a) the two angles are supplementary, then:
(3x - 45) + (2x + 25) = 180
(3x + 2x) + (-45 + 25) = 180
5x - 20 = 180
5x = 180 + 20
5x = 200
x = 200/5
x = 40
Then, the measure of the angles are:
3x - 45 = 3*40 - 45 = 75°
2x + 25 = 2*40 + 25 = 105°
b) the two angles are complementary, then:
(2y) + (6y - 30) = 90
(2y + 6y) - 30 = 90
8y = 90 + 30
8y = 120
y = 120/8
y = 15
Then, the measure of the angles are:
2y = 2*15 = 30°
6y - 30 = 6*15 - 30 = 60°
c) the two angles are vertical angles, then they are congruent, that is,
2z + 7 = 5z - 23
7 + 23 = 5z - 2z
30 = 3z
30/3 = z
10 = z
Then, the measure of the angles are:
2z + 7 = 2*10 + 7 = 27°
5z - 23 = 5*10 - 23 = 27°
d) the two angles are alternative exterior angles, then they are congruent, that is,
4x - 5 = 3x + 15
4x - 3x = 15 + 5
x = 20
Then, the measure of the angles are:
4x - 5 = 4*20 - 5 = 75°
3x + 15 = 3*20 + 15 = 75°
A ski gondola carries skiers to the top of a mountain. Assume that the total weights of adult skiers (including their equipment) are normally distributed with a mean of 200 lb and a standard deviation of 40 lb. Further assume that the gondola can carry a maximum of 25 skiers and has a maximum load limit of 5,000 lb. If the gondola is full, it will be overloaded if the mean total weight of the skiers exceeds 5,000 lb / 25 skiers = 200 lb/skier. If the gondola is filled with 25 randomly selected skiers, what is the probability that it will be overloaded? (Round your answer to three decimal places; add trailing zeros as needed.)
If the gondola is filled with 25 randomly selected skiers, the probability that it will be overloaded is; 50%
How to find the mean weight from normal distribution?The formula to find the maximum mean weight of passengers is;
Maximum mean weight = Load limit ÷ number of passengers
We are given;
Load limit = 5000 lb
Maximum number of passengers = 25
Thus;
Maximum mean weight of passengers = 5000 ÷ 25 = 200lb
Let us find the z-score:
z = (max value - mean) / st. dev
z = (200 - 200)/40
z = 0
From online p-value from z-score calculator, the p-value = 0.5 and so that is the probability that it will be overloaded.
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Need help with this please
Answer:
angle A: 75 degrees
Step-by-step explanation:
because m and n are both 180 degree angles so when you do 180-105 you get 75
a,d,e,h=105 degrees
b,c,f,g= 75
because 105+75=180
Please I need help with this
please, help me
Select the interval where g(x)>0
When f(x) > 0, it means that on a graph, the line is above the x-axis.
Solving the Question
Out of all the options, only in -2 < x < -1 is the graph above the x-axis.
For the other two intervals, the graph is below the x-axis.
Answer-2 < x < -1
While traveling to his grandmother's for Christmas, George fell asleep a quarter of the way through the journey. When
he awoke, he still had to travel half the distance that he had traveled while sleeping. For what part of the entire
journey had he been asleep?
George had been asleep for of the entire journey
(Type an integer or a simplified fraction.)
While traveling to his grandmothers for Christmas, George had been asleep for 50% of the entire journey and this distance is found by reviewing the information given to us.
What is distance travelled?The length of the entire journey taken to get from one point to another is the distance travelled. Travel distance is not a vector. It has no orientation.
In this question,
Let us take that George had been asleep for x distance.
Then according to question, we can form the equation
3/4 = 1/2x + x
3/4 = 3x/2
x = 1/2
so, the total distance travelled is 50% of the entire journey.
What are its displacement and travel distance?Displacement is the straight path between the initial and final points, whereas distance travelled is the actual length the body covers.
What is the travelled distance measured in?The International System of Units defines a meter as the distance unit.
How can velocity be used to calculate distance travelled?
Finding the area under the velocity, in particular when velocity is positive on an interval, allows us to determine the total distance travelled.
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Slope is -1/2 and (-9,3) is on the line.
the equation of the line will be:
[tex](y-3)=-\frac{1}{2}(x-(-9))[/tex]then
[tex](y-3)=-\frac{1}{2}(x+3)[/tex]and we obtain
[tex]y=-\frac{1}{2}x-\frac{3}{2}+3[/tex]and making the subtraction, we have
[tex]y=-\frac{1}{2}x+\frac{3}{2}[/tex]which is the same as
[tex]y=-\frac{1}{2}(x-3)[/tex]4-5g>39 what is the set for the inequality
Answer:
g
<
−
7
Step-by-step explanation:
What is the distance between -112 and -80 on a number line?
Answer: 32
Step-by-step explanation:
You need to take -112 and subtract it by -80 to get 32
Hope this helped! :)
A family of six consisting of a mother, father, and four children line up (shoulder-to-shoulder) for a family portrait in a random order. Find the probability mass function of the random variable X, the number of children located between the father and mother in the photograph.
The probability mass function for this is given by the table that is attached below.
Probability is defined as the proper fraction which signifies the likelihood of an event to occur.
Total number of possible arrangements of 6 people are 6! = 720
Here X can take value 0, 1, 2, 3, or4.
For the probability function : When X= 0 , it means there is no child between mother and father. Taking mother and father as one , number of possible arrangements of 5 people are 5!.
And mother and father can arranged themselves is 2! ways. So for X=0, possible ways are 5! *2 = 240.
Therefore the require probability at X=0 is given by:
P(X=0) = 240 /720 = 0.3333
For the probability function : When X = 1 , then there is one child between mother and father. Number of ways of selecting one child is C(4,1) = 4.
Mother and father can be arrange themselves in 2 ways so possible number of arrangements are 4 * 2 * 4! = 192
Therefore the require probability at X=1 is given by:
P(X=1) = 192 /720 = 0.2667
For the probability function :When X=2 , then there are two children between mother and father. Number of ways of selecting two children is C(4,2) = 6.
Mother and father can arrange themselves in 2 ways, children between mother and father can arranged themselves in 2 ways so possible number of arrangements are 6 * 2 * 2* 3! = 144
Therefore the require probability at X=2 is given by:
P(X=2) = 144 /720 = 0.2
For the probability function : When X=3 , then there are three children between mother and father. Number of ways of selecting three children is C(4,3) = 4.
Mother and father can arrange themselves in 2 ways, children between mother and father can arranged themselves in 3! ways so possible number of arrangements are 4 * 2 * 3!* 2! = 96
Therefore the require probability at X=3 is given by:
P(X=3) = 96 /720 = 0.1333
For the probability function: When X=4 , then there are 4 children between mother and father. Number of ways of selecting 4 children is C(4,4) = 1.
Mother and father can arranged themselves in 2 ways, children between mother and father can arranged themselves in 4! ways so possible number of arrangements are 1 * 2 * 4! = 48
Therefore the require probability at X=0 is given by:
P(X=4) = 48 /720 = 0.0667
Hence the probability mass function can be represented by a table below.
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Which of the following systems linear inequalities does the graph represent? Select all that apply.
To answer this question, first of all, we need to find the equation for each of the lines on the graph. To do so, we have to identify two points for each line, and then use the two-point form equation (of the line) to find the equation of each line.
Then, we have:
Equation of the solid lineWe identify two points: (1, 1) and (2, 2).
Then we have:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Then if we label both points above:
• (1, 1) ---> x1 = 1, y1 = 1
,• (2, 2) ---> x2 = 2, y2 = 2
Therefore:
[tex]\begin{gathered} y-1=\frac{2-1}{2-1}(x-1) \\ y-1=1(x-1)=(x-1) \\ y-1=x-1\Rightarrow y=x-1+1\Rightarrow y=x \end{gathered}[/tex]Therefore, the equation of the line for the solid line is y = x.
Equation of the dotted lineWe can proceed similarly as we did before. Then we have:
The two points are (2, 4) and (4, 8).
Then we can label them as follows:
• (2, 4) ---> x1 = 2, y1 = 4
,• (4, 8) ---> x2 = 4, y2 = 8
[tex]\begin{gathered} y-4_{}=\frac{8-4_{}}{4_{}-2_{}}(x-2) \\ y-4=\frac{4}{2}(x-2) \\ y-4=2(x-2)\Rightarrow y-4=2x-4 \\ y=2x-4+4 \\ y=2x \end{gathered}[/tex]Therefore, the equation for the dotted line is y = 2x.
We need to remember that when we have the symbols < or > the inequality is represented by a dotted line. Conversely, when it appears additionally an equal sign in the inequality symbol, ≥ or ≤ the line is represented as a solid line.
If we see the graph, we can say that the graph is represented by the following inequalities:
[tex]\begin{gathered} y>2x\Rightarrow Dotted\text{ line} \\ y\ge x\Rightarrow Solid\text{ line} \end{gathered}[/tex]Since if we represent them graphically, we have - using a graphing calculator:
We can observe that the shaded area is the same as the one represented in the graph given in the question.
We can prove that if we take a point in the solution region as follows:
1. For example, we can test the point (-2, 2). Then we have:
[tex]\begin{gathered} 2>2(-2)\Rightarrow2>-4\Rightarrow True \\ 2\ge-2\Rightarrow2>-2\Rightarrow True \end{gathered}[/tex]Now, using this we can check if the other system of inequalities is equivalent to this:
We can check the following inequalities:
[tex]\begin{gathered} -2x+y>0\Rightarrow y>2x \\ -x+y\ge0\Rightarrow y\ge x \end{gathered}[/tex]Which is equivalent to the previous one.
In summary, we have that the systems of linear inequalities are the following:
[tex]\begin{cases}-2x+y>0 \\ -x+y\ge0\end{cases}[/tex][Third option]
And
[tex]\begin{cases}y>2x \\ y\ge x\end{cases}[/tex][Fourth option]
[The second and the third options are not answers since both have the symbol, ≥, - and it means that we have two solid lines representing the inequality system.]
[In the first option we have that the first inequality represents a solid line, and this is not the case. The dotted line is represented by y > 2x.]
What is the sum of all the numbers less than 496 that divide evenly into 496?
Answer:
Step-by-step explanation : devise ----> divide496 = 2*2*2*2*31The 2's can be used in 5 ways, that is, not take anytake 1take 2take 3take all 4the 31 can be used in 2 ways, either take or not take itnumber of factors = 5*2 = 10but that includes taking all or noneif we correspond to none as the factor 1 and if we take all we would get 496the factors would be1, 2, 4, 8, 16, 31, 62, 124, 248, and 496
State the z score that is the cutoff for each of the following: a. The top 5% of scores b. The bottom 2.5% of scores c. The top 69.5% of scores d. The top 50% of scores e. The bottom 50% of scores
The z-scores that are the cutoffs are given as follows:
a. z = 1.645.
b. z = -1.96.
c. z = -0.51.
d. z = 0.
e. z = 0.
What is the z-score formula and what does it represent?The z-score of a measure X of a variable that has mean given by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above(in case the score is positive) or below(in case the score is negative) the mean. From the z-score table, the p-value associated with the z-score is found, which represents the percentile of the measure X.For this problem, we have that:
In item a, the cutoff is the 95th percentile, hence z = 1.645, which has a p-value of 0.95.In item b, the cutoff is the 2.5th percentile, hence z = -1.96, which has a p-value of 0.025.In item c, the cutoff is the 30.5th percentile, hence z = -0.51, which has a p-value of 0.305.In item d, the cutoff is the 50th percentile, hence z = 0, which has a p-value of 0.5.In item e, the cutoff is the 50th percentile, hence z = 0, which has a p-value of 0.5.More can be learned about z-scores at https://brainly.com/question/25638875
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Lowes counted the number of customers entering the store for a week. The results were 1,100; 950; 1,100; 1,700; 880; 920; and 1,100. What is the mode?
The mode for the number of customers counted by Lowes entering the store for the week is 1100.
What is the mode of a data?The mode of a data is that with the highest frequency.
According to Lowe's counts, we have the following data:
1100950110017008809201100There are three 1100 in the seven data counted by Lowes
we will notice after careful observation that we have more of the data 1100 with the highest frequency of 3 out 7 data counted.
Thus, we can conclude from our understanding that the mode of the data which is that with the highest frequency is 1100.
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How much should you invest at 2.4 simple interest in Oder to earn $50 interest in 9 months?
By using the method of interest, principle is 2777.7.
What is interest?An expense associated with borrowing money or other assets is interest. The principal is the amount borrowed, and the interest is calculated as a percentage of the principal for a specific period of time. The expense of borrowing money is interest. It equates to a fee or additional charge the borrower pays the lender for the loaned amount, and is sometimes stated as a percentage. When you make a payment on a loan with simple interest, the money first goes toward the interest for that month and the rest is applied to the principal. S.I. = P R T, where P = Principal, R = Rate of Interest in% per annum, and T = Time, typically calculated as the number of years, is the formula used to compute simple interest.
Given that,
S.I= PTR
Simple interest= 50
Time= 9/12= 0.75
Rate of interest= 2.4
Principle amount=?
S.I= PTR
50= P x 0.75 x 2.4
50= P x 1.8
P = 50X1.8
P= 2777.7
Therefore, principle is 2777.7
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HELPPPP!!!!!!!!!!!!!!!
Answer: see answers below
Step-by-step explanation:
F(x) is bascially the y
the absolute value means any numbers that you use for x when substituted into x-2 will always be a positive number even if x-2 is negative as with any number 3 or greater, or any number -3 or less.
for the values that are 0, 1, 2, 3, 4 or 0, -1, -2 the answer for f(x) will be a negative number. All other numbers positive or negative for x will result in a positive answer.
So you need to graph your line with an arrow on each end to show it goes to infinity. in your chart you choose a number for x, and the f(x) number (which is equivalent to the y number for purposes of graphing.
I cannot draw on her a graph for you because I don't have that ability without an app for that.
here are some sample points for your chart. THe first number in each parenthesis is x and the second is f(x)
(-1, -2), (-2, -1), (0, -3), (-3, 0), (1, -4), (2, -5), (3-4), (4,-3), (5-2), (6, -1) All other numbers positive or negative for x will result in f(x) being positive.
You only need two sets of points to put on the graph to draw the line through.
So negative values for f(x) can only be -1, -2, -3, -4, -5. x can include all negative numbers through infinity.
Positive will include all positive numbers through infinity for x and f(x).
F(x) cannot decrease beyond -5. x can decrease all numbers through infinity.
One of the legs of a right triangle measures 16cm and the other leg measures 2cm. Find the measure of the hypotenuse.
Answer:
18.23
Hope this is right! (don't worry I did the math)
Pls help need asap
Which of the following graphs represent and even function?
The first and second graphs represent even function.
What is an even function?If f of x is equal to f of −x for all the values of x, then it is called Function. This implies that function is same for the positive x-axis and the negative x-axis. Trigonometric even function, and secant function are some of the examples of even function.
Following are the properties of an even function:
Sum of two even functions is also even.Difference of two even functions is also even.Product of two even functions is always even.Quotient of the division of two even functions is always even.Composition of two even functions is also even.And composition of an even and odd function is also even.As the graph of first and second is symmetric about the y axis, therefore both represent even functions.
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1. A tool rental company charges $25 for the first hour of a tractor rental. Each additional hour costs $20 per hour. Which statement describes the relationship between total cost and hours?
A It is proportional; each ratio for related pairs is equivalent.
B It is proportional; each x-term is a multiple of the previous term.
C It is not proportional; each ratio y/x for related pairs is not equivalent.
D It is not proportional; each x-term is not a multiple of the previous term.
Answer:
C. It is not proportional. y/x ratios are not equivalent
Step-by-step explanation:
Given a rental charge of $25 for the first hour and $20 for each additional hour, you want to know if the charges are proportional to the time.
ProportionalityIn this situation, if the relationship were proportional, the charge per hour (constant of proportionality) would be the same for every hour. Here, the first hour costs more, so the hourly charge is not constant.
Here, we have, for x=hours, y=dollars, ...
(1, 25) ⇒ y/x = 25
(2, 45) ⇒ y/x = 22.5
(3, 65) ⇒ y/x ≈ 21.67
The y/x values are not constant (because the charge per hour is not constant). The relationship is not proportional.
<95141404393>
14. Find the common difference of the arithmetic sequence.
25, 18, 11, 4,...
A 18/25
B 1 7/18
C -7
D 43
Answer:
C -7
Step-by-step explanation:
the numbers keep on decreasing by 7
Which of the following choices are equivalent to theexpression below? Check all that apply.A. XB. (**)D D. &E (2)19F.
The expression
[tex]x^{\frac{9}{4}}[/tex]is equivalent to
[tex]\sqrt[4]{x^9}[/tex]then the answer is option D
Since the root and the exponent commute, this also can be written as
[tex](\sqrt[4]{x})^9[/tex]then the answer is option B
And by the same reason, this can be written as
[tex](x^9)^{\frac{1}{4}}[/tex]then the answer is option E
_______1.afraction whose denominator is 3 more than it's numerator x
_______A.if x=6, what is the value of the fraction?
_______B. what is the fraction if the denominator is 8?
_______2 the length of a rectangular garden with an area of 32 square meters and has width w meters
_______A. what is the length of the garden if the width 4 meters?
_______B. find the width of the garden if the length is 16 meters?
________3. the rate of a car traveled 240 kilometers in t hours?
_________A. Find the rate of the car if t= 2.5 hour?
_________B. what is the rate of the car if the time is doubled?
1. A fraction whose denominator is 3 more than it's numerator x: x/(x+3)
A. If x =6, then the value of the fraction is 2/3.
B. If the denominator is 8, then the fraction is 5/8.
2. The length of a rectangular garden with an area of 32 square meters and has width w meters: 32/w.
A. The length of the garden if the width 4 meters = 8 meters
B. The width of the garden if the length is 16 meters = 2 meters
3. The rate of a car traveled 240 kilometers in t hours = 240/t km per hour
A. The rate of the car if t= 2.5 hour is 96 km/hour.
B. The rate of the car if the time is doubled is 120/t.
1. Let 'x' be the numerator. Then the denominator is 3 more than its numerator. So the denominator = x +3.
Hence the fraction whose denominator is 3 more than it's numerator x: x/(x+3).
A. If x = 6, then x+3 = 6+3 = 9.
So x/x+3 = 6/9 = 2/3
So the fraction is 2/3
B. Denominator = 8
⇒ x+3 = 8
⇒ x = 8-3 = 5
So the fraction is x/x+3 = 5/8.
2. Area of the rectangular garden = 32 square meters
⇒ length x width = 32
⇒ length x w = 32
⇒ length = 32/w
So the length of a rectangular garden with an area of 32 square meters and has width w meters is 32/w.
A. Width, w = 4 meters
Then, length = 32/w = 32/4 = 8 meters
B. Length = 16 meters
⇒ 32/w = 16
⇒ w = 32/16
⇒ width, w = 2 meters
3. Distance travelled by the car = 240 kilometers
Let 't' be the time taken in hours.
Then, Rate of the car = Distance / Time taken
⇒ Rate of the car in t hours = 240/t kilometers per hour
A. If t = 2.5 hour, then,
Rate of the car = 240/2.5 = 96 kilometers/ hour
B. If the time is doubled, then time = 2t
Rate of the car = 240/2t = 120/t
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write the equation of a line perpendicular to 12y=2x+10 and passing though the point (-2,-1)
The equation of the line perpendicular to 12y = 2x + 10 and passing though the point (-2,-1) is y = -6x -7.
Writing the equation 12y = 2x + 10 in slope intercept form, we get,
y = (1/6)x + 5/6
The slope of the line is 1/6.
We know that,
Product of slope of two lines perpendicular to each other = -1.
Let the slope of the line perpendicular to the given line be m.
Hence, we can write,
m*(1/6) = -1
m = -6
Let the line perpendicular to the given line be y = mx + c.
It is given that the line perpendicular to the given line goes through (-2,-1).
Hence, we can write,
-1 = -6.(-1) + c
-1 = 6 + c
c = -7
Hence, the slope-intercept form of the line perpendicular to the given line is y = -6x -7.
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TRUE OR FALSE?
If 15% of coins are quarters and there are 12 quarters, what is the total # of coins
Based on the given task and the percentage of quarters in the coins, the total number of coins is 80 coins.
How to find total coins?To calculate the total coins;
Let
The total number of coins = xThe percentage of quarters = 15% of x are quartersThe number of quarters = 12Then, you will
Equate the Percentage of quarters and Number of quarters:Percentage of quarters = Number of quarters
15% of x = 12
15/100 × x = 12
0.15 × x = 12
0.15x = 12
divide both sides by 0.15x = 12 / 0.15
x = 80 coins
In conclusion, the total number of coins is 80 coins.
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A list of fixed fees for services recorded on the encounter form is called the
A list of fixed fees for services recorded on the encounter form is called the Superbills.
The purpose of encounter forms, often referred to as super bills, is to "document services performed by recording the diagnostic and procedure codes, which serve as the foundation for billing and receipt of payment for services." Every time a patient or customer receives a service, the provider records that service, often into medical claims software that may automate much of the subsequent procedure.
This technique entails coding (procedure codes and, if necessary, diagnostic codes), billing/invoicing, and/or transmission to the patient's or client's insurance provider. For the client's health and treatment plans as well as for proper billing, it is crucial to make sure that the appropriate information is documented. This is why encounter forms are such a crucial component of healthcare.
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Trigonometry Functions of Any Angle CAA point on the terminal side of angle O is given. Find the exact value of the indicated trigonometric function of e.1) (12, 16) Find csc 0.I need help with #2
1) I'll calculate the hypotenuse
hyp = squared root [(16)^2 + (12)^2]
= squared root [ 256 + 144]
2) the answer is letter C. 5/7
3) calculate the hypotenuse
hyp = squared root [(2^2 + (-3)^2]
= squared root [ 4 + 9]
= squared root [13]
sin 0 = -3/squared root 13
= -3squared root (13) / 13
The answer for number three = letter B
PLEASE HELP I MISSED OUT ON CLASS BECAUSE I WAS SICK AND I DONT UNDERSTAND
Answer:
A)Linear angles
B) they have a sum of 180
C)25x+5+4+32x=180
57x+9=180
57x=171
x=3
D)25(9)+5=
75+5=80
32(3)+4=
96+4=100
Step-by-step explanation:
I will give brainliest, like and rating if u solve this right
Which of the following statements is true?
Answer:
Step-by-step explanation:
c lol
Constructed Response. Be sure to answer all parts of the constructed response.1. A baton twirler releases a baton at a height of 5 feet above the ground with the initial velocity of30 feet per second. The height of the baton t seconds after it is thrown is given by the function,h(t) = -16t2 + 30t + 5, where h(t) is the height of the baton in feet.a.) How high is the baton after 1.5 seconds? Round your answer to the nearest hundredth, ifapplicable.b.) What is the maximum height of the baton? Round your answer to the nearest hundredth, ifapplicable.c.) How long does it take for the baton to reach its maximum height? Round your answer to thenearest hundredth, if applicable.
Given the equation that
There are 24 students in Mrs. Brown’s class and 18 of them like to dance what percent of the class likes to dance 
In Mrs. Brown’s 75% percent of the class likes to dance .
What are mathematics operations?
A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value. The number of operands determines the operation's arity. Most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive and multiplicative inverses.• Zero-arity operations, or nullary operations, are constants, and mixed products are arity three operations, or ternary operations.
Given:
number of students in Mrs. Brown’s class = 24
number of students likes to dance = 18
Then to find the percent of the class likes to dance we divide 18 by 24 and multiply with 100:
percent of the class likes to dance = (18/24) x 100
percent of the class likes to dance = 75%
Therefore, in Mrs. Brown’s 75% percent of the class likes to dance .
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Answer:75%
Step-by-step explanation:
number of students in Mrs. Brown’s class = 24
number of students likes to dance = 18
Then to find the percent of the class likes to dance we divide 18 by 24 and multiply with 100:
percent of the class likes to dance = (18/24) x 100
percent of the class likes to dance = 75%
Therefore, in Mrs. Brown’s 75% percent of the class likes to dance.