Answer:
-2
Step-by-step explanation:
-6x=5x+22
-6x-5x=22
-11x=22
x=22/-11
x=-2
Four more than 5 times the number x is less than 50
Answer:
4+5x<50
Step-by-step explanation:
5n < 50 <--- subtracts 4 from both sides
n < 10 <--- divides both sides by 5
Check: testing n=0, we have 4 + 5(0) = 4 + 0 = 4 < 54, so yes it works
testing n=10, 4 + 5(10) = 4 + 50 = 54.
testing n=11, 4 + 5(11) = 4 + 55 = 59 <--- fails as expected.
X < 10, proven, verified, correct
The inequality 'Four more than 5 times the number x is less than 50' translates to '5x + 4 < 50'. By solving, we find the solution is 'x < 9.2', indicating that x must be less than 9.2.
Explanation:The question "Four more than 5 times the number x is less than 50" can be translated into a mathematical inequality. The 'four more than' suggests addition, and '5 times the number x' indicates multiplication.
Therefore, we have the inequality 5x + 4 < 50. To find the range of values for x, we need to solve the inequality for x.
Step 1: Subtract 4 from both sides to isolate the term with x on one side of the inequality. 5x < 46.
Step 2: Divide both sides by 5 to solve for x. x < 9.2.
So, the solution to the inequality is that x must be less than 9.2. This inequality does not require the quadratic formula as suggested in some parts of the provided information.
The assumption that 'The value of x is not less than 5% of 0.50' is also not relevant to solving this particular inequality.
A middle school contains sixth seventh and eighth graders each grade level contains approximately the same number of students the principal wants to find the answer to a survey question affecting each student in the school he has a sample group what time do you get up in the morning which of these characters is to find the best sample
Answer:
an equal number of students chosen at random from each grade level
In statistics, a sample is a little amount that reveals how the remainder is or should be.
What are statistics?Statistics is the study of collection, analysis, interpretation, and presentation of data or to discipline to collect, and summarise the data.
A middle school contains sixth, seventh, and eighth graders each grade level contains approximately the same number of students the principal wants to find the answer to a survey question affecting each student in the school.
An equal number of pupils from each grade level were chosen at random.
We could simply collect the information of all the pupils by randomly picking some students such that there are an equal number of students from each grade.
More about the statistics link is given below.
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While working at the drugstore, Robbie earns $12 per hour. How many hours will it take Rubbie to earn $48?
Answer:
4 hours.
Step-by-step explanation:
If Robbie earns 12 dollars per hour, it will take him 4 hours to earn 48 dollars. This is because 48/12 = 4.
48/12=hours
12+12+12+12=hours
4 hours
Amanda has 5 pieces of wire that are each 15.5 feet long . She wants to cut the wire into 3.5 feet long pieces. Any extra wire will be considered scrap . How much scrap will Amanda have ?
2 times 10 to the 16th plus 7 times 10 to the 16th in scientific notation
Answer:
The answer is [tex]9\times 10^{16}.[/tex]
Step-by-step explanation:
Given:
2 times 10 to the 16th plus 7 times 10 to the 16th in scientific notation.
Now, to solve in scientific notation.
So, we change into scientific notation:
2 times 10 to the 16th
[tex]=2\times 10^{16}[/tex]
7 times 10 to the 16th
[tex]=7\times 10^{16}[/tex]
Now, to add:
[tex]2\times 10^{16}+7\times 10^{16}[/tex]
As, we see the powers are same so we add the numbers in this standard form:
[tex]=(2+7)10^{16}[/tex]
[tex]=9\times 10^{16}.[/tex]
Therefore, the answer is [tex]9\times 10^{16}.[/tex]
1. In a factory, all employees work a basic week of 38 hours. Any overtime worked during week-days is paid for at time and a half. Overtime worked on Saturday is paid for at double-time,whilst on Sunday it is paid for triple-time. If the basic rate is $8.96 per hour, determine the gross wage of a man who worked 15 hours overtime from Monday to Friday, 3 hours overtime on Saturday and 2 hours overtime on Sunday.
2. In an urea manufacturing plant, all employees work a basic week of 40 hours. Any overtime worked during weekdays is paid for at time -and-a-quarter. Overtime worked on Saturday is paid for time-and-a-half, whilst on Sunday it is paid for at double-time. If the basic rate is $14.60 per hour and a man worked 15 hours overtime during weekdays, 6 hours overtime on Saturday and 5 hours overtime on Sunday. Calculate:
(a) His basic wage
(b) His overtime wage
(c) His gross wage for the week.
3. At a chemical factory, the basic week is 40 hours. During a particular week Mr. James earned a gross wage of $518.00, but $148.00 was for overtime.
(a) Calculate Mr. James basic rate of payment.
(b) If overtime was paid for at double-time,calculate how many hours Mr. James worked overtime.
Answer:
Step-by-step explanation:
1. reg pay: 8.96,week days: 1.5 overtime pay, sat: double pay, sun: triple pay
38 hrs regular pay : 38 * 8.96 = 340.48
15 hrs overtime during week : 15 * 1.5(8.96) = 15 * 13.44 = 201.60
3 hrs overtime on saturday: 3 * 2(8.96) = 3 * 17.92 = 53.76
2 hrs overtime on sunday: 2 * 3(8.96) = 2 * 26.88 = 53.76
Gross wage = (340.48 + 201.60 + 2(53.76) = 649.60 <====
===============================
2. reg pay : 14.60, weekday pay: 1.25,sat pay: 1.5 , sun pay: double
(a) basic wage = 40(14.60) = 584 <==
(b) overtime wage : 15 * 1.25(14.60) + 6 * 1.5(14.60) + 5 * 2(14.60) = (15 * 18.25) + (6 * 21.9) + (5 * 29.2) = 273.75 + 131.40 + 146 = 551.15 <==
(c) gross wage : 584 + 551.15 = 1135.15 <==
================================
3. basic work wk: 40 hrs...earned 518...overtime 148
(a) basic pay rate : (518 - 148) / 40 = 370/40 = 9.25 per hr <==
(b) if overtime is paid for at double time.....so overtime pay is (2 * 9.25) = 18.50 per hr....and he got paid 148....148/18.5 = 8 hrs <==
The gross wage of the man who worked overtime from Monday to Friday, on Saturday, and on Sunday is $582.40.
Explanation:In order to determine the gross wage of the man, we need to calculate the wages for each type of overtime worked. Let's start with the basic wage calculation for each scenario:
Question 1:
The man worked 15 hours overtime on week-days, so he will receive 15 x 8.96 = $134.40 for week-day overtime.
He also worked 3 hours overtime on Saturday, so he will receive 3 x (2 x 8.96) = $53.76 for Saturday overtime.
Lastly, he worked 2 hours overtime on Sunday, so he will receive 2 x (3 x 8.96) = $53.76 for Sunday overtime.
Now let's calculate the gross wage by adding the basic wage and the overtime wages together:
Gross Wage = Basic Wage + Week-day Overtime Wage + Saturday Overtime Wage + Sunday Overtime Wage
= (38 x 8.96) + 134.40 + 53.76 + 53.76
= $340.48 + $134.40 + $53.76 + $53.76
= $582.40
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What is 120 degrees in radians?
Answer:2.0994
Step-by-step explanation:
You would want to set up the equation like this
120°×π/180 which will then be 2.094rad
120 degrees is equal to 2π/3 radians. You can convert degrees to radians by using the conversion factor π/180. This method simplifies to 2π/3 for 120 degrees.
Converting Degrees to Radians
To convert an angle from degrees to radians, you can use the conversion factor that 360° is equal to 2π radians. Therefore, 1 degree is equal to π/180 radians. To convert 120 degrees to radians, you can follow these steps:
Write down the conversion factor: 1° = π/180 radians.Multiply 120 by π/180: 120° × π/180.Simplify the expression: 120/180 × π = 2/3π.Therefore, 120 degrees is equal to 2π/3 radians. This method ensures accurate conversion and is useful in various mathematical calculations.
Question 13 options:
A jar contains 50 coins, all of which are dimes and quarters.
The total value of the coins in the jar is $7.70.
How many dimes/quarters are in the jar?
Answer:
The jar has 32 dimes and 18 quarters
Step-by-step explanation:
To solve this problem we can create a system of linear equations in terms of two-variables (say [tex]x[/tex] and [tex]y[/tex]) and solve it. To begin let us analyze the problem further. We know that the values of each coin type are:
Dimes ( [tex]x[/tex] ) = $0.10
Quarters( [tex]y[/tex] ) = $0.25
Total Value = $7.70
Total Coins = 50
Now let us set up our system of equations as:
[tex]0.10x+0.25y=7.70[/tex] Eqn.(1)
[tex]x+y=50[/tex] Eqn.(2)
Lets take Eqn.(2) and rerrange it to solve for [tex]x[/tex] as:
[tex]x=50-y[/tex] Eqn.(3)
Now lets plug this, in Eqn.(1) so we get the value of [tex]y[/tex] as:
[tex]0.10(50-y)+0.25y=7.70\\\\5-0.10y+0.25y=7.70\\\\-0.10y+0.25y=7.70-5\\\\0.15y=2.7\\\\[/tex]
[tex]y=\frac{2.70}{0.15} \\\\y=18[/tex]
Plugging in [tex]y=18[/tex] back in Eqn.(3) we finally have:
[tex]x=50-18\\x=32[/tex]
Thus we conclude that in the jar the coins are:
Dimes ( [tex]x[/tex] ) [tex]=32[/tex]
Quarters( [tex]y[/tex] ) [tex]=18[/tex]
Keith’s dad is 44 years old if this is 4 years less than three times Keith’s age how old is Keith
Answer:
13
Step-by-step explanation:
Answer:
16
Step-by-step explanation:
44+4=48
48/3=16
Henry is hosting a party at his house, and his guests have requested pizza. He invites four of his best friends and two new friends from his class. If Henry and his friends eat 2/8 slices of pizza, how many pizzas should Henry order? Solve and explain your thinking using mathematical reasoning
Brad plans 27 roses and 36 daffodils. He plants an equal number of each type of flower in each row. What is the greatest possible number of roses in each row?
Answer:
3 rows of roses and 9 daffodils each row. (3x9=27)
4 rows of roses, 9 in each row.
(4x9=36)
Hope that helps!
Step-by-step explanation:
Answer:
Step-by-step explanation:
9 roses in the 3 rows. 9 goes into 27, 3 equal times.
The sum of two numbers is -284. One number is 62 less then the other. Find the numbers
Answer:
It could be -111 and -173
Step-by-step explanation:
-111 is 62 more than -173 and together they are -284.
Simplify each expression. (y + 22) + 3
To simplify, remove the parentheses and combine like terms:
( y + 22) + 3
Y + 22 + 3
Answer: Y + 25
If X = 6 cm and Y = 8 cm, what is the length of Z?
please help me with this
Given a spinner with 9 equal-area sections, a trial of 100 spins resulted in an experimental probability of 13% for the spinner
landing on 4. Which of the following statements must be false?
A. The theoretical probability P(spinner < 4) = 100%
B. The theoretical probability P(spinner =4) = 11%
C. In a new trial of 100 spins, the experimental probability, P(spinner=4) may be different.
D. The experimental probability P(not spinner =4) = 87% for this trial.
Answer:
b
Step-by-step explanation:
Answer:
The answer is spinner B. There are 8 sections on the spinner and 4 of them have letter A, so P(A)= 1/2.
Find g(f(4)).
g(f(4)) =
Answer:
what is the equation of f(x)
Step-by-step explanation:
Answer:
9 is the answer
Step-by-step explanation:
when did WWII start (please dont delete ansers i will do that ok)
There are a couple different dates that people say WW2 started but the main start of the war was when the Nazi’s invaded Poland September 1, 1939
Tyler's age is three less than his brother's age. The sum of their ages is 11.
How old is Tyler?
14
7
4
2
Answer:
His Age is 4 years old
Step-by-step explanation:
His brother is 7
Answer: 4
Step-by-step explanation:
If Tyler is 4 years old then his brother would be 7 and 7+4=11
The difference between two numbers is 9. The first number plus twice the other number is 27. Find the two numbers.
The two numbers are 15 and 6
Solution:
Let the two number be "a" and "b"
Let the first number be "a" and second number be "b"
Given that,
The difference between two numbers is 9
a - b = 9 -------- eqn 1
The first number plus twice the other number is 27
First number + twice the second number = 27
a + 2b = 27 ---------- eqn 2
Let us solve eqn 1 and eqn 2
From eqn 1,
a = 9 + b ------ eqn 3
Substitute eqn 3 in eqn 2
9 + b + 2b = 27
3b = 27 - 9
3b = 18
Divide both sides of equation by 3
b = 6Substitute b = 6 in eqn 3
a = 9 + 6
a = 15Thus the two numbers are 15 and 6
Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 8 people took the trip. She was able to purchase coach tickets for $290 and first class tickets for $980. She used her total budget for airfare for the trip, which was $5080. How many first class tickets did she buy? How many coach tickets did she buy?
Sarah bought 4 first class tickets and 4 coach tickets for a total of 8 tickets, using her entire budget of $5080.
Explanation:Sarah purchased tickets for a total of 8 people with a mix of coach and first class tickets. The cost for coach tickets was $290 each, and the cost for first class tickets was $980 each. With a total airfare budget of $5080, we need to determine how many of each type of ticket she bought.
Let's denote the number of first class tickets as x and the number of coach tickets as y. The two equations representing the situation are:
x + y = 8 (since there are 8 people including Sarah)980x + 290y = 5080 (the total cost of tickets must equal the budget)From the first equation, we can express y in terms of x: y = 8 - x. Substituting this into the second equation gives us:
980x + 290(8 - x) = 5080
Solving for x will give us the number of first class tickets, and using the value of x, we can find y, the number of coach tickets. After simplifying and solving, we find that:
980x + 2320 - 290x = 5080
690x = 2760
x = 4
Thus, Sarah bought 4 first class tickets. To find the number of coach tickets (y), we substitute x into the first equation:
y = 8 - 4
y = 4
Therefore, Sarah also bought 4 coach tickets.
Jackson decided to exercise. He has at most 45 minutes to exercise and he wants to burn at least 400 calories. He burns 10.4 calories per minutes.
Answer: 38.46
Step-by-step explanation:
400/10.4= 38.46
solve the linear system of equations using the linear combination method.
4x-9y=20
2x-6y=16
The solution is (-4,4)
Step-by-step explanation:
Given equations are:
[tex]4x-9y = 20\ \ \ \ Eqn1\\2x-6x = 16\ \ \ \ Eqn2[/tex]
In linear combination method, we have to make coefficients of any one variable opposites by multiplying with an integer
So multiplying 2nd equation by -2
[tex]-2(2x-6y=16)\\-4x+6y=-32\ \ \ \ Eqn3[/tex]
Adding Equation 1 and Equation 3:
[tex]4x-9y-4x+12y = 20-32\\3y = -12[/tex]
Dividing both sides by 3
[tex]\frac{3y}{3} = \frac{-12}{3}\\y = -4[/tex]
Putting y=-4 in equation 1
[tex]4x-9(-4) = 20\\4x +36= 20\\4x = 20-36\\4x = -16[/tex]
Dividing both sides by 4
[tex]\frac{4x}{4} = \frac{-16}{4}\\x = -4[/tex]
Hence,
The solution is (-4,4)
Keywords: Linear combination, linear equations
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A cube has a surface area of 100 square inches. Which choice is closest to the length
of an edge of the cube?
A. 1.7 inches
B. 3.3 inches
C. 10 inches
D. 4.1 inches
Answer:
D. 4.1 inches
Step-by-step explanation:
Which of the following is an even function?
f(x) = (x - 1)2
OMX) = 8x
O f(x) = x2-X
Of(x) = 7
Answer:
F(X)=7 is the even function
Step-by-step explanation:
f(x)=(x-1)2 is neither odd or even
f(x)=8x is a odd function
f(x)=x2-x is neither odd or even
and f(x)=7 is EVEN
$925 at 2.3% for 2.4 years what is the interest earned
Answer:
51.06
Step-by-step explanation:
So
P=$925
R=2.3%
T=2.4
So to get the answer we would need to multiply all of these together so first we would do 925 times 2.3% which would be 21.275. Then we would do 21.275 times 2.4 then we would get the answer of 51.06.
Is 13/8 greater less or equal to 15/12
Greater than bc the pieces is bigger
Samantha wants to invest $6800 in a savings account that pays 6% simple interest. How long will it take for
this investment to double in value? Round your answer to the nearest tenth.
Answer:
years
Step-by-step explanation:est $ 6800
Samantha wants to invest $ 6800 in a saving account that pays 6% simple interest .
Let it will be take x year
Principle =$6800
Interest = $ 6800
Rate of interest = 6%
Time = x(let)
According To Problem
6800=[tex]\frac{6800\times x\times 6}{100}[/tex]
⇔x = [tex]\frac{100}{6}[/tex] = 16.67 year
Therefore ,it will take 16.67 year .
Answer:
16.67 years.
Step-by-step explanation:
Samantha wants to invest $6800 in a savings account that pays 6% simple interest.
Let after y years the amount will be double in value.
So, using the formula of simple interest we can write
[tex]2 \times 6800 = 6800(1 + \frac{6\times y}{100})[/tex]
⇒ [tex]2 = 1 + \frac{6y}{100}[/tex]
⇒ 6y = 100
⇒ y = 16.67 years.
Therefore, after 16.67 years the amount will become double in value. (Answer)
10x^2=6x how do i solve ? quadratic equation
Answer:
x=0 or x=6/10
Step-by-step explanation:
10x^2=6x ⇔ 10x^2 - 6x = 0 ⇔ x(10x-6)=0 ⇔ x=0 or x= 6/10
Y=2/3x+5 find the slope and y-intercept of the linear equation
The slope is always rise/run and has a variable. In this case, 2/3x is the slope.
The y-intercept is always the number at the end, which is the y-value. This would mean that 5 is the y-intercept.
Answer:
Step-by-step explanation:
Y = ⅔X + 5
Comparing with y = mx + c
Where m is the slope and c is the intercept
m = ⅔ and c = 5