Consider triangle ABC with the measure of an angle B = 60ﾟ and sidelinks a equal 4 &c equal 5 what option listed is an expression that is equivalent to the length of side B
Answers
The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. The correct option is B.
What is the Law of Cosine?The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. It is given by the formula,
[tex]c =\sqrt{a^2 + b^2 -2ab\cdot Cos\theta}[/tex]
where
c is the third side of the triangle
a and b are the other two sides of the triangle,
and θ is the angle opposite to the third side, therefore, opposite to side c.
The length of the sidelink b using the cosine rule can be written as,
[tex]b = \sqrt{a^2+c^2-2ac\cos(\angle B)}\\\\b = \sqrt{4^2+5^2 - 2(4)(5)(\cos 60^o)}\\\\b = \sqrt{16+25-20}[/tex]
Hence, the correct option is B.
The complete question is:
Consider ABC with the measure of angle B equal to 60 degrees, and side lengths a=4 and c=5. Which option lists an expression that is equivalent to the length of side b?
Options are given in the image below.
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Related Questions
Question 1. Chose the quadrilaterals that have the following property! * 1 point This geometry shape has 4 sides. Quadrilateral Square Rhombus Triangle Kite Circle
Answers
Answer:
quadrilateral
Step-by-step explanation:
A 4-sided polygon is a quadrilateral.
Complete the factoring.
25x^4 = 5x^2(? )
Answers
Answer:
5x^2(5x^2 - 1) = 0
Step-by-step explanation:
25x^4 = 5x^2
25x^4 - 5x^2 = 0
5x^2(5x^2 - 1) = 0
the equation that models the problem is 3.95m+8.95b=47.65, where m is the number of magazines and b is the number of books
Answers
Based on the calculations, the number of books that were bought by Hugh are 4 books.
How to calculate the number of books?In order to determine the number of books that were bought by Hugh, we would substitute the value of the number of magazines into the given equation and then evaluate as follows:
3.95m + 8.95b = 47.65
3.95(3) + 8.95b = 47.65
11.85 + 8.95b = 47.65
8.95b = 47.65 - 11.85
8.95b = 35.8
b = 35.8/8.95
b = 4.
In conclusion, the number of books that were bought by Hugh are 4 books.
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Complete Question:
Hugh bought some magazines that cost $3.95 each and some books that cost $8.95 each. He spent a total of $47.65. If Hugh bought 3 magazines, how many books did he buy? The equation that models the problem is 3.95m + 8.95b = 47.65, where m is the number of magazines and b is the number of books.
The correlation coefficient for two sets of numbers that are perfectly negatively correlated is
Answers
The correlation coefficient for two sets of numbers that are perfectly negatively correlated is -1.
What is negative correlation?
Correlation is a statistical measure used to measure the relationship that exists between two variables. Negative correlation is when two variables move in different direction. If one variable increases, the other variable decreases.
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Find a degree 3 polynomial having zeros -4, 3 and 8 and the coefficient of x 3 equal 1.
Answers
The required polynomial is [tex]x^{3}-7x^{2} -20x+96[/tex]
Polynomial : If in an expression all of variables, constants and exponents are present with mathematical operations like addition, multiplication, subtraction & division, then it is called polynomial.
If a polynomial has degree 3 as a highest degree, then the polynomial is called degree 3 polynomial or cubic polynomial.
A degree 3 polynomial having zeros α, β, γ and the coefficient of x³ equal a is, a(x- α)(x- β)(x- γ)
Given, Zeros of the polynomial are -4, 3, 8 & coefficient of x³ equal 1.
Hence, the required polynomial is,
[tex]1(x-(-4))(x-3)(x-8)[/tex]
[tex](x+4)(x-3)(x-8)[/tex]
[tex]=(x+4)(x^{2} -11x+24)[/tex]
[tex]=x^{3}-11x^{2} +24x+4x^{2} -44x+96[/tex]
[tex]=x^{3}-7x^{2} -20x+96[/tex]
This is a degree 3 polynomial.
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A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 50 and 52 minutes. Find the probability that a given class period runs between 51.5and 51.75 minutes.
Answers
The required probability of giving class period run between 51.5 and 51.75 is 0.125.
The lengths of her classes are uniformly distributed between 50 and 52 minutes.
What is the probability?
