The type of variable for,
a. The number of counties in California: Quantitative discrete.
b. The stages of childhood: Qualitative ordinal.
c. In the scenario above, 23 minutes is a statistic, because 28 students is a sample.
d. Between 6 minutes and 8 minutes: Approximately 68% of the athlete's mile times are expected to be between 6 and 8 minutes, according to the empirical rule.
e. Between 4 minutes and 7 minutes: Approximately 68% of the athlete's mile times are expected to be between 4 and 10 minutes, according to the empirical rule.
f. Less than 9 minutes: Approximately 84% of the athlete's mile times are expected to be less than 9 minutes, according to the empirical rule.
In statistics, variables can be categorized into two types: qualitative and quantitative.
Qualitative variables describe characteristics or qualities that cannot be measured numerically, such as gender or hair color.
Quantitative variables, on the other hand, represent numerical values that can be measured or counted.
There are two types of quantitative variables: continuous and discrete. Continuous variables can take any numerical value within a range, such as age or weight.
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Write the equation of the line in slope-intercept form.
Answer:
y = 1/2x - 4
Step-by-step explanation:
The y-intercept is at -4 (counting by ones).
The slope would be 1/2, going up one time and to the right twice, plotting the point (2, -3).
television viewers often express doubts about the validity of certain commercials. in an attempt to answer their critics, a large advertiser wants to estimate the true proportion of consumers who believe what is shown in commercials. preliminary studies indicate that about 40% of those surveyed believe what is shown in commercials. what is the minimum number of consumers that should be sampled by the advertiser to be 85% confident that their estimate will fall within 2% of the true population proportion?
To be 85% confident that the estimate will fall within 2% of the true population proportion, the advertiser needs a minimum sample size of 923 consumers to survey.
How to determine the minimum sample size?To determine the minimum sample size required for estimating the true population proportion with a certain level of confidence and margin of error, we can use the formula n = (Z² * p * q) / E², where n is the sample size, Z is the standard normal value corresponding to the desired confidence level, p is the estimated population proportion, q is the complement of p, and E is the desired margin of error.
In this case, the desired confidence level is 85%, the estimated population proportion is 0.40 (40%), and the desired margin of error is 0.02 (2%). Using a standard normal table, we can find that the corresponding Z value for 85% confidence is approximately 1.44. Plugging in these values to the formula, we get:
n = (1.44² * 0.40 * 0.60) / 0.02² ≈ 922.98
Therefore, the minimum number of consumers that should be sampled by the advertiser to be 85% confident that their estimate will fall within 2% of the true population proportion is 923. This means that if the advertiser takes a random sample of 923 consumers and calculates the proportion of consumers who believe what is shown in commercials, there is an 85% chance that this proportion will be within 2% of the true population proportion.
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Find the number of possibilities in each scenario
HW-22.2 Permutations with repetition
A team of 12 lacrosse players need to choose a captain and co-captain ?
The number of possibilities in the given scenario are 144. The solution has been obtained by using permutations.
What is permutation?
Mathematical calculations are used to determine the number of different configurations for a given set, and this procedure is referred to as permutation. A permutation is a phrase that, simply put, refers to the variety of alternative configurations or orders. When employing permutations, the sequence of the arrangement is crucial.
We are given that a team of 12 lacrosse players need to choose a captain and co-captain.
This means that n is 12 and r is 2.
Using permutations, we get
⇒ Total possibilities = [tex]n^{r}[/tex]
⇒ Total possibilities = [tex]12^{2}[/tex]
⇒ Total possibilities = 144
Hence, the number of possibilities in the given scenario are 144.
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The figure shows two semicircles centered at G and H. Point B is on both semicircles. Line DF touches each circle at one point only, points F and E. If DE = 4 and EF = 8, what is the scale factor applied when triangle DEH is dilated to make triangle DFG?
The scale factor applied to make triangle DFG when triangle DEH is dilated is equal to ( 1/3).
From the attached figure,
Side length DE = 4
EF = 8
AB is the diameter of the semicircle with center G,
DF is the tangent at point F.
∠GFD = 90°
BC is the diameter of the semicircle with center H.
DE is the tangent at point E
∠HED =90°
In triangle DFG and DEH,
Each 90 degree.
⇒ ∠GFD = ∠HED
Common angle D
⇒ ∠FDG = ∠EDH
By AA corollary we have,
Triangle GFD and HED are similar triangle.
Corresponding sides are in proportion.
Scale factor applied on triangle DEH is dilated to make triangle DFG.
Scale factor
= DE / DF
= DE / ( DE + EF )
= 4 / ( 4 + 8 )
= 4 / 12
= 1 / 3.
Therefore, the scale factor used to make triangle DFG after dilation of DEH is equal to (1/ 3).
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The above question is incomplete, the complete question is:
The figure shows two semicircles centered at G and H. Point B is on both semicircles. Line DF touches each circle at one point only, points F and E. If DE = 4 and EF = 8, what is the scale factor applied when triangle DEH is dilated to make triangle DFG?
Attached figure.
can someone answer my new math questions please
Answer:
yes
Step-by-step explanation:
NEED HELP NOW PLS!!!!!!!
AB and AD are tangent to circle C. Find x.
Joey deposits $6000 each into the two savings accounts described below. If he doesn’t make any other deposits or withdrawals, find the combined amount of accounts after 10 years.
Account 1
3.5% annual simple interest
Account 2
3.5% annual compound interest
The combined amount in both accounts after 10 years is $16,869.58
What is formula of simple interest and compound interest ?To solve the problem, we need to use the following formulas:
Simple Interest = Principal x Rate x Time
Compound Interest = [tex]Principal * (1 + Rate/ n)^{n * Time}[/tex]
where:
Principal = the initial deposit
Rate = the interest rate (in decimal form)
Time = the number of years
n = the number of times interest is compounded per year
For Account 1:
Simple Interest = Principal x Rate x Time
= $6000 x 0.035 x 10
= $2100
The amount in Account 1 after 10 years will be the initial deposit plus the interest earned:
= $6000 + $2100
= $8100
For Account 2:
Since the interest is compounded annually, n = 1.
Compound Interest = [tex]Principal * (1 + Rate/ n)^{n * Time}[/tex]
= [tex]6000 *(1 + 0.035/1)^{1 * 10}\\= $6000 (1.035)^{10}\\= $8769.58[/tex]
After ten years, the amount in Account 2 will be $8769.58.
After ten years, the combined amount in both accounts will be:
$8100 minus $8769.58 equals $16869.58, resulting in a total of $16,869.58 in both accounts after ten years.
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Can someone help me asap? It’s due tomorrow. I will give brainiest if it’s correct
Answer:
96
Step-by-step explanation:
the mean weight of an adult is 62 kilograms with a variance of 144 . if 195 adults are randomly selected, what is the probability that the sample mean would be greater than 59.5 kilograms? round your answer to four decimal places.
The probability is 0.9835 where the sample mean would be greater than 59.5 kilograms.
The central limit theorem can be used to approximate the sampling distribution of the sample mean as a normal distribution.
where the mean equals the population mean (μ = 62 kg) and the standard deviation equals the population standard deviation divided by the square root of sample size (σ/sqrt (n) = sqrt(144 / 195) = 2.4287 kg).
Next, find the probability that the sample mean is greater than 59.5 kilograms.
z = (59.5 - 62) / (2.4287 / square (195)) = -2.1295
Using an ordinary regular table or calculator, we know that the probability of a Z-score less than -2.1295 is 0.0165.
Therefore, the probability that the sample mean exceeds 59.5 kilograms is
1 - 0.0165 = 0.9835
Rounding to four decimal places gives a probability of 0.9835.
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Evaluate: step by step please
The evaluation of the equation given above after substitution of both X and y would be = 6.
How to evaluate the given equation after substitution?Given that;
X = 2
y = 8
The equation = xy² - x²y/xy
Substitute X = 2 and y = 8 into the equation given above;
=2(8)²- 2²(8)/2×8
= 2×64 - 4×8/16
= 128 - 32/16
= 96/16
= 6.
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find the distance between each pair of points. round your answer to the newest tenth, if necessary.
Answer:
The distance between (0, 3) and (2, 4) is:
[tex] \sqrt{ {(4 - 3)}^{2} + {(2 - 0)}^{2} } [/tex]
[tex] \sqrt{ {1}^{2} + {2}^{2} } [/tex]
[tex] \sqrt{5} = 2.236[/tex]
To the nearest tenth, √5 = 2.2
Find the volume of a pyramid with a square base, where the perimeter of the base is
10.4in 10.4 in and the height of the pyramid is 9.6 in
9.6 in. Round your answer to the nearest tenth of a cubic inch.
Answer:
The volume of a pyramid with a square base can be found using the formula:
V = (1/3)Bh
where B is the area of the base and h is the height of the pyramid.
In this problem, we are given that the perimeter of the base is 10.4 in, which means that each side of the square base has a length of 10.4 in / 4 = 2.6 in. Therefore, the area of the base is:
B = (2.6 in)^2 = 6.76 square inches
We are also given that the height of the pyramid is 9.6 in.
Substituting these values into the formula for the volume of a pyramid, we get:
V = (1/3)(6.76 sq in)(9.6 in)
V = 20.416 cubic inches
Rounding to the nearest tenth of a cubic inch, the volume of the pyramid is approximately 20.4 cubic inches.
what are the positive and negative square roots of 400?
The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, the number is 400. So, the positive square root of 400 is a number that, when multiplied by itself, gives 400, and the same goes for the negative square root of 400.
What are the positive and negative square roots of 400?The positive square root of 400 is 20, because 20 multiplied by itself equals 400. The negative square root of 400 is -20, because -20 multiplied by itself also equals 400.
It is important to note that in many contexts, the square root of a positive number is taken to be the positive root. However, in some cases, such as solving certain equations or working with geometric objects, both the positive and negative roots may be considered.
In summary, the positive and negative square roots of 400 are 20 and -20, respectively.
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23. What is the solution set of the equation
x²-3x - 10 = 0
(1) {5,-2}
(2){-5,-2}
(3) { 5,2}
(4) {-5,2}
Answer:
Step-by-step explanation:
x²-3x - 10 = 0
x² -5x + 2x - 10 = 0
(x² -5x)+ (2x - 10) = 0
x(x - 5) +2(x - 5) = 0
(x + 2) (x - 5) = 0
x +2 = 0
x = -2
OR
x -5 = 0
x = 5
hence ans is, (1) {5,-2}
PLEASE ANSWER ASAP
1. How many atoms are present in 8.500 mole of chlorine atoms?2. Determine the mass (g) of 15.50 mole of oxygen.
3. Determine the number of moles of helium in 1.953 x 108 g of helium.
4. Calculate the number of atoms in 147.82 g of sulfur.
5. Determine the molar mass of Co.
6. Determine the formula mass of Ca3(PO4)2.
IT WOULD BE HELPFUL
SHOW WORK
The Number of atoms ≈ 5.119 x 10^24 atoms
The Mass ≈ 248.0 g
Mass ≈ 248.0 g
How many atoms are present in 8.500 mole of chlorine atoms?To find the number of atoms, we use Avogadro's number, which is 6.022 x 10^23 atoms/mole.
Number of atoms = (8.500 moles) * (6.022 x 10^23 atoms/mole)
Number of atoms ≈ 5.119 x 10^24 atoms
Determine the mass (g) of 15.50 mole of oxygen.To find the mass, we need the molar mass of oxygen, which is 16.00 g/mole.
Mass = (15.50 moles) * (16.00 g/mole)
Mass ≈ 248.0 g
Determine the number of moles of helium in 1.953 x 10^8 g of helium.
To find the number of moles, we need the molar mass of helium, which is 4.00 g/mole.
Number of moles = (1.953 x 10^8 g) / (4.00 g/mole)
Number of moles ≈ 4.883 x 10^7 moles
Calculate the number of atoms in 147.82 g of sulfur.
To find the number of atoms, we first need to find the number of moles of sulfur, and then use Avogadro's number. The molar mass of sulfur is 32.07 g/mole.
Number of moles = (147.82 g) / (32.07 g/mole)
Number of moles ≈ 4.609 moles
Number of atoms = (4.609 moles) * (6.022 x 10^23 atoms/mole)
Number of atoms ≈ 2.772 x 10^24 atoms
Determine the molar mass of Co.
The molar mass of cobalt (Co) is 58.93 g/mole.
Determine the formula mass of Ca3(PO4)2.
To find the formula mass, we need to add up the molar masses of all the elements in the compound.
Ca3(PO4)2 contains 3 calcium (Ca) atoms, 2 phosphorus (P) atoms, and 8 oxygen (O) atoms.
Molar mass of Ca = 40.08 g/mole
Molar mass of P = 30.97 g/mole
Molar mass of O = 16.00 g/mole
Formula mass = (3 * 40.08) + (2 * 30.97) + (8 * 16.00)
Formula mass = 120.24 + 61.94 + 128.00
Formula mass ≈ 310.18 g/mole
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2) yeast is doubling in the container every minute. starting with a small amount, it takes 80 minutes to fill the container. how long will it take to fill one half of the container? what kind of a sequence are we dealing with?
The problems realted to doubling growth rate is solved using an exponential model. If it takes 80 minutes to fill the container, then it will take 79 minutes to fill one half of the container. The dealing sequence is a,a²,a⁴, a¹⁶,...... where a is intial amount.
An exponential model, is used here. The reason for this is that the growth rate is very high which an exponential model can accurately replicate. We have a yeast population is doubling in the container every minute. That is if it's population in container is half at present then the container become full filled in next minute. This also means is that if we know the quantity after a certain number of minutes, the quantity a minute earlier must have been half of that. Let the intial amount be 'x'. Total time taken by yeast to fully fill up the container = 80 minutes
We have to determine the time it take to fill one half of the container. Now, the container gets full in 80 minutes. Half of this quantity must have been meant that the container was half full. Thus, the container was half full 79 minutes after the yeast was put in it. We are dealing with a sequence something like that a, a², a⁴,___.
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Find the value of A that makes the following equation true for all values of x
0. 9^60x = A^x
The value of A that makes the equation true for all x values is 0.9⁶⁰. Using the exponential function we can find out the value of A.
We have to apply the properties of exponential functions to solve for A. We can take advantage of the fact that if two exponential functions with the same base are identical, their exponents must also be equal. To put it another way, if:
aˣ = bˣ
then:
a = b
We may equal the exponents of 0.9 and A using this property:
60x * log(0.9) = x * log(A)
where a log is the logarithm of base ten.
When we simplify this equation, we get:
log(0.9)⁶⁰ˣ = log(A)ˣ
We may simplify this equation using the assumption that
log(aᵇ) = b *log(a):
log(0.9⁶⁰ˣ) = 60x * log 0.9
log (Aˣ) = x log A
log(0.9) * 60x = log(A) * x
When we solve for A, we get:
A = 0.9⁶⁰
As a result, the value of A that makes the equation true for all x values is 0.9⁶⁰.
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If the correlation between x and y is .75 , what percent of the varitince is shared variance (what is the coefficient of determination)? 56% 43% 75% 36%
As a percentage, this is 56.25%, which is closest to 56% from the provided options. Therefore, 56% of the variance is shared variance
The coefficient of determination is calculated by squaring the correlation coefficient (r) between x and y. In this case, the correlation coefficient is 0.75. To find the shared variance (coefficient of determination), simply square this value:
0.75² = 0.5625
As a percentage, this is 56.25%, which is closest to 56% of the provided options. Therefore, 56% of the variance is shared variance.
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The viridine is shared variance percent 56.25%.
The coefficient of determination, also known as R-squared.
The proportion of the variance in the dependent variable (y) that is explained by the independent variable (x).
It is calculated as the square of the correlation coefficient (r) between x and y.
The correlation between x and y is.
.75, the coefficient of determination can be calculated as[tex](.75)^2 = .5625,[/tex]which is equivalent to 56.25%.
This means that 56.25% of the variance in y can be explained by the variance in x.
The remaining 43.75% of the variance is attributed to other factors not accounted for by x.
It is important to note that correlation does not imply causation.
A high correlation between two variables does not necessarily mean that one variable causes the other.
It simply means that there is a strong relationship between the two variables.
It is important to consider other factors and potential confounding variables when interpreting the relationship between x and y.
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Mr. Lewis and Ms. Yonkers are grading 87 papers for a math class. Mr. Lewis has already grade 32, but Ms. Yonkers has only graded 16. Write an equation with the variable (p) and show your work to determine how many papers they have left to grade.
The number of papers they have left to grade is 39.
What is Subtraction?
Subtraction is a mathematical operation that involves taking away or removing a certain number of items or quantity from a larger group. It is the inverse of addition and is denoted by the minus sign (-).
Let p be the number of papers they have left to grade.
The total number of papers is 87, and Mr. Lewis has already graded 32 and Ms. Yonkers has graded 16, so the number of papers they have left to grade is:
p = 87 - 32 - 16
p = 39
Therefore, they have 39 papers left to grade.
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explain whether the mean or the median is amore appropriate measure of center for this data set?
The mean and median are both measures of center, but which one is more appropriate depends on the data set.
What is appropriate?Appropriate behavior is behavior that is socially acceptable and respectful of others. This includes treating others with kindness, politeness, and respect, refraining from using offensive language, and not engaging in hurtful or violent behavior. Appropriate behavior also means following established rules, laws, and cultural norms. Examples of appropriate behavior include being honest and trustworthy, showing respect for others and their property, and being courteous and polite.
The mean is the average of the data set and is affected by extreme values. The median is the middle value in the data set and is not affected by extreme values. If the data set has extreme values, the median is usually the more appropriate measure of center. If the data set does not have extreme values, the mean is usually the more appropriate measure of center.
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2 out of 7 questions. PLEASE help me.
The measure of arc angle KL is determined as 128⁰.
The measure of angle KJL is 26⁰
What is the measure of arc KL?The measure of arc angle KL is calculated by applying the following formula.
The intersecting chord theorem, also known as the intersecting chords inside and outside theorem, is a geometric property that applies to chords (line segments that connect two points on the circumference of a circle) that intersect inside or outside a circle.
Based on the angle of intersecting chord theorem, we will have the following equation.
m∠KML = ¹/₂( arc angle KL )
64 = ¹/₂ KL
KL = 2 x 64
KL = 128⁰
The measure of angle KJL is calculated as follows;
m∠KJL = ¹/₂ (180 - 128) = 26⁰
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will give brainliest!!
Answer:
Remember SOHCAHTOA
SOH- Sin= Opposite/Hypotenuse
CAH- Cosine= Adjacent/Hypotenuse
TOA- Tangent= Opposite/Adjacent
sin Θ is 24/25
cos Θ is 7/25
tan Θ is 24/7
Step-by-step explanation:
If using the SOHCAHTOA method all you have to do is memorize your Pythagorean triples
Ex: 3,4,5
7,24,25
5,12,13
why is there a publication bias against null effects? a. null effects are not real. b. people generally want to read about independent variables that change the outcome. c. null effects are the result of badly designed studies. d. null results happen less often than significant results.
The correct answer is option C, The main reason for publication bias against null is that null results are less frequent than significant results.
In research, a "significant" result is one that meets some level of statistical significance, usually limited to p < . 0.05.
This implies that the watched impact is improbable to have emerged simply by chance and there's proof to bolster the theory being tried.
On the other hand, a 'null' result may be a result that does not meet this level of measurable importance,
proposing no critical contrast between bunches or no critical impact of the autonomous variable on the subordinate variable.
Because research emphasizes statistical significance, null results are often viewed as less interesting and less valuable than significant results.
As a result, researchers are less likely to submit zero results for publication, and journals may be less likely to accept them.
This can lead to a bias in the published literature where only studies with significant results are published and studies with zero results remain unpublished or buried in the "drawer" of researchers.
This can lead to an overestimation of the effects of certain variables and treatments, which can hinder scientific progress by hiding important information about ineffective ones.
It is important to note that null results are not necessarily the result of poorly designed studies.
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the scores of the top quartile of students in a math class were 95, 86, 87, 91, 94, and 87 on the last test. what is the average score of these top students?
90 is the average score of these top students.
What is the average in mathematics?
Mean is defined as the average equal to the ratio of the total number of values in a particular set to the total number of values in the set.
The average in mathematics is the average of a data set obtained by adding all the numbers and dividing the sum of the numbers by the number of numbers. For example, using the following dataset:
8, 9, 5, 6, 7, 8 + 9 + 5 + 6 + 7 = 35, 35/5 = 7, so the average is 7.
the average score of these top students = 95 + 86 + 87 + 91 + 94 + 87/6
= 540/6 = 90
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One rectangle is "framed" within another. Find the area of the shaded region if the "frame" is 2 units wide.
The area of the shaded region with dimensions length=5 units and width=2 units is 10 units².
What is area?
It is the extent to which a flat (2-D) figure, surface, or shape of an object occupies all available space.The area of a flat, two-dimensional figure is the area that is enclosed or covered by the boundary of the figure. Additionally, it is the quantity of unit squares that completely cover a closed figure's surface. Square measurements of area include sq. mm, cm2, and m2. Additionally, it describes the area located inside a closed shape's border or limit.
Area of rectangle = length x width
Given dimensions of outer rectangle:length=9 units & width=6 units
Also given that there is a width of frame is 2 units between outer & inner rectangle on all its boundaries.
To find the area of shaded inner rectangle, we need its dimensions.
Length=length of outer rectangle- 2 times width of frame
=9 - 2(2)
=9-4
=5 units
Widthth=width of outer rectangle- 2 times width of frame
=6 - 2(2)
=6-4
=2 units
Area of shaded portion= area of rectangle
= L x W
= 5 x 2
=10 units²
Area of shaded portion=10 units²
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Out of 25 light bulbs tested, 1 was found to be defective. Out of 2000 light bulbs, how many would you expect to be defective?
Answer:
80
Step-by-step explanation:
If 1/25 lightbulbs were defective, you can set up a ratio to figure out the number of lightbulbs if 2000 were made.
[tex]\frac{1}{25} =\frac{x}{2000}[/tex]
Cross multiply.
[tex]25x=2000[/tex]
Divide both sides by 25.
[tex]\frac{2000}{25} =80[/tex]
Hope this helps! :)
A local pottery studio is offering a beginner pottery class. The instructor is paid a flat rate of $100 plus $32 per student. How many people need to enroll for the instructor to earn $516?
i have a new hobby - a saltwater fish tank that will contain mostly live corals (called a reef tank). i am currently in the planning stage and am gathering knowledge to give me the best chance of success with my tank. as part of the planning stage, i reached out to 700 experienced central florida reefers (people who currently have a reef tank) and asked them to provide the following information: size of the tank (in gallons), type of lighting used (florescent, led, hybrid, or other), and how long (in years) they have been in the hobby. part of the analysis involves trying to estimate the proportion of all central florida reefers who use led lighting. a 95% confidence interval was constructed to be: (.648, .752) which of the following practical interpretations is correct? group of answer choices in repeated sampling, 95% of the intervals created will contain the population mean. we are 95% confident that the proportion of all central florida reefers who use led lighting falls between .648 and .752. we are 95% confident that the proportion of the sampled central florida reefers who use led lighting falls between .648 and .752. all central florida reefers use led lighting 95% of the time.
We are 95% confident that the proportion of all central Florida reefers who use LED lighting falls between .648 and .752.
The correct practical interpretation is: "We are 95% confident that the proportion of all central Florida reefers who use led lighting falls between .648 and .752."
This means that if we were to take multiple random samples of 700 experienced central Florida reefers, 95% of the intervals created would contain the true population proportion of reefers who use LED lighting.
So, based on this sample, we can say with 95% confidence that the true proportion of all central Florida reefers who use LED lighting is somewhere between .648 and .752.
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We are 95% confident that the proportion of all central Florida reefers who use LED lighting falls between .648 and .752 from mean.
The correct practical interpretation is: "We are 95% confident that the proportion of all central Florida reefers who use LED lighting falls between .648 and .752." This means that based on the sample of 700 experienced reefers, we can estimate with 95% confidence that the true proportion of all reefers in central Florida who use LED lighting is likely to be between .648 and .752.
This confidence interval was constructed using sampling techniques, and in repeated sampling, 95% of the intervals created would contain the population mean.
We are 95% confident that the proportion of all central Florida reefers who use LED lighting falls between .648 and .752.
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4. The pH of a liquid is a measure of its acidity or alkalinity. Pure water has a pH of 7, which is neutral. Solutions with a pH less than 7 are acidic while solutions with a pH greater than 7 are basic or alkaline. The dataset FloridaLakes gives information, including pH values, for a sample of lakes in Florida. Computer output of descriptive statistics for the pH variable is shown
Answer:
Step-by-step explanation:
Question #5 I really don’t get it I would appreciate an answer it’s been an hour and no response
The value of x is 11 and the measure of the supplementary angle m∠N is equal to 143°. That is:
a. equation:37° + 3x = 180°
b. x = 11, m∠M = 37°, m∠N = 143°
What are supplementary anglesSupplementary angles are a pair of angles that add up to 180 degrees. In other words, if you have two angles that are adjacent (share a common vertex and side) and their measures add up to 180 degrees, then they are supplementary angles.
Given that m∠M and m∠N are supplementary then:
37° + 3x = 180°
3x = 180° - 37° {collect like terms}
3x = 143°
x = 143/3 {divide through by 3}
x = 11
m∠N = 3(11) = 143°.
Therefore, the value of x is 11 and the measure of the supplementary angle m∠N is equal to 143°.
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