3. A fence on a hill uses vertical posts L and M to hold parallel rails N and P. <4 and <14 are alternate exterior angles. What is the transversal?
Answers
Given information:
A fence on a hill uses vertical posts L and M to hold parallel rails N and P
The diagram is attached below
Here lines N and P are parallel lines
Transversal line for parallel lines N and P is line L
Calculation:
angle 1 and angle 16 are consecutive exterior angles
If parallel lines are cut by a transversal then consecutive exterior angles are supplementary.
<1 +< 16 = 180
115+ < 16 = 180
< 16 = 180 - 15
< 16 = 65
So measurement of angle 16 = 65 degrees.
Related Questions
Consider the polynomial
(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)
Combine all like terms and enter the coefficients for each term into the blanks below
Answers
(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)
First, let's remove the parentheses:
4mn^2 - 2mn + 6 + 6mn^2 - 1 - mn^2 + 2 - 9mn
Next, let's combine like terms by adding or subtracting coefficients of the same variables:
(4mn^2 + 6mn^2 - mn^2) + (-2mn - 9mn) + (6 + 2 - 1)
Simplifying further:
9mn^2 - 11mn + 7
So, the coefficients for each term are:
9, -11, 7
alex, beverly and carl live on the same straight road. alex lives 12 miles from beverly and carl 4 mies from berve,y, how far does alex live from carl?
Answers
Carl to Beverly = 4 miles
So it’s 12 + 4 = 16 miles
please help me asap!!!!!
Answers
Answer:
392
Step-by-step explanation:
1.49×10⁸/3.8×10⁵ = 392
URGENT *EASY 10 POINTS* : Show steps to get the expression ln(sqrt(2) +1) - ln(1/sqrt(2)) equal to -ln(1-(1/sqrt2))
Answers
Answer:
Step-by-step explanation:
To show that the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\), we can simplify both sides of the equation using the properties of logarithms. Here are the steps:
Step 1: Simplify the expression on the left side:
\(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\)
Step 2: Apply the logarithmic property \(\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)\) to combine the logarithms:
\(\ln\left(\frac{\sqrt{2} + 1}{\frac{1}{\sqrt{2}}}\right)\)
Step 3: Simplify the expression within the logarithm:
\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)}\right)\)
Step 4: Simplify the denominator by multiplying by the reciprocal:
\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)} \cdot \sqrt{2}\right)\)
\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{\left(\frac{1}{\sqrt{2}}\right) \cdot \sqrt{2}}\right)\)
\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)
Step 5: Simplify the numerator:
\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)
\(\ln\left(\sqrt{2}(\sqrt{2} + 1)\right)\)
\(\ln\left(2 + \sqrt{2}\right)\)
Now, let's simplify the right side of the equation:
Step 1: Simplify the expression on the right side:
\(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\)
Step 2: Simplify the expression within the logarithm:
\(-\ln\left(\frac{\sqrt{2} - 1}{\sqrt{2}}\right)\)
Step 3: Apply the logarithmic property \(\ln\left(\frac{a}{b}\right) = -\ln\left(\frac{b}{a}\right)\) to switch the numerator and denominator:
\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)
Step 4: Simplify the expression:
\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)
\(-\ln\left(\frac{\sqrt{2}(\sqrt{2} + 1)}{1}\right)\)
\(-\ln\left(2 + \sqrt{2}\right)\)
As we can see, the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) simplifies to \(\ln(2 + \sqrt{2})\), which is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\).
Marcus needs to find out the number of cakes he can make from a 50-pound bag of flour. If it takes 2 cups of flour to make one cake and there are 4 cups to every pound of flour, how many cakes can Marcus make with the bag of flour?
A. 5
B. 12
C. 20
D. 80
Answers
Answer:
20
Step-by-step explanation:
I don't know I just Lucky guessed but hope it helps and I was right
Answer:
Answer is 100
Step-by-step explanation:
It's given that there are 4 cups to every pound,so with one pound of flour Marcus can make 2 cakes.With 50 pound of flour he can make
50 × 2 = 100.
