Answers
Using complementary angles, the numerical value of the given expression is as follows:
2.
What are complementary angles?Complementary angles are angles whose sum of the measures is of 90º.
The relevance of complementary angles in the context of this problem is that if a and b are complementary angles, then the sine of one angle is the cosine of the other angle, as follows:
sin(a) = cos(b).
Considering the angles of 40º and 50º in this problem, we have that:
sin(40º) = cos(50º).sin(50º) = cos(40º).Hence these following simplifications are applied:
sin²(40º) + sin²(50º) = sin²(40º) + cos²(40º) = 1.cos²(40º) + cos²(50º) = sin²(50º) + cos²(50º) = 1.sin(40º)cos(50º) = sin(40º)sin(40º) = sin²(40º).cos(40º)sin(50º) = cos(40º)cos(40º) = cos²(40º).Then the numerical value of the expression is given as follows:
1/1 + sin²(40º) + cos²(40º) = 1 + 1 = 2.
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Related Questions
x + m = p - n + yx Solve for x
Answers
Answer:
[tex]x=\frac{-m-n+p}{-y+1}[/tex]
Step-by-step explanation:
What do you call each part of an expression that is separated by a + or a -?
Answers
Alexis has two job offers. Job #1 pays $12 an hour and will allow her to work 40 hours a week. Job #2 pays $8 an hour and also requires a 40-hour week. However, Job #2 also pays bonuses based on sales. The other salespersons told Alexis they average about $100 a week in bonuses. Which job will likely pay the most money per week?
Answers
Answer:
$8 an hour and also requires a 40-hour week
Step-by-step explanation:
PLEASE ANSWER ALL THE QUESTIONS FOR 50 POINTS!!!!!
Answers
b. 72.1 - 45.6 = 26.5
c. 82.2 - 41.3 - 29.2 = 11.7
d. 17.1 - 11.7 - 0.8 = 4.6
e. 29.2 - 12.5 - 0.9 = 15.8
f. 21 - 14 = 7
g. 71 - 37 - 18 = 16
h. 50 - 19 - 8 = 23
i. 92 - 57 - 16 = 19
Answer:
a. 4.2 - 2.8 = 1.4
b. 72.1 - 45.6 = 26.5
c. 82.2 - 41.3 - 29.2 = 11.7
d. 17.1 - 11.7 - 0.8 = 4.6
e. 29.2 - 12.5 - 0.9 = 15.8
f. 21 - 14 = 7
g. 71 - 37 - 18 = 16
h. 50 - 19 - 8 = 23
i. 92 - 57 - 16 = 19
j. 44 - 18 - 9 = 17
Identify the reaction type for each generic chemical equation. a b → ab: ab → a b: hydrocarbon o2 → co2 h2o: ab cd → ad cb:
Answers
For all the given reactions there is a type name for it they are,
1. A + B → AB
2. AB → A + B
3. Hydrocarbon + O₂ → CO₂ + H₂O
4. AB + CD → AD + CB
All the above-mentioned chemical reactions are of the following types
1 → Synthesis
2 → Decomposition
3 → Combustion
4 → Replacement
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5/7 of the teaching staff in a certain primary school are females, what fraction of the staff are males
Answers
Answer: 2/7
Step-by-step explanation:
Substract 7/7 AKA the whole, by 5/7 tp get 2/7
2/7 is the fraction of males.
In 3 hours, 5 people can paint a hall with the area of 750 ft 2. How long would it take for 2 people to paint the hall with the same rate of speed?
Answers
ANSWER:
STEP-BY-STEP EXPLANATION:
In this case, we can make a proportion, since we know the time when there are 5 people, we need to know the time when there are two people
[tex]\frac{5}{3}=\frac{2}{x}[/tex]solving for x:
[tex]undefined[/tex]2x-4<6
what is the solution to this inequlity
Answers
Answer:
x < 5
Step-by-step explanation:
[tex]2x - 4 < 6[/tex]
[tex]2x < 10[/tex]
[tex]x < 5[/tex]
.........................................................
a binomial experiment with probability of success and trials is conducted. what is the probability that the experiment results in or more successes? do not round your intermediate computations, and round your answer to three decimal places. (if necessary, consult a list of formulas.)
Answers
The probability that the experiment results in 9 or more successes = 0.0676
A binomial distribution is given by,
P(X = x) = ⁿCₓ pˣ (1-p)ⁿ⁻ˣ ,
where p is the probability of success and x is the random variable for success in n trials.
A binomial experiment has only two outcomes- success or failure.
Here, the number of trials, n = 10
Probability of success = 0.63
The probability for 9 or more success = P( X = 9, 10)
= P (X = 9) + P(X = 10)
So P( X = 9) = ¹⁰C₉ (0.63)⁹ (1-0.63)¹⁰⁻⁹
= 10 x 0.0156 x 0.37
= 0.05772
and P(X = 10) = ¹⁰C₁₀ (0.63)¹⁰(1-0.63)¹⁰⁻¹⁰
= 1 x 0.009849 x 1
= 0.009849
Hence probability for 9 or more success = 0.05772 + 0.009849
= 0.067569
= 0.0676
The question is incomplete. Find the complete question below:
A binomial experiment with probability of success 0.63 and 10 trials is conducted. What is the probability that the experiment results in 9 or more successes? Do not round your intermediate computations, and round your answer to three decimal places. (If necessary, consult a list of formulas.)
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PLEASE HELP I NEED THIS ASAP PLEASE!!!!
Answers
I can only help with one bc of school but if I’m correct,The second one is Radius is 24 centimeters, Diameter is 48 centimeters, Circumference is 150.72 centimeters
Answer: Radius (r) 5.99848 in
Diameter 11.99696 in
Circumference (c) 37.68955 in
Area 113.04in²
Radius (r) 5.99848 in
Diameter 11.99696 in
Circumference (c) 37.68955 in
Area 113.04 in²
Radius (r) 0.999493 in
Diameter 1.998986 in
Circumference (c) 6.28 in
Area 3.13841 in²
Radius (r) 8.49569 in
Diameter 16.99138 in
Circumference (c) 53.38 in
Area 226.75 in²
Radius (r) 2.5 cm
Diameter 5 cm
Circumference (c) 15.70796 cm
Area 19.63495 cm²
Radius (r) 1.1 yd
Diameter 2.2 yd
Circumference (c) 6.9115 yd
Area 3.80133 yd²
Radius (r) 2 in
Diameter 4 in
Circumference (c) 12.56637 in
Area 12.56637 in²
Step-by-step explanation: I hope this helps.
a number m is randomly selected from the set {11, 13, 15, 17, 19}, and a number n is randomly selected from {1999, 2000, 2001, . . . , 2018}. what is the probability that mn has a units digit of 1?
Answers
According to Euler's Theorem, if gcd(a,n) = 1, then a(n) 1. (mod n). The number of relatively prime integers in the range of 1, 2,..., n-1 is represented by the Euler totient function.
The probability that mn has a units digit of 1 = 2/5
What is Euler's theorem ?According to Euler's Theorem, if gcd(a,n) = 1, then a(n) 1. (mod n). The number of relatively prime integers in the range of 1, 2,..., n-1 is represented by the Euler totient function, or (n). This theorem is simply Fermat's little theorem when n is a prime.The remainder of a(m), when divided by a positive integer m that is relatively prime to a, is 1, according to Euler's Theorem. Because Fermat's Theorem is merely a special case of Euler's Theorem, this is the only way we can demonstrate Euler's Theorem. This is because (p)=p1 holds for a prime number p.By Euler's Theorem, we have that [tex]$a^{4} \equiv 1 \pmod {10}$[/tex] if [tex]$\gcd(a,10)=1$[/tex] Hence[tex]$m=11,13,17,19$,[/tex][tex]$n=2000,2004,2008,2012,2016$[/tex] work.
Also note that [tex]$11^{\text{any positive integer}}\equiv 1 \pmod {10}$[/tex] because [tex]$11^b=(10+1)^b=10^b+10^{b-1}1+...+10(1)+1$[/tex], and the latter[tex]$\pmod {10}$[/tex]is clearly [tex]$m=11$[/tex], [tex]$n=1999,2001,2002,2003,2005,...,2018$[/tex] work (not counting multiples of 4 as we would be double counting if we did).
We can also note that [tex]$19^{2a}\equiv 1 \pmod {10}$[/tex] because[tex]$19^{2a}=361^{a}$[/tex], and by the same logic as why [tex]$11^{\text{any positive integer}}\equiv 1 \pmod {10}$[/tex]we are done. Hence [tex]$n=2002, 2006, 2010, 2014, 2018$[/tex] and [tex]$m=19$[/tex] work (not counting any of the aforementioned cases as that would be double counting).
We cannot make any more observations that add more[tex]$m^n$[/tex] with unit digit [tex]$1$[/tex], hence the number of [tex]$m^n$[/tex] that have units digit one is [tex]$4\cdot 5+1\cdot 15+1\cdot 5=40$.[/tex] And the total number of combinations of an element of the set of all [tex]$m$[/tex]and an element of the set of all n is [tex]$5\cdot 20=100$[/tex]. Hence the desired probability is [tex]$\frac{40}{100}=\frac{2}{5}$[/tex].
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Carmen participated in a walkathon to
raise money for the local library. Before the
hour-long event began, Carmen estimated
that she would walk 3.5 miles, but she
ended up walking 4 miles. What is the
percent error for Carmen's estimate?
Answers
Answer:
Step-by-step explanation:
12%
Answer:
12.5%
Step-by-step explanation:
one sheet of paper in a notebook is 8 1/2 inches by 11. a smaller notebook has a similar shape, and its pages are 5 1/2 inches long. what is the width of the paper in the smaller notebook?
Answers
The width of the paper in the smaller notebook is 4 1/4 inches.
When two shapes are similar, the ratio of their corresponding sides are equal, and their corresponding angles are equal.
For two notebooks in the shape of a rectangle, the ratio of their lengths must be equal to the ratio of their widths.
If one sheet of paper in a notebook is 8 1/2 inches by 11, and the pages of the smaller similar notebook are 5 1/2 inches long, then the width of the paper in the smaller notebook is
11 inches / 5 1/2 inches = 8 1/2 inches / width of smaller notebook
width of smaller notebook = 4 1/4 inches
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Find the slope of the line that passes through (64, 94) and (48, -3).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answers
The slope of the points has a value of 97/16
How to determine the slope of the points?From the question, the line passes through the following points
(64, 94) and (48, -3).
The slope of the line that passes through the points is then calculated using
Slope = (y₂ - y₁)/(x₂ - x₁)
Where x and y are the coordinates above
Substitute the known values in the above equation
So, we have the following equation
Slope = (94 + 3)/(64 - 48)
Evaluate the difference and the sum
Slope = 97/16
Hence, the slope is 97/16
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The set of ordered pairs shown below is a relation that is
a function of x.
{(-5, 1), (-4, 1), (−3, 1), (−2, 1)}
Which ordered pairs could be included in the set so that
the relation remains a function of x?
O (-3,0), (-1, 1)
O (-6, 1), (-5, 1)
O (-6, 1), (-1, 1)
O (-2, 2), (-1, 1)
Answers
The ordered pairs that could be included in the set so that the relation remains a function of x is (-6, 1), (-1, 1).
What is defined as the relation of function?A function is a relation that states that there must be only one output for each input (or) we can say that a function is a special type of relation (a set of ordered pairs) that follows a rule, i.e., every X-value should be related with only one y-value.The Cartesian product is a subset of it. Alternatively, a slew of points (ordered pairs). In other words, the relationship between the two sets is described as a collection of a ordered pair, where the ordered pair is formed by an object from each set.For the given relation that is a function of x.
{(-5, 1), (-4, 1), (−3, 1), (−2, 1)}
As, from the definition of the function, the domain of the function will not repeat in the set.
Thus, (-6, 1), (-1, 1) is the ordered pairs that could be included in the set so that the relation remains a function of x.
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a company produces steel rods. the lengths of the steel rods are normally distributed with a mean of 140.9-cm and a standard deviation of 1-cm. for shipment, 22 steel rods are bundled together. find the probability that the average length of a randomly selected bundle of steel rods is less than 140.7-cm.
Answers
The most typical or average value among a group of numbers is called the mean. It is a statistical measure of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."
Steel rods are produced by a firm. The lengths of the steel rods have a mean of 140.9 cm and a standard deviation of 1 cm, and they are regularly distributed. 22 steel rods are packaged together for shipping. determine the likelihood that the average length of a bundle of steel rods chosen at random is less than 140.7 cm.
mean is N (M) (109,1.6)
Looking for P(M 108.7) to P(z ???) conversion utilizing N(0,1) z-statistic transformation
P(z [M - population mean]/[SD/square root(sample size)]) = P(z [108.7-109)/[1.6/sqrt(27)] = P(z -0.974] = 0.165.
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During two games, the number of points scored by a basketball team increased from 5 to 3 by what did the number of points scored increase?
Answers
EXPLANATION
Let's see the facts:
The increasing rate is:
[tex]Increa\sin g\text{ rate=}\frac{5}{3}=1.67[/tex]The increasing rate is 1.67
In percentage this is:
[tex]Increa\sin g=\frac{3}{5}\cdot100=\frac{3}{5}\cdot100=60[/tex]The percentage of increasing is of 60%.
In the community of Greendale, a local restaurant donates 15% of the total sales to student-based clubs on certain funding nights.
A- Write an equation to represent the relationship between the dinner sales (d) and the amount (a) the organization will receive.
B- What is the constant of proportionality? Interpret the constant proportionally for the problem situation.
C- How much will the organization receive if dinner sales are $3600?
NEED BY 2:35 CENTRAL TIME!!! OFFERING 35 POINTS! MIDDLE SCHOOL MATH!
Answers
The equation that represents the relationship between dinner sales and the amount the organisation would receive is a = 0.15d
The constant of proportionality is 0.15.
Th amount the organisation will receive if dinner sales is $3600 is $540
What is the relationship between dinner sales and the amount the organisation would receive?The equation that would be used to represent the relationship between dinner sales and the amount the organisation would receive is a linear equation.
A linear equation is an equation that has one variable that is raised to the power of one. A linear equation can either be either be a positive function or a negative equation. When a linear equation is drawn on a graph, the graph is a straight line.
The form of the linear equation would be:
total amount received by the organisation = percentage x amount the restaurant receives.
a = 0.15d
0.15 is the constant of proportionality. It is the value that relates the amount the organisation would receive and the amount the restaurant would receive.
a = 0.15 x 3600
a = $540
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Which statement about the location of √ 7 on a number line is true?
Answers
The location of √ 7 on a number line between 2 and 3.
What is a number line?A number line is a picture of a graduated straight line that serves as a visual representation of real numbers in primary mathematics. Every number line point is considered to correspond to a real number and every real number to a number line point.
A number line is a long straight line with numbers marked at equal intervals. On a number line, we can argue that as we move to the right, the value of numbers increases. This signifies that the numbers on the right are more than those on the left.
A number line shows how numbers are related. It's a line with check marks next to each number. The numerals get smaller as you move left on the number line. The numbers grow larger as you move closer to the number line.
In this case, ✓7 is 2.65. This number can be found between 2 and 3. This should be the true statement since the options aren't given.
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A pottery studio has 11 pounds of clay. It takes 7/8 of clay to make a coffee mug find 11 divided by 7/8.Then interpret the question.
Answers
The number of coffee mugs that can be made is 12.
How to calculate the fraction?From the information, the pottery studio has 11 pounds of clay and it It takes 7/8 of clay to make a coffee mug.
The number of coffee mugs that can be made will be:
= Number of pounds of clay / Fraction used for each mug
= 11 / 7/8
= 11 × 8/7
= 88 / 7
= 12
There'll be 12 coffee mugs.
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The volume of a gas in a container varies inversely with the pressure on the gas. If a gas has a volumeof 230 cubic inches under a pressure of 8 pounds per square inch, what will be its volume if thepressure is increased to 18 pounds per square inch? (Round off your answer to the nearest cubic inch.)
Answers
Answer:
Explanation:
The volume of a gas in a container varies inversely with the pressure on the gas
Let V represent volume
Let P represent Pressure
Rewrting the statement above Mathematically:
[tex]\begin{gathered} V\text{ }\alpha\text{ }\frac{1}{P} \\ V\text{ = k}\frac{1}{P} \end{gathered}[/tex]when V = 230 in³
P = 8 lb/in³
Substitute the value of P and V in the equation in order to ger k:
when a grizzly bear hibernates, its heart rate drops to 101010 beats per minute, which is 20\ , percent of its normal value. what is a grizzly bear's normal heart rate when not hibernating? beats per minute
Answers
A grizzly bear's normal heart rate when not hibernating is 50 beats per minute.
What is a heart rate?
The number of heartbeats that occur in a specific amount of time, usually one minute. The wrist, side of the neck, back of the knees, top of the foot, groin, and other areas of the body where an artery is close to the skin can all detect the heartbeat.
Here,
We let his normal heart rate = h
and given in the question,
20% of h = 10
20/100 * h = 10
h = 10*5
= 50 beats/min
Hence, a grizzly bear's normal heart rate when not hibernating is 50 beats per minute.
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What is -2=-1+n/8? I’ve been stuck on it for a while
Answers
Answer: n= -8
Step-by-step explanation:
1. -2 = -1 + [tex]\frac{n}{8}[/tex]
2. -1 = [tex]\frac{n}{8}[/tex]
3. -8 = n
Consider the line y = = 8 x-4. Find the equation of the line that is parallel to this line and passes through the point (7, -2). Find the equation of the line that is perpendicular to this line and passes through the point (7, -2).
Answers
Answer: y=8x-58
Step-by-step explanation:
1. find the slope
Since the new line is parallel to the first one that means the slope of 8x will remain the same.
2. plug it into the point slope formula y-y1=m(x-x1)
which would look like
y-(-2)=8(x-7)
3. solve for y
y-(-2)=8(x-7)
y+2=8x-56
y=8x-58
Parallel slope = 8
Perpendicular slope = -1/8
Use point slope. Use point and respective slope.
y-y1= m(x-x1)
y+2 = 8(x-7)
y+2 = 8x - 56
y= 8x - 58 (parallel equation)
y-y1= m(x-x1)
y+2 = -1/8(x-7)
y+2 = -1/8x +7/8
y= -1/8x - 11/8 (perpendicular equation)
Does that help?
Simplify one over x raised to the negative eighth power.
Answers
Answer:
1/x to the -8 power simplified would be x^8
Step-by-step explanation:
When there is a negative exponent you put the fraction under 1
[tex]\frac{1}{\frac{1}{x^{8} } }[/tex] and its the same as x^8
The simplified expression is [tex]x^8[/tex].
What is exponent?Exponent is the power of the variable or constant to which it is raised.
The expression 1 over x is denoted by 1/x.
The exponent of the obtained expression will be -8. So, the expression will be [tex](\frac{1}{x})^{-8}=\frac{1}{x^{-8}}[/tex].
The exponents of the denominator change from negative to positive when they move from denominator to numerator.
[tex]\frac{1}{x^{-8}}=x^8[/tex]
Thus, the simplified expression will be x raised to the power 8.
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Point(2,8) , (4,7.5) rise over run so what's the answer
Answers
The slope of the line with the given coordinates (2,8) and (4,7.5) is -0.25.
What is the slope of the line with the given coordinates?Slope is simply expressed as change in y over the change in x.
Rise over run.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Given the data in the question;
Point 1( 2,8) )
x₁ = 2y₁ = 8Point 2( 4,7.5 )
x₂ = 4y₂ = 7.5To find the slope, plug the given x and y values into the slope formula and simplify.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 7.5 - 8 )/( 4 - 2 )
Slope m = ( -0.5 )/( 2 )
Slope m = -0.5 / 2
Slope m = -0.25
Therefore, the slope of the line is -0.25.
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31. a statistics class has 26 students. the instructor would like to select a random sample of 3 students to work together on a group project. a. how many different samples are possible? b. if 13 of the 26 students in class are freshmen, what is the probability that all 3 of the selected students are freshmen?
Answers
a. 2600 ways different samples are possible.
b. 0.11 is the probability that all 3 of the selected students are freshmen.
total student = 26
3 students are randomly selected on group project
a. the possible different sample are
[tex]26 C_{3}[/tex] = [tex]\frac{26}{3 (26-3)}[/tex]
= [tex]\frac{26}{3 (23)}[/tex]
= 2600 ways.
b. 13 students are freshmen
Pr ( 3 selected students is freshman)
[tex]\frac{13C_{3} }{26C_{3} }[/tex] = [tex]\frac{286}{2600}[/tex] = 0.11
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
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Consider the density curve plotted below:1.63.24.86.480.050.10.150.20.25XPDF(X)Density CurveFind P(X<1.6) : Find P(X>4.8) :
Answers
Given:
There is a density curve given in the question
Required:
We need to find for
[tex]\begin{gathered} P(X<1.6) \\ P(X>4.8) \end{gathered}[/tex]Explanation:
Part a
We want to find P(X<1.6)
For this we just need to find the area below the curve until x=1.6, since we have a triangle we can do this:
[tex]P(X<1.6)=\frac{1}{2}*1.6*0.05=0.04[/tex]Part b
For this case we want to find this probability:
P(X>4.8)
and we can complement rule and we got
[tex]P(X>4.8)=1-P(X<4.8)=1-\frac{1}{2}*4.8*0.15=0.64[/tex]Final answer:
0.04
0.64
8. The smaller of two numbers is five less than half the larger number. Their sum is 13. Find the numbers,
Answers
Larger number: 12
Smaller number: 1
Let Statements:
Let x = the larger number
Let 1/2x - 5 = the smaller number
Equation:
x + (1/2x - 5) = 13
1.5x - 5 = 13
1.5x = 18
x = 12
Solutions:
The larger number = x = 12
The smaller number = 1/2x - 5 = 1/2(12) - 5 = 6 - 5 = 1
do blood-building drugs help brain development in babies born prematurely? researchers randomly assigned 53 babies, born more than a month premature and weighing less than 3 pounds, to one of three groups. babies either received injections of erythropoietin (epo) three times a week, darbepoetin once a week for several weeks, or no treatment. results? babies who got the medicines scored much better by age 4 on measures of intelligence, language, and memory than the babies who received no treatment.how many different treatments were there and what principle of experimental design does that address?
Answers
There were three different treatments: erythropoietin, darbepoetin, and no treatment. This selection exemplifies the principle of randomization principle.
What is a treatment?In experiments, the word treatment refers to the use of a specific medicine, therapy, or condition that is controlled by the research to test the effect of the treatment on subjects. For example, if the researcher wants to find out the ideal amount of water for a plant to grow, the treatment would be the amount of water.
In the case presented, there are three treatments:
Erythropoietin (epo) three times a week.Darbepoetin once a week for several weeks.No treatment.What principle of experimental design does that address?Randomization is the principle applied because the subjects are selected randomly for each of the groups and this reduces bias.
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