully modulus polynomial if I can't factor it anymore using any of the methods of parsing. This is a polynomial that has been completely factored. The power of it is mostly attributed to its effectiveness.
The completely factorized polynomial of the polynomial 2x² - x - 6 is (2x + 3)(x -2).
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Equations and Fun
Guided Practice
What is the domain of the set of ordered pairs {(-4, 0), (-2, 2), (0, 1), (2, 3), (3, 4)}?
A. {-4,-2,0, 2, 4}
B. (-4,-2, 0, 1, 2}
C. {0, 1, 2, 3, 4)
D.
(-4,-2,0, 2, 3}
Answers
Answer:
D
Step-by-step explanation:
Remember that domain is the set of all x-values. Therefore, looking at ONLY the first number for each of the listed ordered pairs, your answer D would be the only answer to include all the correct x-values.
Given the equation y = 3x + 7, which word(s) best describes the 3? Select all that apply.
*
slope
y-intercept
x-intercept
coefficient
constant
Answers
This equation is a linear equation in slope-intercept form. The 3 describes the slope of the line and is a coefficient for the variable x.
W X and ←→ Y Z intersect at point V. If m ∠ W V Y = ( 4 a + 58 ) ° and m ∠ X V Y = ( 2 b − 18 ) ° , find the values of a and b such that ←−→ W X is perpendicular to ←→ Y Z
Answers
The values of a and b are 8 and 54 respectively.
As WX and YZ are perpendicular to each other and they intersect at point V, so both ∠WVY and ∠XVY are 90°.
Given that,
∠WVY = (4a + 58)°
∠XVY = (2b - 18)°
Which means:
4a + 58 = 90
4a = 90-58
4a = 32
a = 32/4
a = 8
and 2b - 18 = 90
2b = 90+18
2b = 108
b = 108/2
b = 54°
hence we get the values of a and b as 8° and 54°
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Create a polynomial that has 4 terms, a degree of 6, a leading coefficie
and a constant term of -5.5.
Answers
-6 is the product of this equation,
therefore there are no constant term or leading coefficient.
enter image source here
The degree of a polynomial is the highest degree of its terms
The leading coefficient of a polynomial is the coefficient of the leading term
Any term that doesn't have a variable in it is called a "constant" term
types of polynomials depends on the degree of the polynomial
x5 = ax2+bx2+c =0
x4 = quadratic
x3 = cubic
x2 = quadratic
A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using the mathematical operations such as addition, subtraction, multiplication and division
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Tell which property is represented.
3(4 + 7) = (3 x 4) + (3 x 7)
Answers
the following data represents the price(R) of 50 items purchaced by a shopper. price(R) 0.00<20.00, 20.00<40.00, 40.00<60.00, 60.00<80.00, 80.00<100.00. frequently 6, 9, 18, 13, 4. Determine with calculations:
a) mean price
b)median price
c)modal price
d)standard deviation
Answers
The correct answer is The mean price is 50.
The median price is 41.111.
The modal price is 52.857.
The standard deviation price is 22.271.
The data table represents the prices (in R) of 50 items purchased by a shopper is,
Price Frequency
0<20 6
20<40 0
40<60 18
60<80 13
80<100 4
Explanation:
The mean of the data is the average of the given values.
The mean of the data is calculated as,
Price frequency (f) Mid point (xi) f.xi
0-20 6 10 60
20-40 9 30 270
40-60 18 50 900
60-80 13 70 910
80-100 4 90 360
Total 50 250 2500
Mean = ∑fx1/N
Mean = 2500/50
Mean = 50
Price frequency (f) cf
0-20 6 6
20-40 9 15
40-60 18 33
60-80 13 46
80-100 4 50
Total 50 150
The median class is 40 -60 as cf ≥ N/2
which is 33 ≥ 25
medain = 40 + |25-15|/18 ×20
medain = 40 + 200/18
median = 41.111
Mode = lower limit + f1-f0/2f1-f0-f2 × height
Here, f1 is the frequency of the modal class = 18.
f0 is the frequency of the preceding modal class = 9.
f2 is t/he frequency of the succeeding modal class = 13.
Mode = 40+ 18-9/2(18)-9-13
Mode = 52.857
Hence, the modal price is 52.857.
Price frequency (f) Mid point (xi) f.(xi)^2
0-20 6 10 600
20-40 9 30 8100
40-60 18 50 45000
60-80 13 70 63700
80-100 4 90 32400
Total 50 149800
The standard deviation of the data is calculated as,
SD = √(∑f(x1)^2)/N - (mean)^2
SD = √149800/50- (50)^2
SD = 22.271
Hence, the standard deviation of the data is 22.271.
