Answer:
x = 30 degrees
y = 67 degrees
z = 83 degrees
Step-by-step explanation:
Since x, y , and z are the angle measure for the first, second and third angle respectively, we can write the following equations following the statements given:
The sum of the measures of the angles of a triangle is 180:
(1) x + y + z = 180
The sum of the measure of the second and third angle is five times the measure of the first angle:
(2) y + z = 5 x
The third angle is 16 more than the second:
(3) z = y + 16
Now we solve the system of three equations. We use the third equation to replace z in the second one:
y + (y + 16) = 5 x
then : 2 y = 5 x - 16; then y = 2.5 x - 8
So , now we can replace this expression for y in the third equation:
z = (2.5 x - 8) +16 = 2.5 x + 8
and finally we made the replacements of y and z shown above in bold, in the first equation:
x + (2.5 x - 8) + (2.5 x + 8) = 180
x + 5 x = 180
6 x = 180
then x = 180/6 = 30 degrees
From this, we get the value of the other angles:
y = 2.5 (30) - 8 = 67 degrees
z = 2.5 (30) +8 = 83 degrees
Mr. Stewart bought a new battery for his car. The battery cost $72. Since batteries are a taxable item, he had to pay a sales tax of 7.5%. What was the total cost of the battery in dollars and cents?
Mr. Stewart spent $77.40 on his new car battery.
Answer: $77.40
Step-by-step explanation:
First you take the 7.5% and turn it into a decimal and to do that you have to divide 7.5 by 100 which gives you .075. You then multiply 72 by .075 to know how much money you will pay with tax and you get $5.40. then you add $5.40 to $72 to get the total coast of the battery, which is $77.40.
The total cost of the battery was $77.40.
At 6 am, the temperature was 73 degrees Fahrenheit. By noon, then temperature had rose 8 degrees. At 4 pm, the temperature was 5 degrees warmer than it was at noon. By 9 pm, the temperature had dropped 16 degrees. What was the temperature at 9 pm?
Answer:
70 degrees Fahrenheit
Answer:
70
Step-by-step explanation:
We started at 73 degrees and the temperature rose by 8 degrees so 73 + 8 = 81. At 4 pm, the temperature rose again by 5 degrees so 81 + 5 = 86. By 9 pm, the temperature dropped 16 degrees so 86 - 16 = 70, Therefore, the temperature at 9 pm was 70 degrees.
There are nine different positions on a baseball team. If a team has 17 players how many different line-ups can the team make? (Assume every player can play every position.) The team can make different line-ups. Baseball games consist of nine innings. A team wants to change its line-up every inning. If no game goes to extra innings, and a season consists of 147 games, how many complete seasons can the team play without repeating a line-up? The team can play complete seasons without repeating a line-up. (Your answer should be an integer.)
Answer:
A) 24310
B) 18 seasons
Step-by-step explanation:
A) We are given the team has 17 players and there are 9 different positions in the team.
This is a combination question and thus, the number of different line-ups the team can make is;
C(17, 9) = 24310
B) We are told the basketball games consists of 9 innings.
Thus,
Number of games you can fill = 24310/9 = 2701.1111
And then we are told a season consists of 147 games.
Thus;
Number of complete seasons can the team play without repeating a line-up =
2701.1111/147 ≈ 18 seasons
Answer:
a
Step-by-step explanation:
5. There are two kinds of products (called DA and GA) produced in your company every day. Alsothere are two kinds of materials (denoted by A and B) in need One DA costs one unit of A, one unit of B: one GA costs one unit of A, two units of B. You get $3000 when you sell one DA and $5000 for one GA. The supply of the two materials every day is 12,22. a)What is the maximal profit $ b) How many DA and GA should be produced every day to obtain this maximal profit? Number of DA = Number of GA
Answer:
a) $56000b) DA = 2, GA = 10Step-by-step explanation:
Given
DA = A + B ⇒ $3000GA = A + 2B ⇒ $5000Number of A = 12Number of B = 22We can see from the equations that
GA - DA = B ⇒ $2000 andA = $1000 and B = $2000 in terms of profitSo greater use of unit B brings greater profit. We don't want any unit is left over, so get this equation.
A + B = 12A + 2B = 22Is the equation set to indicate use of the units A and B
Solving we get
A = 2 and B = 10It this case all the units are used and profit is maximum
2*$3000 + 10*$5000 = $56000Number of DA = 2Number of GA = 10Four relatives are going to give you money for your birthday. The amount each relative gives you is equally likely to be any number between $0 and $200. The chance that the total amount of money you receive is at most $300 is
Helppp I don’t understand
Answer:
p = 2L + 2W
total fencing = 100 feet
we have w = 20
then
100 = 2L + 2W
100 = 2L + 2*20
100 -40 = 2L
2L = 60
L= 60/2 = 30
-3/7(x-52) given x=10
Answer:
18
Step-by-step explanation:
-3/7 * ( x-52)
Let x = 10
-3/7 ( 10-52)
-3/7 * -42
-3 * -42/7
-3 * -6
18
Use function notation to represent the average speed of the car on the interval from t = 2 to t = 7 .
Answer:
[tex]Average\ Speed = \frac{s(7) - s(2)}{5}[/tex]
Step-by-step explanation:
Given
t = 2 to 7
Required
Find the average speed over these intervals
The function is not given; so, I'll represent the function as s(t)
When [tex]t = 2;[/tex]
[tex]s(t)= s(2)[/tex]
When [tex]t = 7[/tex]
[tex]s(t) = s(7)[/tex]
[tex]Average\ Speed = \frac{Change\ in\ Distance}{Change\ in\ Time}[/tex]
This gives:
[tex]Average\ Speed = \frac{s(7) - s(2)}{7 - 2}[/tex]
[tex]Average\ Speed = \frac{s(7) - s(2)}{5}[/tex]
Consumers sometimes make choices that cause negative information to be put on their credit reports. Which of these is the most likely number of years that this negative information will remain on their credit reports? O A. 3 to 6 years OB. 7 to 10 years O C. 11 to 14 years OD. 15 to 18 years
Answer:
7-10 years
Step-by-step explanation
A negative choice will stay on for about 7 years in real life, so it would be B since the answer choice B was the only one with the number 7 in it
The most likely number of years that this negative information will remain on their credit reports will be 7 to 10 years.
What is a negative credit card report?Generally speaking, negative information such as late or missed payments, accounts that have been sent to collection agencies, accounts not being paid as agreed, or bankruptcies stays on credit reports for approximately seven years.
Here is a breakdown of some of the different types of “negative” information and how long you can expect the information to be on your Equifax credit report:
Late payments remain on a credit report for up to seven years from the original delinquency date -- the date of the missed payment.
Bankruptcy public records stay on your Equifax credit report from seven to 10 years, depending on the type of bankruptcy.
Other negative accounts, such as repossessions, can also stay on your report for up to seven years from the date of the first missed payment that led to the negative status.
Hence The most likely number of years that this negative information will remain on their credit reports will be 7 to 10 years.
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Ms. Bailey is taking her children and their friends to the movies. She will pay $10 for her adult ticket and $6 for each child ticket. Ms. Bailey spends $46.00 at the movies. Write and solve an equation to determine the number of child tickets Ms. Bailey purchases.
Please include the Variable, Equation, and the Solution
Answer:
Ms. Bailey purchases 6 children tickets
Step-by-step explanation:
x=number of adult tickets
y=number of children tickets
10x+6y=46
plug in what you know
10(1)+6y=46
10+6y=46
subtract 10 from both sides
6y=36
divide both sides by 6
y=6
6 children tickets
A rectangular plot of land measures .25 miles In width and .75 miles in length. Find the area of the plot in square feet
Answer:
1,875
Step-by-step explanation:
by the way next time use a calculator not in a mean way ^^
If UV = 13, VW = 3x − 5, and UW = 5x − 18, what is UW? Simplify your answer and write it as a proper fraction, mixed number, or integer.
I got stuck here. If you could (or not) type step by step.
Since UV and VW make up UW, we can set add together UV and VW and set them equal to UW.
5x - 18 = 13 + 3x - 5
Let's combine like terms on the right side.
5x - 18 = 3x + 8
Subtract 3x from both sides and add 18 to both sides.
2x = 26
Divide both sides by 2
x = 13
We know that UW = 5x - 18. Let's plug 13 in for x.
UW = 5(13) - 18 = 65 - 18 = 47.
andrews bank account changed by -$50 after making four equal withdrawals. how much was each withdrawal
(57 + 4) x 4 - 16 I need this for my math test
Answer:
228
Step-by-step explanation:
(57 + 4) * 4 - 16
61 * 4 - 16( To get 61 solve the ones in brackets first)
244 - 16( Solve the multiplication to get 244 _ 61 * 4=244)
228 ( Then solve the subtraction - 244-16= 228)
SO THE ANSWER IS 228.
YOU JUST NEED TO FOLLOW BODMAS.
HOPE IT HELPED
what two numbers would 39 fall between on a number line
Answer:
38 and 40
Step-by-step explanation:
Hope this helps you :)
Answer:
39 would fall between 38 and 40
Step-by-step explanation:
How do you simplify 8^3
Steps to solve:
8^3
~Simplify
8 * 8 * 8
~Multiply all
4,096
Best of Luck!
what is the difference between (5+3)x3 (5+3)x9
Answer:
If you were asking the difference as in subtraction then the answer is 18.
(-5)+5 s )
What type of property is the equation
Answer:
-5 multiplied by positive five is your answer
Step-by-step explanation:
Point Q lies on AB. What definition, property, or postulate justifies the statement AQ + QB = AB?
Answer:
Segment Addition Postulate.
Step-by-step explanation:
The segment addition postulate justifies the statement:
[tex]AQ+QB=AB[/tex]
To help this make sense, you are namely adding segments on a line in order to achieve a complete line segment.
Your target number of calories is 2400 per day to lose weight, but you are consuming 3200 calories per day. Your target is what percentage of your consuming calories? Insert your answer as a whole percentage WITHOUT the % symbol.
Answer:
75
Step-by-step explanation:
Your target number of calories is 2,400 per day inorder to lose some amount of weight.
Instead 3,200 calories is consumed
Therefore the percentage of target that is consumed can be calculated as follows
= 2,400/3,200 × 100
= 0.75 × 100
= 75
Hence the percentage of calories that is consumed is 75
On a marathon course Amanda is 2mile behind Beverley and chad is 1 mile ahead of Beverly how far apart are Amanda and chad?
If random variable X has a binomial distribution with n=15 and P(success) =p= 0.6, find the mean of X. That is, find E(X). Round to the whole number. Do not use decimals. Answer:
Answer:
9
Step-by-step explanation:
E(X) = np
E(X) = (15) (0.6)
E(X) = 9
The mean of the X is 9.
What is the mean of the binomial distribution?The mean of a binomial distribution is the expected value (long-run average) of the number of successes in the given number of trials.
Formula for calculating mean of binomial distribution[tex]\mu_{x} = n.p[/tex]
where,
[tex]\mu_{x}[/tex] is the mean of the binomial distribution
n is the number of trials
and, p is the probability of success
According to the given question.
We have
Number of trials, n = 15
Probability of success, p = 0.6
Therefore, the mean of X is given by
[tex]E(X) = 15(0.6)[/tex]
⇒ [tex]E(X) = 9[/tex]
Hence, the mean of the X is 9.
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what is the place value of 5 in 7,832.951
All pictures are below please help Sandi had the following problem on her math test: . She showed her work on the test as follows: Given: Step 1: Step 2: Step 4: Step 5: In at least two paragraphs, explain the steps Sandi took to arrive at her answer. If she made any errors in her process clearly explain what she did wrong and how she could have made the error. If there is an error, provide the correct steps in your explanation of Sandi’s work. Use correct math terminology wherever appropriate.
Answer:
the answer is 6
Step-by-step explanation:
hope this helps!!!
Answer:
18
Step-by-step explanation:
6 × 4 + 2 ÷ 2 - 7
24 + 1 - 7
25 - 7
= 18
thanks
Why is it useful to write a ratio of fractions as a unit rate?
Answer:
When a ratio is written in fraction form, the fraction should be simplified. If it is an improper fraction, we do not change it to a mixed number. Because a ratio compares two quantities, we would leave a ratio as 41 instead of simplifying it to 4 so that we can see the two parts of the ratio.
What is the value of x?
Answer:
35 degrees
Step-by-step explanation:
180-95=85
180-(85+60)=35
what are the steps and answer for - 5n - 2 = 38
Answer:
n = -8
Step-by-step explanation:
[tex]- 5n - 2 = 38[/tex]
Collect like terms and simplify
[tex]-5n = 38+2\\\\-5n = 40[/tex]
Divide both sides of the equation by -5
[tex]\frac{-5n}{-5n} = \frac{40}{-5}[/tex]
Simplify
[tex]n = -8[/tex]
Lupe has 500 Mexican pesos. If 1 U.S. dollar equals 12.87333 pesos, about how many dollars can Lupe buy for her pesos?
Answer:
the answer is C. $38.84
Step-by-step explanation:
Which term best describes a figure formed by three segments connecting
three noncolinear points?
A. Angle
B. Obtuse
C. Vertex
D. Triangle
Answer:
The term that best describes a figure formed by three segments connecting three non-collinear points is:
Triangle.
Step-by-step explanation:
Step-by-step explanation:
We know that with the help of just one point we can't form any figure.
With the help of two points a line segment can be formed.
And with the help of three points if the three points are collinear a triangle can be formed.
Hence, the term that best describes a figure formed by three segments connecting three non-collinear points is:
Triangle.
The area of the Pacific Ocean is more than 60 million square miles.
What is that in scientific notation?
6x 10^-7
6x10^7
60 x 10^-6
60x10^6
Answer:
60x10^6
Step-by-step explanation: