Answer:
153/250
Step-by-step explanation:
did this in 4th grade
The ages of two girls are in the ratio of 2:3 . 6 years hence the ratio of the girls will be 11 : 13 find their present age .
Brown Law Firm collected data on the transportation choices of its employees for their morning commute. The table shows the percentages of the type of transportation of the male and female employees. A 5-column table has 3 rows. The first column has entries Male, female, total. The second column is labeled public with entries 12, 8, 20. The third column is labeled Own with entries 20, 10, 30. The fourth column is labeled other with entries 4, 6, 10. The fifth column is labeled total with entries 36, 24, 60. Consider the following events: A: The employee is male. B: The employee is female. C: The employee takes public transportation. D: The employee takes his/her own transportation. E: The employee takes some other method of transportation. Which two events are independent? A and C A and D B and D B and E.
The two events out of the listed events which are independent events are given by: Option A: A and C
What is chain rule in probability?For two events A and B, by chain rule, we have:
[tex]P(A \cap B) = P(B)P(A|B) = P(A)P(A|B)[/tex]
What is law of total probability?Suppose that the sample space is divided in n mutual exclusive and exhaustive events tagged as
[tex]B_i \: ; i \in \{1,2,3.., n\}[/tex]
Then, suppose there is event A in sample space.
Then probability of A's occurrence can be given as
[tex]P(A) = \sum_{i=1}^n P(A \cap B_i)[/tex]
Using the chain rule, we get
[tex]P(A) = \sum_{i=1}^n P(A \cap B_i) = \sum_{i=1}^n P(A)P(B_i|A) = \sum_{i=1}^nP(B_i)P(A|B_i)[/tex]
How to form two-way table?Suppose two dimensions are there, viz X and Y. Some values of X are there as [tex]X_1, X_2, ... , X_n[/tex] values of Y are there as [tex]Y_1, Y_2, ..., Y_k[/tex]rows and left to the columns. There will be [tex]n \times k[/tex]values will be formed(excluding titles and totals), such that:
Value([tex]i^{th}[/tex] row, [tex]j^{th}[/tex] column) = Frequency for intersection of [tex]X_i[/tex] and [tex]Y_j[/tex]values are going in rows, and Y values are listed in columns).
Then totals for rows, columns, and whole table are written on bottom and right margin of the final table.
For n = 2, and k = 2, the table would look like:
[tex]\begin{array}{cccc}&Y_1&Y_2&\rm Total\\X_1&n(X_1 \cap Y_1)&n(X_1\cap Y_2)&n(X_1)\\X_2&n(X_2 \cap Y_1)&n(X_2 \cap Y_2)&n(X_2)\\\rm Total & n(Y_1) & n(Y_2) & S \end{array}[/tex]
where S denotes total of totals, also called total frequency.
n is showing the frequency of the bracketed quantity, and intersection sign in between is showing occurrence of both the categories together.
How to calculate the probability of an event?Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.
Then, suppose we want to find the probability of an event E.
Then, its probability is given as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]
where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.
Suppose that two events are denoted by A and B.
They are said to be independent event if and only if:
[tex]P(A \cap B) = P(A)P(B)[/tex]
The given frequency table is:
[tex]\begin{array}{ccccc} &\text{Public}&\text{Own}&\text{Others}&\text{Total}\\\text{Male}&12&20&4&36\\\text{Female}&8&10&6&24\\\text{Total}&20&30&10&60\end{array}[/tex]
The probability table for the same labels would be:
[tex]\begin{array}{ccccc} &\text{Public}&\text{Own}&\text{Others}&\text{Total}\\\text{Male}&12/60&20/60&4/60&36/60\\\text{Female}&8/60&10/60&6/60&24/60\\\text{Total}&20/60&30/60&10/60&1\end{array}[/tex]
The events A, B,C,D and E are given as:
A: The employee is male. B: The employee is female. C: The employee takes public transportation. D: The employee takes his/her own transportation.E: The employee takes some other method of transportation.Checking all the listed options one by one, for them being independent:
Case 1: A and CP(A) = P(The employee is male. ) = 36/60
P(C) = P(The employee takes public transportation.) = 20/60[tex]P(A \cap C) = 12/60 \\\\ P(A)P(C) = \dfrac{36 \times 20}{60^2} = 12/60[/tex]
[tex]P(A \cap C) = P(A)P(C)[/tex]
Thus, A and C are independent events.
Case 2: A and DP(A) = P(The employee is male. ) = 36/60
P(D) = P(The employee takes his/her own transportation.) = 30/60
[tex]P(A\cap D) = 20/60\\\\P(A)P(D) = \dfrac{30 \times 36}{60^2} = 12/60 \neq P(A \cap D)[/tex]
Thus, A and D are not independent events.
Case 3: B and DP(B) = P(The employee is female. ) = 24/60
P(D) = P(The employee takes his/her own transportation.) = 30/60
[tex]P(B \cap D) = 10/60 \neq P(B)P(D)=\dfrac{24 \times 30}{60^2} = 12/60[/tex]
Thus, B and D are not independent events.
Case 4: B and EP(B) = P(The employee is female. ) = 24/60
P(E) = P(The employee takes some other method of transportation.) = 10/60
[tex]P(B \cap E) = 6/60 \neq P(B)P(E)= \dfrac{24 \times 10}{60^2} = 4/60[/tex]
Thus, B and E are not independent events.
Thus, the two events out of the listed events which are independent events are given by: Option A: A and C
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Answer:
First option!!
"A and C"
Step-by-step explanation:
Edge 2022
hehehehehehhelphelphelpgelpggepkepewnwe
(6,5)
If you start at the origin (which is (0,0)) and go 6 right, that's six for x. If you then go 5 up, that means y is 5.
(6,5)
Answer:
(6,5)
Step-by-step explanation:
6 is on the x-axis, and 5 is on the y-axis
Please show work, thank you
Answer:
[tex]\displaystyle \lim_{x \to 36} \frac{\sqrt{x} - 6}{x - 36} = \frac{1}{12}[/tex]
General Formulas and Concepts:
Calculus
Limits
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]
Special Limit Rule [L’Hopital’s Rule]: [tex]\displaystyle \lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x \to c} \frac{f'(x)}{g'(x)}[/tex]
Indeterminate FormsDifferentiation
DerivativesDerivative NotationDerivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Derivative Rule [Basic Power Rule]:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle \lim_{x \to 36} \frac{\sqrt{x} - 6}{x - 36}[/tex]
Step 2: Find Limit Pt. 1
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to 36} \frac{\sqrt{x} - 6}{x - 36} = \frac{\sqrt{36} - 6}{36 - 36}[/tex]Simplify: [tex]\displaystyle \lim_{x \to 36} \frac{\sqrt{x} - 6}{x - 36} = \frac{0}{0}[/tex]We see that we get 0 divided by 0, an indeterminate form.
Step 3: Find Limit Pt. 2
Use L'Hopital's Rule.
[Limit] Differentiate: [tex]\displaystyle \lim_{x \to 36} \frac{\sqrt{x} - 6}{x - 36} = \lim_{x \to 36} \frac{(\sqrt{x} - 6)'}{(x - 36)'}[/tex][Limit] Rewrite [Derivative Property - Addition/Subtraction]: [tex]\displaystyle \lim_{x \to 36} \frac{\sqrt{x} - 6}{x - 36} = \lim_{x \to 36} \frac{(\sqrt{x})' - (6)'}{(x)' - (36)'}[/tex][Limit] Differentiate [Derivative Rule - Basic Power Rule]: [tex]\displaystyle \lim_{x \to 36} \frac{\sqrt{x} - 6}{x - 36} = \lim_{x \to 36} \frac{\frac{1}{2\sqrt{x}}}{1}[/tex][Limit] Simplify: [tex]\displaystyle \lim_{x \to 36} \frac{\sqrt{x} - 6}{x - 36} = \lim_{x \to 36} \frac{1}{2\sqrt{x}}[/tex][Limit] Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to 36} \frac{\sqrt{x} - 6}{x - 36} = \frac{1}{2\sqrt{36}}[/tex]Evaluate: [tex]\displaystyle \lim_{x \to 36} \frac{\sqrt{x} - 6}{x - 36} = \frac{1}{12}[/tex]∴ the limit as x approaches 36 of the given function is equal to one-twelfths.
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---
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
We are given with a limit and we need to find it's value , but first recall the identity which is the main key to this question :
[tex]{\boxed{\bf{a^{2}-b^{2}=(a+b)(a-b)}}}[/tex]Now , consider the limit we have ;
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 36}\dfrac{\sqrt{x}-6}{x-36}}[/tex]
Let's try direct substitution first ;
[tex]{:\implies \quad \displaystyle \sf \dfrac{\sqrt{36}-6}{36-36}}[/tex]
[tex]{:\implies \quad \displaystyle \sf \dfrac{6-6}{0}=\dfrac00}[/tex]
Here , we get an indeterminate form , so direct substitution didn't worked. So , consider again :
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 36}\dfrac{\sqrt{x}-6}{x-36}}[/tex]
Can be further written as ;
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 36}\dfrac{\sqrt{x}-6}{(\sqrt{x})^{2}-6^{2}}}[/tex]
Using the above identity we have ;
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 36}\dfrac{(\sqrt{x}-6)}{(\sqrt{x}-6)(\sqrt{x}+6)}}[/tex]
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 36}\dfrac{\cancel{(\sqrt{x}-6)}}{\cancel{(\sqrt{x}-6)}(\sqrt{x}+6)}}[/tex]
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 36}\dfrac{1}{\sqrt{x}+6}}[/tex]
Now , put the limit
[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{\sqrt{36}+6}}[/tex]
[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{6+6}}[/tex]
[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{12}}[/tex]
[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{\displaystyle \bf \lim_{x\to 36}\dfrac{\sqrt{x}-6}{x-36}=\dfrac{1}{12}}}}[/tex]
Juan wants to change the shape of his vegetable garden from a square to a rectangle, but keep the same area so he can grow the same amount of vegetables. The rectangular garden will have a length that is 2 times the length of the square garden, and the width of the new garden will be 16 feet shorter than the old garden. The square garden is x feet by x feet. What is the quadratic equation that would model this scenario? x2 = (2x)(x – 16) x2 = (x)(x – 16) x2 = (x)(x 16) x2 = (2x)(x 16).
The quadratic equation that would model this scenario is
[tex]x^{2} = 2x(x-16)[/tex]
Let us take the side of the square = x
Area of the square = x²
Length of the rectangular garden = 2x
Width of the rectangular garden = x-16
So, the area of the new vegetable garden = length*width
Area of the new or rectangular vegetable garden = 2x(x-16)
What is a quadratic equation?The polynomial equation whose highest degree is two is called a quadratic equation. The equation is given by [tex]ax^2+bx+c[/tex]coefficient [tex]x^{2}[/tex]non-zero.
Since it is given that
Area of square garden = area of the rectangular garden
[tex]x^{2} = 2x(x-16)[/tex]
Thus, the quadratic equation that would model this scenario is
[tex]x^{2} = 2x(x-16)[/tex]
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Answer:
its a
Step-by-step explanation:
evaluate the function when x=4
The graph of the function is defined in the attached file please find it.
Graph function:[tex]\to \bold{x=4}[/tex]
In the given question, the x-axis holds a value that is "4".The holding value is "4" which is a positive number, and in the graph, it represents the positive value, which is defined in the attached file please find the attached file.Find out more information about the function here:
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help me. I need help
Answer:
3 ------------- √9
6 ------------- ³√216
7 ------------- ³√343
8 ------------- √64
9 ------------ ³√729
10 ----------- √100
Step-by-step explanation:
Hope this helps .
Answer:
[tex]1. \sqrt{9} =3[/tex]
[tex]2. \sqrt[3]{729}=9[/tex]
[tex]3. \sqrt{100} =10[/tex]
[tex]4. \sqrt[3]{216} =6[/tex]
[tex]5. \sqrt{64} =8[/tex]
[tex]6. \sqrt[3]{343} = 7[/tex]
Step-by-step explanation:
[tex]1. \sqrt{9} =3[/tex] [tex]3*3=9[/tex]
[tex]2. \sqrt[3]{729}=9[/tex]
[tex]\sqrt[3]{9^3}=9[/tex]
[tex]3. \sqrt{100} =10[/tex] [tex]10*10=100[/tex]
[tex]4. \sqrt[3]{216} =6[/tex]
[tex]\sqrt[3]{6^3}=6[/tex]
[tex]5. \sqrt{64} =8[/tex] [tex]8*8=64[/tex]
[tex]6. \sqrt[3]{343} = 7[/tex]
[tex]\sqrt[3]{7^3}=7[/tex]
Hope this helps!
if it jake 2/3 hours to paint 2/5 of his room, how long would it take to paint his sister's room?
B. Translate each word into algebraic eqaution. (Use any letter)
1. Twice a number is 18. _____
2. The difference of a number and 5 is equal to 8. _____
3. The quotient of a number and 7 is 21. _____
4. Thrice a number plus 5 is 12. _____
5. The product of two and a number is 18. ______
Help me in Mathematics ASAP ASAP ASAPPP
Answer
1. 9
1. 13
1. 147
1. 7/3
1. 9
Step-by-step explanation:
Algebraic equations
1. 2x=18
2. x-5=8
3. (x/7)=21
4. 3x+5=12
5. 2x=18
I need help with these two questions please !
Answer:
9. 60
10. 12
Step-by-step explanation:
9.
We need to find the least common multiple (LCM) of 12 and 15.
Here are two methods:
Method 1
List several multiples of each number until you find the smallest number that is a multiple of both.
Multiples of 12: 12, 24, 36, 48, 60, 72
Multiples of 15: 15, 30, 45, 60, 75
60 is the LCM of 12 and 15.
Answer: 60
Method 2
Find the prime factorization of both numbers.
12 = 2² × 3
15 = 3 × 5
The LCM is the product of the following factors:
Common and not common prime factors with greater exponent.
2 is not common. Use 2².
3 is common. Use 3.
5 is not common. Use 5.
LCM = 2² × 3 × 5 = 60
Answer: 60
10.
We need the LCM of 4 and 6.
I'll use the second method above which is prime factorization.
4 = 2²
6 = 2 × 3
LCM = 2² × 3 = 12
Answer: 12
.
Question 3 of 5
Ms. Bowen has 36 students in her class. This is 8 more
students than Ms. Arnold has.
How many students does Ms. Arnold have? Choose the correct equation and
answer
O A. x+8 = 36
x = 28 students
O B. x+8 = 36
x = 44 students
O C. X+44 = 36
x = 70 students
D. x+ 36 = 8
x = 44 students
SUBMIT
I will mark brainiest on
Answer:
A
Step-by-step explanation:
28 + 8 is 26
David saves $25.78 to buy a video game. After he buys the video game, he has $3.04 left over. How much does David spend on the video game?
Answer:
He spent 22.74
Step-by-step explanation:
because 25.78−22.74 = 3.04
Solve this problem. What is x?
Don’t forget to use the equation a^2 + b^2 = c^2
SHOW YOUR WORK.
Step-by-step explanation:
a²+b²=c²
THIS is the Pythagorean theorem which is:
Hypotenuse² + Base² = perpendicular ²
Thus inputting values:
(√117)² + (6)² = (x)²
117 + 36 = x²
x² = 153
x= √153 (ans)
What do the grid boxes in a punnett square represent?.
Answer:
All the possible allele combinations in the offspring
Step-by-step explanation:
Hope this helps!
Edward drove 275 miles in 212 hours and 357.5 miles in 314 hours. If he drove at a constant rate, how much distance did he travel every hour? Enter your answer in the box below.
The average distance that he travelled every hour is; 2.4357 miles per hour
What is the average distance?He drove 275 miles in 212 hours.
Now, to find the rate of distance per hour;
Distance per hour = 275/212 = 1.2972 miles per hour
He drove 357.5 miles in 314 hours.
Distance per hour = 357.5/314
Distance per hour = 1.1385 miles per hour
Thus, his average distance per hour = 1.2972 + 1.1385 = 2.4357 miles per hour
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Problème:
Une épreuve de patinage de vitesse se déroule sur une piste dont les dimensions sont les suivantes:
Deux lignes droites de 82,19 m chacune et deux virages semi-circulaires de 75 m de diamètre.
1)Quelle est la longueur de la piste?
2)Les filles disputent une course sur 3000 m et les hommes sur 5000 m. Combien les concurrents doivent-ils parcourir de tours?
Merci d'avance.
Answer:
1) 314.38 m
2) Je ne sais pas.
The table shows values for functions f(x) and g(x). X f(x)=0. 25x g(x)=−0. 75x 1 −3 64 3. 25 −2 16 2. 5 −1 4 1. 75 0 1 1 1 0. 25 0. 25 2 0. 0625 −0. 5 3 2000. 015625 −1. 25 What is the solution to f(x)=g(x) ? Select each correct answer. X=−3 x=−2 x=−1 x = 0 x = 1 x = 2 x = 3.
Solution to f(x)=g(x) will be x=0 and x=1 because functional value on these two points is same for both the functions.
it is given that
[tex]f(x)= 0.25^x\\g(x)= -0.75x+1[/tex]
given table is,
x f(x) g(x)
-3 64 3.25
-2 16 2.5
-1 4 1.75
0 1 1
1 0.25 0.25
2 0.625 -0.5
3 0.015625 -1.25
what is the solution of two functions?solutions of two functions are the points where two functions intersect or we can say that points where the values of two functions is equal.
as we can see that for x=0 and for x=1, the value of functions i.e. f(0)=g(0)=1 and f(1)=g(1)=0.25
it means these two functions will intersect at x=0 and x=1 so these values(0 and 1) of x will be the solution to f(x)=g(x)
therefore, solution to f(x)=g(x) will be x=0 and x=1
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Write a quadratic function whose graph has a vertex of (3,2) and passes through the point (4,7).
f(x) =_
Answer:x^4 +y+1
Step-by-step explanation:
Circle O has a circumference of 88 cm.
What is the length of the radius of the circle?
cmין
Answer:
r = 14 cm
Step-by-step explanation:
Circumference = 2πr = 88
=> r = 88 / 2 x 22/7
=> r = 88 x 7 / 44
=> r = 2 x 7
=> r = 14 cm
4/1 = 12/3 so 12 cups =_____ quarts
Answer:
3 quarts
Step-by-step explanation:
4/1 = 12/3 so 12 cups =3 quarts
Ya'll FR get 50 points if you answer this.
Why is the graph shown a line of best fit?
A) The graph shows a line of best fit because the association is zero.
B) The graph shows a line of best fit because the points fit around the line.
C) The graph shows a line of best fit because there is a straight line.
D) The graph shows a line of best fit because the points are plotted evenly above and below the line.
Answer:
I would say B
Step-by-step explanation:
A. would make no sense and the graph will always have a straight line unless its compairing something and it does not have anything to do with 0 because it shows where it starts
How much money will be in Account A at the end of 3 years? $ How much money will be in Account B at the end of 3 years? $.
Account A is having $1,093 after 3 years. and Account B is having $1,120 after 3 years.
What is compound interest?Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.
Elisa put $1,000 in each bank.
Account A: gives her at a rate of 3% per annum compounded annually.
Account B: $40 bonus is added to the account each year.
After 3 years, account A will have
[tex]\rm Account \ A = 1000(1.03)^3\\\\Account \ A = 1093[/tex]
Account A is having $1,093 after 3 years.
After 3 years, account B will have
[tex]\rm Account \ B= 1000 + 3(40)\\\\Account \ B= 1,120[/tex]
Account B is having $1,120 after 3 years.
More about the compound interest link is given below.
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Answer:
A ; 1092.73
B ; 1120
Step-by-step explanation:
Tommy’s team has won 15 games and lost 10 games. What percent of its games has the team won?
Answer:
60%
Step-by-step explanation:
10 + 15
25
15/35 = 60%
We need to first find the total number of games so 15 plus 10 gets us 25. Then we take and divide the number of games won by the total number played, getting us 60%.
Have an amazing day!!
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Which of the following is the total number of pennies on Rows 1-4 (the first 32 squares)? 232 – 1 232 232 1.
The total number of pennies on Rows 1-4 (the first 32 squares) is 4,294,967,295 or 2³².
What is geometric progression?A geometric progression is the series of numbers such that the ratio of any two consecutive numbers of the series is the same.
If we look closely at the problem we will understand that on each of the square boxes the number of pennies will get double from the previous one therefore, we can say that it is forming a geometric progression where the first term of the sequence is 1, while the common ratio is of 2. thus,
The total number of pennies on Rows 1-4 (the first 32 squares) is the sum of the geometric progression for the first 32, terms, therefore,
[tex]S_n = a_1(\dfrac{r^n-1}{r-1})[/tex]
Now, as we know that the first term of the series is 1, while the common ratio(r) is 2, and the number of terms(n=32). Thus, the sum can be written as,
[tex]S_n = a_1(\dfrac{r^n-1}{r-1})\\\\S_n = 1(\dfrac{2^{32}-1}{2-1})\\\\S_n = 4,294,967,295[/tex]
The number can also be written as,
[tex]S_n = 4,294,967,295\\\\S_n = 2^{32}[/tex]
Hence, the total number of pennies on Rows 1-4 (the first 32 squares) is 4,294,967,295 or 2³².
Learn more about Geometric progression:
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Answer:
A: 2^32 – 1
Step-by-step explanation:
Identify the linear inequality from the graph
Answer:
B) y < 3/4x -2
Step-by-step explanation:
First, to eliminate 2 options let's see what sign we should use. The ≤ is a solid line where < is a dotted line. Next, you need to know which way to flip the sign. If it is under the line it is the < symbol.
Pls help! Answer quick
Answer:
Thursday
Step-by-step explanation:
Positive sign denotes that it has gained
I NEED HELP BAD PLEASE HELP ME!!!!!!
Many bank accounts never go below zero. But some banks will allow a negative balance, at least for a short time, called an overdraft. It means someone has taken out, or 'drafted', more money than was in the account to begin with. Mila's account went into overdraft. To get back to a positive balance, she deposited money at a steady rate of $39.92 per week. After 3 weeks, she had $93.29 in the account. What was the balance when the account went into overdraft?
Answer:
The balance when the account went into overdraft was -38.02
Explanation:
Let x be the balance when the account went into overdraftTo get back to a positive balance he deposited money at a steady rate of $20.06 per week. Amount deposited per week = $20.06Amount deposited 8 weeks = Now amount in account after 8 weeks =x+160.48We are given that After 8 weeks, he had $122.46 in the account.So,x+160.48=122.46x=122.46-160.48x=-38.02
If the discriminant of an equation is positive, which of the following is true of
the equation?
A. It has one real solution.
B. It has two complex solutions.
C. It has one complex solution.
ОО
D. It has two real solutions.
SUBMIT
Answer:
D
Step-by-step explanation:
Two real and distinct roots
Answer:
D
Step-by-step explanation:
The conditions for the discriminant and the roots of the equation are
• If b² - 4ac > 0 then 2 real and distinct roots
• If b² - 4ac = 0 then 2 real and equal roots
• If b² - 4ac < 0 then roots are complex
here the discriminant is positive , that is greater than zero , then
the equation has two real solutions D
help me pleaseeeeeeeee
Answer:
Angles on a straight line add up to 180 degrees so for the 129 degrees you will take 180 - 129 = 51. In the triangle you will add 51 and 55 = 106 but remember in a triangle all angles should be equal to 180. So 180 - 106 = 74. X=74degrees
I WILL GIVE BRAINLIEST
Dan’s dog-walking job pays $15 per hour. His job as a car-wash attendant pays $400 each week. Dan wants to know how many hours he needs to spend walking dogs to earn more than $520 in a week.
Which three inequalities can model this situation?
Select all the correct answers.
A. x(15 + 400) > 520
B. 520 < 400 + 15x
C. 15x > 120
D. 15x + 520 > 400
E. 520 < 15x + 400x
F. 15x + 400 > 520
[tex]\large\underline{\underline{\maltese{\purple{\pmb{\sf{\: Explanation :-}}}}}}[/tex]
Let the number of hours be x for his job of Dog walking..
So, The equation would be:
[tex] \blue \dashrightarrow \green{ \sf15x +400}[/tex]
Dan wants to earn more than $520 in a week, so this means that the expression is greater than 520:
[tex] \blue \dashrightarrow \green{ \sf15x + 400 > 520}[/tex]
If we move the constant to the right-hand side and change its sign, The equation would be:
[tex] \blue \dashrightarrow \green{ \sf15x > 520 - 400} \\ \blue \dashrightarrow \green{ \sf15x > 120}[/tex]
Also, the first inequality can be rearranged as:
[tex] \blue \dashrightarrow \green{ \sf520 < 400 + 15x}[/tex]