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Which figure is 34 ft
Answers
Answer:
Yup, u need answer choices
Determine whether the following procedure results in a binomial distribution or a distribution that
can be treated as binomial (by applying the 5% guideline for cumbersome calculations). If it is not
binomial and cannot be treated as binomial, identify at least one requirement that is not satisfied.
In a Pew Research Center survey of 150 subjects, the ages of the respondents are
recorded.
Answers
The correct statement regarding whether the situation results in a binomial distribution is:
C. It is not binomial because there are more than two possible outcomes.
What is required for the binomial distribution to represent a situation?Three things are needed for a situation being represented by the binomial distribution:
Each trial having only two possible outcomes, one equivalent to success and one to failure.Fixed number of trials.Each trial is independent, that is, the probability of a success on a single trial is independent of any other trial.For this problem, for each respondent, there are multiple possible ages, a number greater than 2, hence the binomial distribution cannot be used and option c is correct.
The trials are independent, because the age of a respondent is not related to the age of any other respondent, hence option b is wrong.
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please help me in my maths question
Mike have Two pairs of shoes he is wearing red shirt his height is 6ft calculate his hair..
Answers
Answer:
It is a buzz cut.
Step-by-step explanation:
It is well-known that football players are around that height and own at least two pairs of shoes. Considering his shirt color, I would say he is a Cardinal player. Considering how terrible they did last time they played (I don't watch football), I'd say he would want to cut his hair in shame.
"24 hours per day" in math
Answers
Answer:
24 hours/day
Step-by-step explanation:
!WILL GIVE BRAINLIEST! The temperature of a city changed by a total of -20 over a 4 week time span.
Answers
The average rate of change in temperature per week will be -5°C.
How to calculate the average temperatureIt should be noted that from the information, the temperature of a city changed by a total of -20 over a 4 week time span.
Therefore, let the average rate of change per week be illustrated as x
Therefore, the average rate of change in temperature per week will be:
= Total change in temperature / Number of weeks
= -20 / 4.
= -5
Therefore, the average rate of change in temperature per week will be -5°C.
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Write an equation in slope-intercept form for each table below. Show how you found the slope and y-intercept.
Answers
The linear functions for the tables given are as follows:
1. y = 2.5x.
2. y = x + 1.
3. y = 3x - 1.5.
4. y = -4x + 3.
5. y = 4x + 1.
What is a linear function?A linear function is modeled in slope-intercept form by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For each function, the slope and the intercept are found as follows:
For item 1, when x = 0, y = 0, hence the intercept is of b = 0. When x increases by 1, y increases by 2.5, hence the slope is of m = 2.5.For item 2, when x = 0, y = 6, hence the intercept is of b = 1. When x increases by 1, y increases by 1, hence the slope is of m = 1.For item 3, when x = 0, y = -1.5, hence the intercept is of b = -1.5. When x increases by 1, y increases by 3, hence the slope is of m = 3.For item 4, when x = 0, y = 3, hence the intercept is of b = 3. When x increases by 1, y decreases by 4, hence the slope is of m = -4.For item 5, when x = 0, y = 1, hence the intercept is of b = 1. When x increases by 1, y increases by 4, hence the slope is of m = 4.Hence the functions are given as follows:
1. y = 2.5x.
2. y = x + 1.
3. y = 3x - 1.5.
4. y = -4x + 3.
5. y = 4x + 1.
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50 POINTS + 50 MORE BRAINLIEST! IF YOU SEE THIS PLEASE ANSWER.
The mass of a paperclip is 7.0 * 10^(-4) mg. If a box of paper clips has (3.18 10^(4) paper clips, determine the total mass of the paper clips in the box. Write the final answer in scientific notation with the correct number or significant digits.
2.2 * 10^1 mg
2 * 10^1 mg
2.226 * 10^1 mg
2.23 * 10^0 mg
Answers
The total mass of the paper clips in scientific notation is 2.226*10 mg
How to get the total mass of the paper clips?
We know that the mass of a single paper clip is:
M = 7.0*10⁻⁴ mg
And in one box has a total of 3.18*10⁴ clips inside of it, then the total mass of the paper clips on the box will be equal to the product between the mass of a single clip and the total number of clips.
We will get:
total mass = (7.0*10⁻⁴ mg)*(3.18*10⁴)
Using the associative property we can rewrite:
total mass = (7.0*3.18)*(10⁻⁴*10⁴) mg
= (22.26)*(10⁰) mg = 22.26 mg
Now we want to write this in scientific notation, so we need to have a single digit in the left of the decimal point, then we can rewrite this as:
22.26 mg = 2.226*10 mg
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During the past week, an accounting firm made a total of 77 long distance calls to its clients. Twenty-four of the calls were less than or equal to 30 minutes in duration while 41 of the calls were less than or equal to 40 minutes. The longest call was one hour and fifty-five minutes and the tenth percentile of the length of calls was 20 minutes.
Step 4 of 5 : What percentage of the calls were greater than 30 minutes in duration? Round your answer to the nearest whole number percentage.
Answers
The percentage of the calls were greater than 30 minutes in duration is 69%.
How to illustrate rye information?Let N = 77 Total long-distance calls
X= 24 calls are less than or equal to 30 minutes duration
Y = N - X= 77 - 24= 53 calls are greater than 30 minutes duration
To find the percentage of calls greater than 30 minutes duration. This goes thus:
= Number of calls greater than 30 minutes / Total calls
= 53 / 77
= 0.69
Therefore, 69% of the call were greater than 30 minutes in duration.
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Can you help me I ve tried so many times already, can’t seem to get it right
Answers
The following numbers are tested based on the divisibility rule:
Number: 1,843Sum of the digits: 1 + 8 +4 + 3 = 16Divisible by 2: NoDivisible by 3: NoDivisible by 6: NoNumber: 4,677Sum of the digits: 4 + 6 + 7 + 7 = 24Divisible by 2: NoDivisible by 3: YesDivisible by 6: NoNumber: 324,930Sum of the digits: 3+2+4+9+3+0= 21Divisible by 2: YesDivisible by 3: YesDivisible by 6: yesNumber: 866Sum of the digits: 8+6+6 = 20Divisible by 2: YesDivisible by 3: NoDivisible by 6: NoNumber: 32,458Sum of the digits: 3+2+4+5+8 = 22Divisible by 2: YesDivisible by 3: NoDivisible by 6: NoNumber: 925Sum of the digits: 9+2+5 = 16Divisible by 2: NoDivisible by 3: NoDivisible by 6:NoNumber: 7,254Sum of the digits: 7+2+5+4 = 18Divisible by 2: YesDivisible by 3: YesDivisible by 6: YesNumber: 81,212Sum of the digits: 8+1+2+1+2 = 14Divisible by 2: YesDivisible by 3: NoDivisible by 6: NoNumber: 77,770Sum of the digits: 7+7+7+7+0 = 28Divisible by 2: YesDivisible by 3: NoDivisible by 6: NoTesting each number for divisibility ruleA number is divided by 2 if it is an even numberEven numbers are 2, 4, 6, 8, 10....A number is divided by 3 if the sum of its digits can be divided by 3Read more about divisibility rule:
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What is 6.4% plus 39.3% ?
Answers
Answer:
45.7%
Step-by-step explanation:
5.21 x 10 to the power of 9 in standard notation
Answers
Answer: 5210000000
Step-by-step explanation:9 places to the right from the decimal
Answer:
5210000000
Step-by-step explanation:
Move the decimal point nine places to the left to get your answer.
PLS HELP ME 50 POINTS!!!!! I NEED AN ANSWER ASAP!!!!!!
A large downtown hotel consists of twenty-four levels. Any level above ground is referred to as a" floor". There are twenty-two floors and each floor corresponds to its number on the number line (2 is second floor, 3 is third floor, etc...) and two underground levels reserved for underground parking. The first level below ground level is Parking A, and the second level below ground level is labeled Parking B.
Use the provided horizontal number line to help you answer the following questions.
If you start at Parking B and take the elevator to the fourteenth floor, how many levels have you gone up? [Type your answer as a number.]
Answers
Answer:
They went up 16 levels.
Step-by-step explanation:
You can find that by finding the distance from -2 to 14.
To find the distance from two numbers, [tex]a[/tex] and [tex]b[/tex], we can substitute both in the formula [tex]d = |b - a|[/tex], where d is the distance between them.
[tex]d = |14 - (-2)| \to |14 + 2|\to|16|\to16[/tex]
Answer:
16 levels
Step-by-step explanation:
since there is 24 levels
and parking b is the lowest of the twenty-four
2(underground levels) + 14 ( floors)
= 16 levels
What is the result when the number 25 is increased by 20%?
Answers
Correct answer gets brainly!
Answers
answer this please just take your time no rush
Answers
Answer:
see explanation
Step-by-step explanation:
1
[tex]\frac{6x^2+11x-10}{3x^2+x-2}[/tex] ← factorise numerator and denominator
= [tex]\frac{(2x+5)(3x-2)}{(x+1)(3x-2)}[/tex] ← cancel common factor (3x - 2) on numerator/ denominator
= [tex]\frac{2x+5}{x+1}[/tex]
2
[tex]\frac{10}{12}[/tex] - [tex]\frac{6}{12}[/tex]
= [tex]\frac{10-6}{12}[/tex]
= [tex]\frac{4}{12}[/tex]
= [tex]\frac{1}{3}[/tex]
3
[tex]\frac{3x}{x+2y}[/tex] - [tex]\frac{4y}{x+2y}[/tex]
= [tex]\frac{3x-4y}{x+2y}[/tex]