In the real world, functions are mathematical representations of input-output situations. A vending machine is one such example. The input is the money combined with the selected button. The output is the product.
Here is another example: The formula for converting a temperature from Fahrenheit to Celsius is a function expressed as:
C = (5/9)*(F - 32), where F is the Fahrenheit temperature and C is the Celsius temperature.
If it is 77 degrees Fahrenheit in Phoenix Arizona, then what is the equivalent temperature on the Celsius thermometer?
Our input is 77.
C = (5/9)*(77 - 32)
C = (5/9)*(45)
C = 25
The equivalent temperature is 25 degrees Celsius.
To complete the Discussion activity, please do the following:
Choose your own function or choose from the list below and then provide a unique example of a function and evaluate the function for a specific input (like the example above).
Arm length is a function of height.
The circumference of a circle is a function of diameter.
The height of a tree is a function of its age.
The length of person's shadow on the ground is a function of his or her height.
Weekly salary is a function of the hourly pay rate and the number of hours worked.
Compound interest is a function of initial investment, interest rate, and time.
Supply and demand: As price goes up, demand goes down.
Answers
The correct answer is John's weekly salary is $240 based on his hourly pay rate and the number of hours worked.
Let's choose the function "Weekly salary is a function of the hourly pay rate and the number of hours worked."Example: John works as a part-time employee at a grocery store. His hourly pay rate is $12, and he worked for 20 hours in a week. We can evaluate the function to find his weekly salary.
Weekly salary = Hourly pay rate * Number of hours worked
Weekly salary = $12/hour * 20 hours
Weekly salary = $240
So, John's weekly salary is $240 based on his hourly pay rate and the number of hours worked.
Learn more about temperature here:
https://brainly.com/question/25677592
#SPJ8
which values of x are solutions to the eqaution below? 4x^2-30=34
Answers
In the following equation, what are the possible values for c and d?
Answers
PQRS is a quadilateral in which <PQR=74°;
<PSR 48°, <SRQ=116°. If <QPS is bisected to
meet QR at M, calculate the size of <PMQ
Answers
What are the coordinates of the vertex of the parabola with the equation y = x + 2x - 3?
Answers
Answer:
The coordinates of the vertex are (-1,-4).
Step-by-step explanation:
Equation of the Quadratic Function
The vertex form of the quadratic function has the following equation:
\(y-k=a(x-h)^2\)
Where (h, k) is the vertex of the parabola that results when plotting the function, and a is a coefficient different from zero.
We are given the function:
\(y=x^2+2x-3\)
We must transform the equation above by completing squares:
The first two terms can be completed to be the square of a binomial. Recall the identity:
\(x^2+2xy+y^2=(x+y)^2\)
Thus if we add and subtract 1:
\(y=(x^2+2x+1)-3-1\)
Operating:
\(y=(x^2+2x+1)-4\)
The trinomial in parentheses is a perfect square:
\(y=(x+1)^2-4\)
Adding 4:
\(y+4=(x+1)^2\)
Comparing with the vertex form of the quadratic function, we have the vertex (-1,-4).
The coordinates of the vertex are (-1,-4).
We are given a Student's t distribution with d.f. = 11 and t = 1.910. We wish to find an interval containing the corresponding P-value for a two-tailed test. To do this, we will use the Critical values for Student's t Distribution. Below is an excerpt from this table.
one-tail area 0.250 0.125 0.100 0.075 0.050 0.025 0.010 0.005 0.0005
two-tail area 0.500 0.250 0.200 0.150 0.100 0.050 0.020 0.010 0.0010
d.f. \ c 0.500 0.750 0.800 0.850 0.900 0.950 0.980 0.990 0.999
⋮
9 0.703 1.230 1.383 1.574 1.833 2.262 2.821 3.250 4.781
10 0.700 1.221 1.372 1.559 1.812 2.228 2.764 3.169 4.587
11 0.697 1.214 1.363 1.548 1.796 2.201 2.718 3.106 4.437
To determine where the given t-value would fall, we look for the row with heading d.f. =
. In this row, the sample statistic t = 1.910 falls between t = 1.796 and t =
Answers
To determine where the given t-value would fall, we look for the row with heading d.f. =11. In this row, the sample statistic t = 1.910 falls between t = 1.796 and t = 2.201
How to determine the t values?The given parameters are:
Degree of freedom, df = 11Sample statistic, t = 1.910This means that
df = 11 and t = 1.910
To calculate the t value,
We check the row where the heading of the degree of freedom is 11
i.e. df = 11
On this row, the t value 1.910 would be between 1.796 and 2.201
This is because 1.910 is greater than 1.796 and it is less than 2.201
Hence, the complete statement is
To determine where the given t-value would fall, we look for the row with heading d.f. =11. In this row, the sample statistic t = 1.910 falls between t = 1.796 and t = 2.201
Read more about degree of freedom at:
https://brainly.com/question/17305237
#SPJ1
The length of a new rectangular playing field is 4 yards longer than quadruple the width. If the perimeter of the rectangular playing field is 488 yards, what are its dimensions?
Answers
Answer:
w = 48
w = 196
Step-by-step explanation:
Width = w
Length = l = 4 + 4w
Use the values for length and width above along with the given value for perimeter in the formula for perimeter.
P = 2l + 2w
488 = 2(4 + 4w) + 2w
488 = 8 + 8w + 2w
488 = 8 + 10w
488 - 8 = (8 + 10w) - 8
480 = 10w
(480)/10 = (10w)/10
48 = w
w = 48
The width is 48 yards. Use this value to solve for length.
l = 4 + 4w
l = 4 + 4(48)
l = 4 + 192
l = 196
The length is 196 yards.
The manufacturer of a drink wishes to compare the taste appeal of the standard formula (formula A) with that of a new formula (formula B). Each of the four judges is given three glasses in random order, two containing formula A and the other containing formula B. Each judge is asked to state which glass he or she most enjoyed. Suppose that the two formulas are equally attractive. Let Y be the number of judges stating a preference for the new formula. What is the distribution of Y
Answers
Answer:
P(y) = 4Cy * (2/3)^y * (1/3)^4-y
Step-by-step explanation:
Two distinguishable categories ; A and B ;
Number of cups of formula A given to each judge = 2
Number of cups of formula B given to each judge = 1
Total number of cups = 3
P(formula A) = 2/3
P(formula B) = 1/3
Hence, Probability of each of the two formulas is the same for each judge
Number of judges = 4
Each outcome is independent
y = Number of judges who prefer the new formula
Since, it meets all requirements for a binomial probability distribution :
Hence. The distribution of y ;
4Cy * p(A)^y * p(B)^4-y
P(y) = 4Cy * (2/3)^y * (1/3)^4-y
Easy question right here!
Answers
Answer: z=-9.5
Step-by-step explanation: -9.5/2=-4.75
You can use the notation P(A), read “the probability of event B, given event A” to write a
A. Probability distribution
B. Frequency table
C. Conditional probability
D. Cumulative probability
Answers
You can use the notation P(A), read “the probability of event B, given event A” to write a conditional probability. The correct answer is C.
Conditional probability refers to the probability of one event occurring given that another event has already occurred. In this case, we are interested in the probability of event B occurring given that event A has already occurred, and we can represent this using the notation P(B|A), where '|' means 'given'.
For example, let's say we are interested in the probability of getting a head on a coin toss (event B), given that the coin was flipped and landed on heads (event A). We could represent this using the notation P(B|A). The value of P(B|A) would be 1, because if the coin already landed on heads, then the probability of getting a head on the next flip is certain.
Conditional probability is an important concept in probability theory and is often used in real-world applications, such as predicting the likelihood of a disease given certain symptoms, or the probability of an event occurring given certain conditions.
The correct answer is C.
To learn more about probability click on,
https://brainly.com/question/29259732
#SPJ1
4) Martin compares the prices of paper towels. A 3-roll package is priced at $2.89. A single
rollis priced at $89. Based on price alone, which is the better buy?
Answers
Answer:
assuming prices are correctly shown: 3-roll packageassuming a typo: single rolls.Step-by-step explanation:
If single rolls are indeed priced at $89 each, the 3-roll package is a much better buy.
We suspect that the single rolls are priced at $0.89 each, which means you can buy 3 of them for less than $2.70. At this price, single rolls are a better buy.
Identify the angles of rotational symmetry for the figure.
there can be more than one options
Answers
(0.020(5/4) + 3 ((1/5) – (1/4)))
Answers
Answer:
- 0.125
Step-by-step explanation:
Given the equation :
(0.020(5/4) + 3 ((1/5) – (1/4)))
0.020(5/4) = 0.025
3((1/5) - (1/4)) = 3(1/5 - 1/4) = 3(-0.05) = - 0.15
0.025 + - 0.15 = 0.025 - 0.15 = - 0.125
Maricopa's Success scholarship fund receives a gift of $ 145000. The money is invested in stocks, bonds, and CDs. Stocks pay 6.7 % interest, bonds pay 2.5 % interest, and CDs pay 5.75 % interest. Maricopa Success invests $ 10000 more in bonds than in CDs. If the annual income from the investments is $ 6977.5 , how much was invested in each account?
Maricopa Success invested $ in stocks.
Maricopa Success invested $ in bonds.
Maricopa Success invested $ in CDs.
Answers
Answer:
stocks: $45000bonds: $55000CDs: $45000Step-by-step explanation:
You want to know the amounts invested in stocks, bonds, and CDs when the total investment is $145000, $10000 more is invested in bonds than CDs, earnings are $6977.50, and rates of return are 6.7% for stocks, 2.5% for bonds, and 5.75% for CDs.
SetupWe can write three equations in 3 unknowns for this problem. Let s, b, c represent amounts invested in stocks, bonds, and CDs, respectively. Then the problem statement tells us the relations are ...
s + b + c = 145000b - c = 100000.067s +0.025b +0.0575c = 6977.50SolutionThese equations can be solved using any of several methods. The second equation offers a nice relation between b and c, so substitution for one or the other of those will reduce the equations to two equations in two unknowns.
We prefer a calculator solution using an augmented matrix of the coefficients. That is shown in the attachment. It tells us the investment amounts are ...
stocks: $45000bonds: $55000CDs: $45000__
Additional comment
Using b = c +10000, the two remaining equations are ...
s +2c = 1350000.067s +0.0825c = 6727.50<95141404393>
Solve the equation for x: 126 = 3x.
A. x = 378
B. x = 129
C. x = 123
D. x = 42
Answers
Answer:
The answer is answer D, x=42.
Step-by-step explanation:
To isolate the variable, you need to divide both sides of the equation by three, using the division property of equality. 126/3=42 , and 3x/3=x , this gives you 42=x, or x=42, meaning the answer is D.
PLEASE HELP!!!!Choose the equation below that is equivalent to 4(x - 7) - 2(x + 1) = -10
2(x - 7) + (x + 1) = -5
2(x - 7) - (x + 1) = 5
-2(x - 7) + (x + 1) = -5
-2(x - 7) + (x + 1) = 5
Answers
Answer:
\(-2(x-7)+(x+1)=5\)
Step-by-step explanation:
We can divide both sides by -2 to obtain
\(-2(x-7)+(x+1)=5\)
Which fractions are equivalent to 1012?
Answers
\(50/60\)
That should be your answer
Answer:
Hello, There! I'm here to help!
QuestionWhich fractions are equivalent to 10/12?
AnswerAccording to The Question I'm guessing you mean 10/12
If so The Following Fractions are Equilvalent to 10/12
1. 20/24
2. 30/36
3. 40/48
5. 50/60
Step-by-step explanation:
To get Eqilvalent You Can Multiply Number to the fractions to find out what's Equilvalent
Therefore, I hope this helps you!