Probability, can be define as the ratio of favorable events to the n number of total events.
since,
[tex]p(r) = \frac{51.75-51.5}{52-50}[/tex]
p(r) = 0.125
Thus, the required probability of class period runs between 51.5 and 51.75 is given by 0.125
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A new phone system was installed last year to help reduce the expense of personal calls that were being made by employees. Before the new system was installed, the amount being spent on personal calls followed a normal distribution mean of $700 per month and a standard deviation of $50 per month
Answers
Using the normal distribution, it is found that there was a 0.9579 = 95.79% probability of a month having a PCE between $575 and $790.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 700, \sigma = 50[/tex].
The probability of a month having a PCE between $575 and $790 is the p-value of Z when X = 790 subtracted by the p-value of Z when X = 575, hence:
X = 790:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{790 - 700}{50}[/tex]
Z = 1.8
Z = 1.8 has a p-value of 0.9641.
X = 575:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{575 - 700}{50}[/tex]
Z = -2.5
Z = -2.5 has a p-value of 0.0062.
0.9641 - 0.0062 = 0.9579.
0.9579 = 95.79% probability of a month having a PCE between $575 and $790.
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The director of a health clinic has a quarterly budget of $600,000. She
would like to allocate this budget to maximize the number of patient visits, P, which is
given as a function of the number of doctors, D, and the number of nurses, N, by
[tex]P=1000D^0^.^6N^0^.^3[/tex].
A doctor’s quarterly salary is $40,000; nurses is $10000.
Maximize the number of patient visits given the pay constraints.
Find the value of the LaGrange multiplier and interpret its meaning in this
problem.
Answers
The meaning of this problem is that with 7 nurses they can only hire D=13.25
What is the meaning of this problem.?Generally, the equation for the model is mathematically given as
[tex]P=1000D^{0.6}N^{0.3}[/tex]
Therefore,
[tex]dv/dD=0.6*1000*D^{0.4}N)^{0.3}[/tex]
[tex]dv/dD=600* \frac{N6.1}{D6.1}=0[/tex]
Also
[tex]dv/dN=300* \frac{N6.8}{N6.7}=0[/tex]
Equations 1 and 2
[tex]300* \frac{D6.8}{N6.7}=600* \frac{N6.1}{D6.1}[/tex]
.sub D=(60N)/4
[tex]300* \frac{((60N)/4)6.8}{N6.7}=600* \frac{N6.1}{((60N)/4)6.1}[/tex]
N=6.67
N=7
solve for D
D=(60(7))/4
D=13.25
In conclusion, with 7 nurses they can only hire D=13.25
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Mathematics and body temperature? Please answer the questions in 3.
Answers
Answer:
keep the model answer photo
Marcelina uses a blend of white corn and yellow corn to make tortilla chips at her restaurant. She needs to buy 50\,\text{kg}50kg50, start text, k, g, end text of corn in total for her next order. White corn costs \$0.30$0.30dollar sign, 0, point, 30 per kilogram, yellow corn costs \$0.15$0.15dollar sign, 0, point, 15 per kilogram, and she wants to spend \$12$12dollar sign, 12 total.
What does point EEE represent in this context?
Answer:
CORRECT (SELECTED)
Marcelina spends the intended amount of money and buys the intended amount of corn.
Point EEE is on line aaa, so it represents a scenario where she spends \$12$12dollar sign, 12. Also, point EEE is on line bbb, so it represents a scenario where she buys 50\,\text{kg}50kg50, start text, k, g, end text of corn.
Answers
The point EEE represent option b is correct: Marcelina spends the intended amount of money but she bought more than she did intended amount of corn.
What is the case about?She buy 50kg of corn in total
White corn costs = $0.30 per kilogram,
Yellow corn costs = $0.15 per kilogram,
She wants to spend $12 total.
So the equation will be:
C= (20, 50) = 20 white, 50 yellow
But 30 while and 20 yellow is needed.
Since C = 20 +50
= 70 corns
While: 30 + 20
= 50 corns.
This therefore tells that Marcelina spends the intended amount of money but she bought more than she did intended amount of corn and therefore, option b is correct.
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Answer:
Marcelina spends less than the intended amount of money and buys less than enough corn.
Step-by-step explanation:
The equation of line
Khan
PLEASE HELP ME WITH THIS MATH PROBLEM
Answers
m∠ A = 60°, m∠ A = 60°, m∠ A = 60° and the sum of the angles in the triangle is 180°
How to determine the angles
It is important to note that the sum of angles in a triangle equals 180°
The given structure is a triangle, thus, the angles sum up to 180°
m ∠ A + m ∠ B + m ∠ C = 180°
m∠ A = 60°
m ∠ B = 60°
m ∠ C = 60°
The sum of the angle in the triangle = 60° + 60° + 60° = 180°
Thus, m∠ A = 60°, m∠ A = 60°, m∠ A = 60° and the sum of the angles in the triangle is 180°
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7.
