Given:
In a right angle triangle, the measure of exterior angle is \((9x+16)^\circ\).
The measure of opposite interior angle is \((5x-14)^\circ\).
To find:
The value of x.
Solution:
Exterior angle theorem: In a triangle the measure of an exterior angle is equal to the measure of sum of two interior angles.
Using exterior angle theorem, we get
\((9x+16)^\circ=90^\circ+(5x-14)^\circ\)
\((9x+16)^\circ=(5x+76)^\circ\)
\(9x+16=5x+76\)
Isolate the variable x.
\(9x-5x=-16+76\)
\(4x=60\)
\(x=\dfrac{60}{4}\)
\(x=15\)
The value of x is 15. So, the measure of the exterior angle is:
\((9x+16)^\circ=(9(15)+16)^\circ\)
\((9x+16)^\circ=(135+16)^\circ\)
\((9x+16)^\circ=151^\circ\)
Therefore, the value of x is 15 and the measure of the exterior angle is 151 degrees.
when calculating basic temperature data, the difference between the highest and lowest monthly means is called ________.
When calculating basic temperature data, the difference between the highest and lowest monthly means is called temperature range.
Temperature range refers to the difference or interval between the highest and lowest monthly mean temperatures. It provides information about the variability in temperatures experienced over a specific period, typically within a month. This range is obtained by subtracting the lowest monthly mean temperature from the highest monthly mean temperature.
Temperature range is an essential metric in climate and weather analysis. It helps to understand the extent of temperature fluctuations and the overall temperature variability in a particular region.
A larger temperature range indicates greater variable, while a smaller range suggests more consistent temperatures.
By examining the temperature range, climatologists, meteorologists, and researchers can gain insights into seasonal temperature patterns, diurnal temperature variations, and potential climate trends.
Temperature range is also relevant for various applications, such as agriculture, energy management, and human comfort assessments.
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Anyone know???????????
Answer:
I cant help I wish I could but its a test
Step-by-step explanation:
60 is the LCM of which of the following pair of number
Answer:
The pair of number that has the LCM of 60 is;
\(15\text{ and 20}\)Explanation:
Given the pairs of number in the answer choices, we want to select the pair that has a LCM of 60;
Let us find the LCM of each of the pairs;
\(\begin{gathered} 12=2\times2\times3 \\ 18=2\times3\times3 \\ \text{LCM = 2}\times2\times3\times3=36 \end{gathered}\)\(\begin{gathered} 10=2\times5 \\ 30=2\times3\times5 \\ \text{LCM}=2\times3\times5=30 \end{gathered}\)\(\begin{gathered} 15=3\times5 \\ 20=2\times2\times5 \\ \text{LCM}=2\times2\times3\times5=60 \end{gathered}\)\(\begin{gathered} 20=2\times2\times5 \\ 25=5\times5 \\ \text{LCM}=2\times2\times5\times5=100 \end{gathered}\)Therefore, the pair of number that has the LCM of 60 is;
\(15\text{ and 20}\)In a quiz contest, Mary answers 90% of the questions correctly without any additional clues from the quiz coordinator. The randomly generated numbers below simulate this situation.
The numbers 0 to 8 represent questions answered correctly without additional clues, and the number 9 represents questions that needed additional clues.
Random Numbers
44 51 99 66 23
68 72 20 20 59
50 89 39 36 20
90 13 51 47 92
49 20 89 10 13
52 82 52 52 99
28 10 33 35 73
40 44 30 95 22
99 10 55 10 35
36 78 92 37 96
The estimated probability that it would take at least three questions for Mary to need additional clues is .
The estimated probability that Mary needed additional clues to answer two consecutive questions is .
The estimated probability that it would take at least three questions for Mary to need additional clues is 0.0014.
To calculate this probability, we can use the formula P(X≥3) = 1 - P(X<3). P(X<3) is the probability of Mary needing additional clues for fewer than three consecutive questions, which is equal to the sum of all the probabilities of Mary needing additional clues for zero, one, and two consecutive questions. This sum is equal to 0.9986. Therefore, P(X≥3) = 1 - 0.9986 = 0.0014.
The estimated probability that Mary needed additional clues to answer two consecutive questions is 0.0166. This is because there are six instances of two consecutive questions requiring additional clues (the 99 and 10 in the last row, the 20 and 20 in the second row, the 39 and 36 in the third row, the 13 and 51 in the fourth row, the 52 and 52 in the fifth row, and the 10 and 55 in the last row).
To calculate this probability, we can use the formula P(X=2) = 1 - P(X<2) - P(X>2). P(X<2) is the probability of Mary needing additional clues for less than two consecutive questions, which is equal to the sum of all the probabilities of Mary needing additional clues for zero and one consecutive questions.
This sum is equal to 0.9850. P(X>2) is the probability of Mary needing additional clues for more than two consecutive questions, which is equal to the probability of Mary needing additional clues for three or more consecutive questions. This probability is equal to 0.0014.
Therefore, P(X=2) = 1 - 0.9850 - 0.0014 = 0.0166.
Therefore, the estimated probability that it would take at least three questions for Mary to need additional clues is 0.0014.
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The height of a ball kicked into the air from the ground can be approximated by the function
h=-5t^2 + 15t, where h is the
height in meters and t is the time in seconds.
Find the time it takes the ball to hit the ground. Show all work
Check the picture below, so that happens when h = 0.
\(\stackrel{h}{0}~~ = ~~-5t^2+15t\implies 0=-5t(t-3)\implies 0=t(t-3)\implies t= \begin{cases} 0\\ 3~\checkmark \end{cases}\)
now, notice, 0 is also a solution, which means at 0 seconds the ball was touching the ground, well, it was kicked "from" the ground, so at 0 seconds it was initially on the ground anyway.
Question 9 of 10
Which of the following rational functions is graphed below?
The rational function that represents the graph is (B) f(x) = x / (x-1) (x+1)
What is the rational function?The ratio of two polynomial functions with a non-zero denominator is known as a rational function. R(x) = P(x)/Q(x), where P(x) and Q(x) are polynomial functions, is the typical way to describe it. We studied the idea of the rational number in previous grades. It is the ratio or product of two integers with a non-zero denominator. As a result, the word ratio is where the name rational comes from.
Given, the graph of the function
To find out vertical asymptote we set the denominator =0
f(x) = x / (x-1) (x+1)
x-1 = 0
⇒ x = 1
x+1 = 0
⇒ x = -1
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If you take out a loan that costs 561.60 over 35 months at an interest rate of 9% how much interest do you owe on the loan
Answer: $167.86
Step-by-step explanation:
Assuming the rate is an annual rate. Convert it to a monthly rate:
= 9% / 12
= 0.75%
Use compound interest formula to find out the total owed:
= Amount * ( 1 + rate) ^ period
= 561.60 * ( 1 + 0.75%)³⁵
= $729.46
Interest = Total owed - cost of loan
= 729.46 - 561.60
= $167.86
How do you add rational expressions examples?
The Example of addition of Rational Expressions is "Add 2/3 and 6/7" .
The Rational Expression is defined as the expression , that is represented in the form of p/q , where q ≠ 0 .
Example of Addition of Rational Expression is
Add 2/3 + 6/7 .
In order to add the above two rational expression , we first make the denominator of both the terms same by taking LCM ,
the LCM of denominators 3 and 7 is 21 .
So , the expression becomes ⇒ 14/21 + 18/21 .
⇒ (14 + 18)/21
Simplifying further ,
we get ;
⇒ 32/21
Therefore , the example of addition of rational expressions is explained above .
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Find the slope of the line.
On a coordinate plane, a line goes through (0, negative 7) and (7, 0).
a.
Negative 7
c.
Negative 1
b.
7
d.
1
Calculations ↓
When we have two points that a line passes through and asked to determine the slope of the line, the slope formula is going to come in handy.
This is the formula :
\(\boxed{\\\begin{minipage}{3cm}slope~formula~: \\ $\displaystyle\frac{y2-y1}{x2-x1}$ \\ \end{minipage}}\)
y2 and y1 are y-coordinates, and x2 and x1 are x coordinates
Plug in the values :
\(\boxed{\\\begin{minipage}{3cm}$\displaystyle\frac{0-(-7)}{7-0} $\end{minipage}}\)
\(\boxed{\\\begin{minipage}{3cm}$\displaystyle\frac{0+7}{7} \end{minipage}}\)
Which simplifies to \(^7/_7\), or 1
Slope ↓1 (Option D.)
hope helpful ~
Two-fifths of a gallon
of deck stain covers
one quarter of a deck.
How much stain is
needed for the entire
deck?
Answer:
8 / 5
Step-by-step explanation:
Since 2/5 gallons cover 1/4 of the deck you would have to multiply 2/5 times 4 to so how much it would take to cover the whole deck so your answer is 8/5 gallons
I really need the answer for this. My teacher about to grade it. Yall please help me out.
Answer: i think that its D
Step-by-step explanation:
im really sorry if its wrong
Answer:
Step-by-step explanation:
Take my answer with a grain of salt as this is an educated guess based on the problem.
The exponentiation rule for raising a power to another power (a^b)^c = a^{bc} therefore a power to a power is equal to the powers multiplied together. so if the base is equal to (32/5) and the power is -2x. some number raised to the x is equal to (32/5)^-2x therefore because -2^x is equal to -2x the answer is B which is the original base (32/5) with the exponent -2 when raised to the x will be equal to (32/5)^-2x.
Therefore, B is the answer
The length of a rectangle is 2cm less than twice the width. If y represents the width, state the inequality that the area of a rectangle is at least 15cm^2
The inequality that represents the area of the rectangle is: y(2y - 2) ≥ 15
What is the Area of a Rectangle?Area of Rectangle = length × widthGiven:
width of rectangle = y cm
length of rectangle = (2y - 2) cm
Area = y(2y - 2)
We are given that the area of the rectangle is at least 15 sq cm.
Therefore, the inequality that represents the area of the rectangle is: y(2y - 2) ≥ 15
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Explain! Reward! Thank you!!!!!
Answer:
1 lb/$4 is the correct answer.
Step-by-step explanation:
its $4 per pound
a. j. lawrance. on conditional and partial correlation. the american statistician, 30:146–149, 1976.
A. J. Lawrance's article sheds light on the concepts of conditional and partial correlation, emphasizing their differences and importance in statistical analysis.
The article titled "On Conditional and Partial Correlation" by A. J. Lawrance, published in The American Statistician in 1976, discusses the concepts of conditional correlation and partial correlation. The main focus of the paper is to explain the difference between these two correlation measures.
Conditional correlation refers to the relationship between two variables while holding a third variable constant. It helps in understanding how the correlation between two variables changes when a third variable is taken into account.
On the other hand, partial correlation measures the strength and direction of the relationship between two variables after removing the influence of other variables.
The author emphasizes that conditional correlation and partial correlation are related but distinct concepts. While conditional correlation considers the correlation between two variables given a third variable, partial correlation quantifies the relationship between two variables by removing the effects of other variables.
The article provides mathematical formulas and explanations to illustrate the calculations of conditional and partial correlations. It highlights the importance of considering these measures in statistical analysis to better understand the underlying relationships between variables.
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how other statistucal values are used to summarize data
Statistics regularly employs tables, charts, and graphs to present data visually.
What is meant by statistical values?Data can be summarized graphically or numerically (see "Graphical techniques in Statistics" for further information on the latter). The methods for numerical and graphical summarization that can be utilized depend on the type of data that was collected.
Statistics regularly employs tables, charts, and graphs to present data visually. The evaluation of raw data for patterns, data entry errors, and outlier values that can affect the statistical interpretation of the data is frequently started with examples like these.
It is important to show the data in tables, charts, and other statistical figures in a way that is both accurate and simple to understand. Additionally, tables are helpful for distilling the original data that forms the basis of a study's findings. To convey a lot of information in a small amount of area, they are effective.
The complete questions is:
Describe why charts/tables and other statistical values are used to summarize data and address the particulars of this assignment (be sure to include a thesis statement).
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Lily begins solving the equation 4(x – 1) – x = 3(x + 5) – 11. Her work is shown below. 4(x – 1) – x = 3(x + 5) – 11 4x – 4 – x = 3x + 15 – 11 3x – 4 = 3x + 4 How can her partial solution be interpreted?
Answer: C
Step-by-step explanation: I just did it in e2020
Answer:
C
Step-by-step explanation:
I took the quiz edge2021
select all the line that have a slope of 5/2
adding a tracking variable to count the number of times a loop executes can be an effective way to measure of answer choicestruefalse
Adding a tracking variable to count the number of times a loop executes can be an effective way to measure the answer choice's truthfulness.
Adding a tracking variable to count the number of loop executions can indeed be a useful technique for various purposes. By incrementing the tracking variable within the loop, we can keep track of the number of times the loop body is executed. This information can be valuable in measuring the accuracy or efficiency of the loop and evaluating the truthfulness of an answer choice.
For example, when comparing different algorithms or approaches, counting loop iterations can help determine which solution performs better. It provides a quantitative measure to assess time complexity or resource usage. Additionally, the tracking variable can be used to validate the correctness of a loop by ensuring that the expected number of iterations is reached.
By monitoring the loop execution count, we can gain insights into the behavior of the code, identify potential issues such as infinite loops, and make informed decisions based on the observed results. Hence, adding a tracking variable to count loop executions can be an effective technique to measure the truthfulness or performance of an answer choice in certain scenarios.
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Given points A(-1,4) and B(x,7), determine the value(s) of x if AB=5cm
The value of x is either 3 or -5 based on the distance formula.
What is a co-ordinate system?
In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.
Main body:
according to question
Given points A(-1,4) and B(x,7)
Also AB = 5 cm
Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)
here by using points ,
5 = \(\sqrt{(x+1)^{2} +(7-4)^{2} }\)
taking square on both side ,'
25 = \((x+1)^{2} +3^{2}\)
25-9 = (x+1)²
16 = (x+1)²
taking square root on both sides,
x+1= ±4
x = 4-1 = 3 or x = -4-1 = -5
Hence value of x is either 3 or -5.
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OK!!! I NEED HELP AGAIN AND ITS HONESTLY SUPER EASY :/ I DONT KNOW WHY IM NOT doing it BY MYSELF BUTTTTT---- GIVING BRAINLIEST, FIVE STARS AND THANKSSS!
Which measurement is most accurate to describe the amount a soup bowl could hold?
4 fl. oz.
16 fl. oz.
3 pints
1 quart
Answer: 16 fl oz
Step-by-step explanation:
Answer:
1 quart sorry if I'm wrong
Step-by-step explanation:
choose an american adult at random. the probability that you choose a woman is 0.52. the probability that the person you choose has never been married is 0.25. the probability that you choose a woman who has never been married is 0.11. the probability that person you choose is either a woman or has never been married (or both) is therefore about a. 0.77 b. 0.66 c. 0.44 d. 0.38
Using probability of union set,
the probability that person you choose is either a woman or has never been married is 0.66..
We have given that
If X be random variable that an American adult selected.
Assume that
A : selected adult is a women
B : selected adult has never married
Probability that you choose a woman, P(A) = 0.52
Probability that the person you choose has never been married , P(B) = 0.25
Probability that you choose a woman who has never been married , P(A∩B) = 0.11
we have to calculate probability that person you choose is either a woman or has never been married, P(A∪B)
Using the formula,
P(A∪B ) = P(A) + P(B) - P(A∩B)
pluging all known values in above formula we get
=> P(A∪B ) = 0.52 + 0.25 - 0.11
=> P(A∪B) = 0.77 - 0.11 = 0.66
Hence, the required probability is 0.66..
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Which of the following is equal to 7?
A. /81
B. /49
C. /64
D. /36
A(-1,-5), B(5,-2) and C(1, 1).
ABCD is a trapezium.
AB is parallel to DC and angle BAD is 90°.
Find the coordinates of D.
Answer:
D(-3, -1)
Step-by-step explanation:
The given coordinates are;
A(-1, -5), B(5, -2) and (1, 1)
The coordinates and the coordinates of the point D form a trapezium
The parallel sides of the trapezium ABCD = AB and DC
The angle ∠BAD = 90°
The coordinates of the point D = Required
Let (x, y) represent the x and y-coordinates of the point D, by the given information, we get;
The slope of the line DC = The slope of the line AB
The slope of AB = (-2 - (-5))/(5 - (-1)) = 3/6 = 1/2
∴ The slope of CD, m = 1/2
From the point C(1, 1),the equation of the line CD is therefore;
y - 1 = (1/2)·(x - 1)
∴ y = x/2 - (1/2) + 1 = x/2 + 1/2
y = x/2 + 1/2
Given that ∠BAD is 90°, therefore, AD is perpendicular to DC and we have;
The slope of AD = -1/m
∴ The slope of AD = -1/(1/2) = -2
From the point A(-1, -5), the equation of the line AD is therefore;
y - (-5) = -2·(x - (-1))
y = -2·x - 2 - 5 = -2·x - 7
y = -2·x - 7
Equating both (simultaneous) values of y to find the value of x gives;
y = y, therefore;
x/2 + 1/2 = -2·x - 7
x/2 + 2·x = 5·x/2 = -7 - (1/2) = -15/2
∴ 5·x/2 = -15/2
x = (-15/2) × (2/5) = -3
x = -3
From y = -2·x - 7, and x = -3, we get;
y = -2 × (-3) - 7 = 6 - 7 = -1
The coordinates of the point D(x, y) = (-3, -1).
one less than the product of a number and 3 is 5 more than the number itself.
Answer:
x=3
Step-by-step explanation:
3x-1=5+x is the equation.
So 2x-1=5 and 2x=6
x=3
if a bookmaker quotes payoff odds of 99 to 1 against a particular horse winning a race, does that suggest the chance that the horse will win
The quoted payoff odds of 99 to 1 against a particular horse winning a race suggests the chance that the horse will not win the race.
Odds are a term used to describe the likelihood of an event. The odds are the ratios between the number of possibilities for an event and the number of possibilities for its non-occurrence.
The ratio of the number of possible outcomes to the number of possible outcomes that cannot occur is known as the odds in favor.
Odds in favor = Number of successes: Number of failures.
The ratio between the number of ways an outcome cannot occur and the number of ways it can occur is known as the odds against.
Odds against = Number of failures: Number of successes.
In the question, we are asked that if a bookmaker quotes payoff odds of 99 to 1 against a particular horse winning a race, suggest the chance that the horse will win.
The ratio given to us is 99:1, implying that 99% chance is the failure of the horse, whereas 1% chance is there for the horse winning the race since it is for the odds against a particular horse winning a race.
Thus, the quoted payoff odds of 99 to 1 against a particular horse winning a race suggests the chance that the horse will not win the race.
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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
What value of p makes the equation true?
Answer:
1/8
Step-by-step explanation:
●●○•°°°□□●○○○○○••••
find the range f(n)=-4n-5 if the domain is -7
Answer:
23
Step-by-step explanation:
y=f(n)=( -4× -7)-5
f(n)=28-5 =23
find the value of x.
55+5x degrees
Answer:
If 55 + 5x = 0 then x = -11
Step-by-step explanation:
To find x just get it by itself
55 + 5x = 0
subtract 5x
55 = -5x
then divide by -5
-11 = x
Marta is making a flag with the given dimensions. The perimeter of the flag is 100 inches. A triangle has side lengths of 18 inches and 41 inches. How much material, in square inches, is needed to make the flag? square inches If the material costs $0.15 per square inch, how much will Marta spend on materials to make the flag? $
Answer: 54
Step-by-step explanation:
trust me
360 sq feet
$54
source: truuuuust me bro
Which expression has a value closest to 1? (Use 3.14 as the value of .)