A group of collage students are going to a lake house for the weekend and plan on renting small cars(s) and large(l) cars to make the trip. Each car can hold 5 people and each large car 8 people. A total of 15 cars were rented which can hold 90 people altogether. Determine the number of large car and rental cars.
Answers
Answer:
10 small, 5 large
Step-by-step explanation:
if they were all small cars, 5x15 would be 75. there need to be 15 more spots, and each large can hold an extra 3. 15/3 is 5. so there are 10s and 5l
students would need to rent 5 small cars and 8 large cars
the resale value of a go-kart decreased by $20 for every hour it is used after how many hours does the value decreased by $400
Answers
In order to find after how many hours the value will decrease by $400, we just need to divide this value by the change per hour of $20, so we have:
\(\frac{400}{20}=20\)So after 20 hours the value will decrease by $400.
what is 12/$0.89 because i need help like now. So please give me the right answer this time cause last time i failed because i asked brainly.
Answers
Answer:
$13.4 is the answer
Step-by-step explanation:
PLEASE MARK BRAINLIEST
what was the key to getting support for converting from petroleum to synthetic lubricants?
Answers
Answer:
Step-by-step explanation:
Suppose Derrick is an insect enthusiast who measured the body length and weight of three insects in his backyard. His data are shown in the table.
Answers
Answer:
Step-by-step explanation:
You are performing a right-tailed test.
If
α=.001, find the critical value, to three decimal places.
zα =
Answers
If α = 0.001, the critical value, to three decimal places is; 3.090
How to find the Critical Value of a right tailed test?We are told that it is a right-tailed test with a significance value of α = 0.001
This is where all the probability is to the right of some z-score, and that probability has to be 0.001.
Due to the fact that the z-table only reads from the left, right area of 0.001 is equivalent to left area of 0.999.
Thus, we have to find the area that is closest to 0.999 or when the values cross over 0.999. The values are 0.9989 and 0.99901.
Then we now look at the row for the first-decimal and then the columns for the second-decimal of the z-score.
The z-score corresponding to area of 0.99898 is 3.089, and the z-score corresponding to the area of 0.99901 is 3.090
We will choose the bigger (absolute) z-score and conclude that the critical value is 3.09
Read more about critical value at; https://brainly.com/question/7472579
#SPJ1
are births equally likely across the days of the week? a random sample of 150 births give the following sample distribution:
Answers
Expected values are = 150/7 .Ci-square distribution is Day of the week observed count Expected Chi-square = O E (O -E )2/E
testing is an act in statistics whereby an analyst tests an assumption regarding a population parameter. The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis. Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data. Statistical hypothesis: A statement about the nature of a population. It is often stated in terms of a population parameter.
Null hypothesis: A statistical hypothesis that is to be tested. : The alternative to the null hypothesis.
Test statistic: A function of the sample data.
The critical value for the chi-square statistic is determined by the level of significance (typically . 05) and the degrees of freedom. The degrees of freedom for the chi-square are calculated using the following formula: df = (r-1)(c-1) where r is the number of rows and c is the number of columns.
To know more about birth distribution and chi-square :
https://brainly.ph/question/16132639
#SPJ4
Expected values are = 150/7 .Ci-square distribution is Day of the week observed count Expected Chi-square = O E (O -E )2/E
testing is an act in statistics whereby an analyst tests an assumption regarding a population parameter. The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis. Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data. Statistical hypothesis: A statement about the nature of a population. It is often stated in terms of a population parameter.
Null hypothesis: A statistical hypothesis that is to be tested. : The alternative to the null hypothesis.
Test statistic: A function of the sample data.
The critical value for the chi-square statistic is determined by the level of significance (typically . 05) and the degrees of freedom. The degrees of freedom for the chi-square are calculated using the following formula: df = (r-1)(c-1) where r is the number of rows and c is the number of columns.
To know more about chi-square :
brainly.com/question/14082240
#SPJ4
What is the the slope-intercept form of (-5,-2)
Answers
Answer:
Step-by-step explanation:
we can't say because we don't have a couple of coordinates