Give an example to show that each statement below is not true.
a) "The product of two different primes is never even."
b) "The sum of two different primes is never prime."
ection One - Number
Answers
Answer:
a) 1 + 3 = 4
b) 2 + 3 = 5
(all prime)
hope this helps! :)
Three postal workers can sort a stack of mail in 45 minutes, 25 minutes, and 225 minutes, respectively. Find how long it takes them to sort the mail if all three work together.
Answers
If the three postal workers sort the mail together or work in parallel, it will take them 15 minutes.
What is parallel working?Parallel working refers to the system that can process a common task simultaneously by many workers communicating with one another.
When workers perform the same task together, they tend to achieve greater speed, unlike when they work individually without communicating.
Data and Calculations:Time to sort a stack of mail by A = 45 minutes or 1/45
Time to sort a stack of mail by B = 25 minutes or 1/25
Time to sort a stack of mail by C = 1/225
Time for the three workers to sort the stack together = 1/45 + 1/25 + 1/225
= 15 minutes (5 + 9 + 1)
Thus, if the three postal workers sort the mail together or work in parallel, it will take them 15 minutes.
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your restaurant serves 50 bowls of French onion soup daily and each serving has 8 ounces of onion per portion. Do you think it would be better to purchase whole onions at $1.99 per pound, and cut them yourself, or purchase pre-sliced onions at $2.99 per pound?
Answers
Answer:
Step-by-step explanation:
It would be better to purchase onions at 1.99 per pound
Help with this exponential function!
A species of animal is discovered on an island. Suppose that the population size P (t) of the species can be modeled by the following function, where time t is measured in years.
Find the population size after 6 years and after 8 years.
Round your answers to the nearest whole number as necessary.
Answers
The population size after 6 years and after 8 years are 147 and 169 population respectively
Exponential functionsThe standard exponential function is expressed as y = ab^x
where
a is the base
x is the exponent
Given the function that represents the population size P (t) of the species as shown;
[tex]p(t)=\frac{550}{1+5e^{-0.1t}} \\[/tex]
For the population size after 6 years
[tex]p(t)=\frac{550}{1+5e^{-0.1(6)}} \\P(6)=\frac{550}{3.744}\\ P(6)=147 population[/tex]
For the population after 8 years
[tex]p(t)=\frac{550}{1+5e^{-0.1(8)}} \\P(8)=\frac{550}{3.2466}\\ P(8)=169 population[/tex]
Hence the population size after 6 years and after 8 years are 147 and 169 population respectively
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20-26 JIT production, relevant benefits, relevant costs. The Knot manufactures men's neckware at its Spartanburg plant. The Knot is considering implementing a JIT production system. The following are estimated costs and benefits of JIT production: a. Annual additional tooling costs $250,000 annually. b. Average inventory would decline by 80% from the current level of $1,000,000. c. Insurance, space, materials-handling, and setup costs, which currently total $400,000 annually, would decline by 20%. d. The emphasis on quality inherent in JIT production would reduce rework costs by 25%. The Knot currently incurs $160,000 in annual rework costs. e. Improved product quality under JIT would enable The Knot to raise the price of its product by $2 per unit. The Knot sells 100,000 units per year. The Knot's required rate of return on inventory investment is 15% per year. 1. Calculate the net benefit or cost to The Knot if it adopts JIT production at the Spartanburg plant. 2. What nonfinancial and qualatative factors should The Knot consifer when making the decision to adopt JIT production? 3. Suppose The Knot implements JIT production at its Spartanburg plant. Give examples of performance measure The Knot could use to evaluate and control JIT production. What would the benefit of The Knot implementing an enterprise resource planning (ERP) system?
Answers
The net benefit to The Knot if it adopts JIT production at the Spartanburg plant is $200000.
How to illustrate the information?Based on the information given, the net benefit will be:
= $1,000,000 × (1 - 80%)
= $1,000,000 × 0.2
= $200,000
The nonfinancial and qualatative factors that The Knot should consider when making the decision to adopt JIT production are:
Development of a detailed system.Willingness of suppliers to deliver smaller and more frequent orders. Skill level of workers should be enhanced.The benefit of The Knot implementing an enterprise resource planning (ERP) system is that it gives access to operating information in response to the supply.
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calculate the number of ways that the coach can assign the 4 positions to his 16 players.
Answers
The number of ways that the coach can assign the 4 positions to his 16 players would be 43, 680 ways
How to calculate the permutation
The formula for permutation is given as;
Permutation = [tex]\frac{n!}{(n - r)!}[/tex]
n = 16
r =4
Permutation = [tex]\frac{16!}{12!}[/tex]
Permutation = [tex]\frac{16 *15*14*13*12*11*10*9*8*7*6*5*4*3*2*1}{12*11*10*9*8*7*6*5*4*3*2*1}[/tex]
Permutation = 43, 680 ways
Thus, the number of ways that the coach can assign the 4 positions to his 16 players would be 43, 680 ways
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Please help, multiple choice question
Select the correct inequality for the graph below:
y > −2x + 2
y ≥ −2x + 2
y < −2x + 2
y ≤ −2x + 2
Answers
The correct answer is option D which is y ≤ −2x + 2.
What is inequality?The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than, or < ‘less than.
When we draw the graphs we will see that the inequality y ≤ −2x + 2 is showing the same graph. It is cutting the y-axis at (0,2) and the x-axis at (2,0).
Therefore the correct answer is option D which is y ≤ −2x + 2.
The graph is attached with the answer below.
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Help me with this algebra
Answers
Answer:
Step-by-step explanation:
fita operates her own lawn mowing business. A new customer will pay an initial start-up fee, plus a constant fee fro each time the customer would liek to have their lawn mowed. Customer A had his lawn mmowed 10 times and paid a total of $370. Customer B had her lawn mowed 7 times and paid a total of $265. What is the initial start-up fee for signing up with Rita's lawn mowing service?
Answers
The initial start-up fee for signing up with Rita's lawn mowing service is $20, using simultaneous equations.
What are simultaneous equations?Simultaneous equations are two or more algebraic equations that share variables like x and y and can be solved at the same time.
Data and Calculations:Let y = fixed cost (initial start-up cost)
Let x = variable cost per lawn mowing
Formation of Simultaneous Equations:Equation 1: Customer A = y + 10x = $370
Equation 2: Customer B = y + 7x = $265
Elimination Method:Subtract equation 2 from equation 1 to get:
3x = $105
x = $35
Substitute x in any of the two equations to find the value of y, thus:
Customer A:
y + 10($35) = $370
y + #350 = $370
y = $20 ($370 - $350)
Thus, the initial start-up fee for signing up with Rita's lawn mowing service is $20, using simultaneous equations.
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An isosceles triangle has side lengths of 15.6 units and 20.33 units. What is the greatest possible value of the perimeter of the triangle?
Answers
Answer:
56.26
Step-by-step explanation:
An isosceles triangle has two sides that are the same length, and one side that is the same length. We have two sizes, so two find the greatest possible perimeter we must assume that the greater size is the value for the two sides, and the smaller size the value for the single side. In other words:
[tex]x = 15.6 + 2(20.33)[/tex]
[tex]x = 56.26[/tex]
need help with parts 1-6
Answers
The value of F(g(1)) will be equal to 0.
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
From the given table we can see that the value of f(x) at 1 is 3 and the value of g(x) at 1 is 0.
The value of f(xg(x) at x = 1 will be:-
f(xg(x) = f(x) x g(x)
= 3 x 0
= 0
Therefore the value of F(g(1)) will be equal to 0.
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Jerry bought 680 square feet of wood flooring to liven up his retail store. He has 1/4 of the flooring left over. How many square feet does he have left?
Answers
Answer:
170
Step-by-step explanation:1/4 is just like dividing 4 so 680 divided by 4 equals 170
Please solve this question, i have exams tommorow :(
Answers
Explanation:
Step1: find the the common denominator
In this case the common denominator is 3ab so the equation is rewritten as xy+5xy/3ab
Step 2: add like terms
If like terms are added the new equation is 6xy/3ab since xy+5xy=6xy
Step 3: simplify
To simplify you must find a least common factor which is this case is 3 so therefore when 3 is factored from 6xy/3ab the new equation is 2xy/ab
Answer:
2xy/ ( ab)
Step-by-step explanation:
xy/ ( 3ab) + 5xy/(3ab)
Since the denominator is the same, we can add the numerators
xy+5xy = 6xy
6xy/ (3ab)
We can simplify 6/3 = 2
2xy/ ( ab)
Rewrite 32/35 and 9/10
Answers
The question was incorrect. Please find the correct content below.
Compare 32/35 and 9/10.
Comparing 32/35 and 9/10 we have 32/35 is greater than 9/10, that is 32/35 > 9/10.
Fraction is the ratio of two numbers. The upper number is called Numerator and the Lower number is called the Denominator.
We know that if the denominators are the same for two fractions then which has the greatest numerator is a greater fraction than the other.
Given the fractions are 32/35, 9/10
To compare this two fractions we have to make denominators equal first.
LCM of 10,35 = 70
Calculating the fractions,
32/35 = (32*2)/(35*2) = 64/70
9/10 = (9*7)/(10*7) = 63/70
Since 64 > 63
So 64/70 > 63/70
Therefore, 32/35 > 9/10
Hence fraction 32/35 is greater than the other fraction 9/10.
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How many characteristics of a population does a random variable represent?
1. As many as you wish
2. Single
3. Less than one
4. Two or more
Answers
The characteristics of a population that a random variable represents are 1. As many as you wish and 4. Two or more.
What is a random variable?A random variable is a variable with unknown outcomes.
A random variable can have either discrete or continuous values.
It is discrete when it has specific values. It is continuous when it assumes some continuous values.
Thus, the characteristics of a population that a random variable represents are 1. As many as you wish and 4. Two or more.
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Determine the length of CD. Show your work.
Answers
The length of line CD is 20. 9
How to determine the lengthNote that triangle CDY is an isosceles triangle
Using the Pythagoras theorem
Hypotenuse square = opposite square + adjacent square
Hypotenuse = line CD
opposite = 20
Adjacent = 6
Substitute into equation
[tex]Line CD^2 = 20^2 + 6^2[/tex]
[tex]Line CD^2 = 400 + 36[/tex]
[tex]Line CD^2 = 436[/tex]
Make line CD^2 subject by find the square root of the other side
[tex]Line CD = \sqrt{436}[/tex]
[tex]Line CD = 20.9[/tex]
Therefore, the length of line CD is 20. 9
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What is the equation of line b d, simplified? y − y1 = m(x − x1) y − 0 = (startfraction 2 b over 2 a minus c endfraction)(x − c) y = (startfraction b over a minus c endfraction)x − (startfraction 2 b c over 2 a minus c endfraction) y = (startfraction 2 b over 2 a minus c endfraction)x − (startfraction b c over 2 a minus 2 c endfraction) y = (startfraction 2 b over 2 a minus c endfraction)x − (startfraction 2 b c over 2 a minus c endfraction) y = (startfraction 2 b over a minus c endfraction)x − (startfraction 2 b c over a minus c endfraction)
Answers
The required equation of line BD is option d.) [tex]y=\frac{2b}{2a-c} x-\frac{2b}{2a-c} c[/tex]
Equation of the line is given be in standard form is
[tex]y-y_{1} =\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
Line, curve of the shortest distance between two points.
The questions seem to be incomplete the question, the complete question could be
a)[tex]y=\frac{2b}{2a-c} (x-c)\\[/tex]
b)[tex]y=\frac{b}{-c} x-\frac{2b}{2a-c}[/tex]
c)[tex]y=\frac{2b}{2a-c} x-\frac{bc}{2a-2c}[/tex]
d)[tex]y=\frac{2b}{2a-c} x-\frac{2b}{2a-c} c[/tex]
e)[tex]y=\frac{2b}{a-c} x-\frac{2b}{a-c}[/tex]
Now all the Equation in option represents the triangle with coordinates A(0, 0), B (2a, 2b), C(2c,0) and D(c, 0).
For equation of line BD we have coordinates, (2a, 2b) and (c, 0).
putting these coordinates in the standard form of equation of line i.e.
[tex]y-y_{1} =\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
⇒ [tex]y=\frac{2b}{2a-c} x-\frac{2b}{2a-c} c[/tex]
Thus the required equation of the line is [tex]y=\frac{2b}{2a-c} x-\frac{2b}{2a-c} c[/tex].
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Answer:
C
Step-by-step explanation:
Edg
HELP PLEASE I will give brainly!!!!!
Answers
This is because you first solve for x and substitute the value for x into the equations given. x =1 and y= 2
Answer:
(1,2)
Step-by-step explanation:
first, make the equations equal each other so you can solve for x
8x-6=2x
this gives you 1
then, use what you got for x and plug it in for one of the original questions. I am gonna use 2x since its the easiest to plug in and solve
2(1)=2, so y is 2
so then x=1 and y=2
then put that into (x,y) which is (1,2)
Use the function below to find F(2).
Answers
Answer:
D
Step-by-step explanation: