If 8 people can mow the lawn in 6 hours, then the rate at which a single person mows the lawn is 1/6 of the total area. When 3 people take the day off, the number of people mowing the lawn becomes 8 - 3 = 5.
Therefore, the rate at which the 5 remaining people mow the lawn is 5 * 1/6 = 5/6 of the total area.
The time it takes to mow the lawn is inversely proportional to the rate at which the people mow the lawn.
So, to find the time it takes to mow the lawn with 5 people, we can divide the original time of 6 hours by the new rate of 5/6:
6 hours / (5/6)
= 6 * (6/5) hours
= 7.2 hours
So, it will take 7.2 hours to mow the lawn with 5 people.
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Three adjacent angles are at a point. The second angle is 25 degrees more than the first, and the third is 25 degrees more than the second, Find measurements of all 3 angles.
PLEASE NEED ANSWER ASAP
The measurement of the angles are 95°, 120°, and 145°.
How to calculate the angle?Let the smallest angle = x
Second angle = x + 25
Third angle = x + 25 + 25 = x + 50
x + x + 25 + x + 50 = 360
3x + 75 = 360
3x = 360 - 75
3x = 285
x = 285/3
x = 95°
Second angle = 95 + 25 = 120°
Third angle = 95 + 50 = 145°
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-5+9+(-5)+(-10)+(1) is equal to
Answer:
- 10
Step-by-step explanation:
Distribute the '+' into the '-' and simplify:
-5+9+(-5)+(-10)+(1) =
-5 + 9 - 5 - 10 + 1 =
-10
Answer:
\( \boxed{ \boxed{ \bold{ \purple{ - 10}}}}\)Step-by-step explanation:
\( \sf{ - 5 + 9 + ( - 5) + ( - 10) + 1}\)
When there is a ( + ) in front of an expression in parentheses, the expression remains in same.
⇒\( \sf{ - 5 + 9 -5 - 10 + 1}\)
Calculate
⇒\( \sf{ 4 - 5 - 10 + 1}\)
⇒\( \sf{ - 1 - 10 + 1}\)
⇒\( \sf{ - 11 + 1}\)
⇒\( \sf{ - 10}\)
Hope I helped!
Best regards!!
A town's population is currently 8,000. If the population doubles every 98 years, what will the population be 294 years from now?
Answer:
the answer is 24,000
Step-by-step explanation:
294*98=3
3*8,000= 24,000
Answer: 24000
Step-by-step explanation: 294 divided by 98 is 3, 8000 x 3 = 24000
Which is an example of a quadratic trinomial
Answer:
Option 1 4x^3+6x^2-10x
Step-by-step explanation:
when the highest value for x has a cube root, it is a trinomial. Tri for 3. When it is squared it is a binomial. Bi for 2.
Hope that helps :)
what is the median of this distribution ?
Answer:
The median of a distribution, denoted as xmed, is defined as the value of x such that are equal probabilities of getting a larger value and getting a smaller value than xmed. In other words, P(xmed)=0.5.Step-by-step explanation:
Guys it’s due in 3hrs help
Answer:
-0.01333333333
Step-by-step explanation:
I wish you well on that assignment <3
Answer:
-1/3
Step-by-step explanation:
Convert decimals to fraction and Multiply/Divide
Solve this pleasee!!!!!!!!!!!
Answer:
1) Solution (2,-3)
2) Solution (-1, \(-\frac{3}{2}\))
3) Solution (\(\mathbf{-\frac{1}{2},-\frac{5}{2}}\))
Step-by-step explanation:
We need to solve equations using elimination
1) \(2x+2y=-2\\3x-2y=12\)
Let:
\(2x+2y=-2--eq(1)\\3x-2y=12--eq(2)\)
Adding both equations:
\(2x+2y=-2\\3x-2y=12\\--------\\5x=10\\x=\frac{10}{5}\\x=2\)
We get value of x = 2
Now, put value of x into equation 1 to find value of y
\(2x+2y=-2\\Put\:x=2\\2(2)+2y=-2\\4+2y=-2\\2y=-2-4\\2y=-6\\y=-6/2\\y=-3\)
So, we get y = -3
Solution (2,-3)
2) \(4x-2y=-1\\-4x+4y=-2\)
Let:
\(4x-2y=-1--eq(1)\\-4x+4y=-2--eq(2)\)
Adding both equations
\(4x-2y=-1\\-4x+4y=-2\\------\\2y=-3\\y=\frac{-3}{2}\)
We get: y= -3/2
Now find value of x by putting value of y in eq(1)
\(4x-2y=-1\\Put\:y=\frac{-3}{2}\\4x-2( \frac{-3}{2})=-1\\4x+3=-1\\4x=-1-3\\4x=-4\\x=\frac{-4}{4}\\x=-1\)
We get x = -1
Solution (-1, \(-\frac{3}{2}\))
3) \(x-y=2\\x+y=-3\)
let:
\(x-y=2--eq(1)\\x+y=-3--eq(2)\)
Add both equations:
\(x-y=2\\x+y=-3\\-----\\2x=-1\\x=-\frac{1}{2}\)
We get x = -1/2
Now, put value of x in equation 2
\(x+y=-3\\-\frac{1}{2}+y=-3\\y=-3+ \frac{1}{2}\\y=\frac{-6+1}{2}\\y=\frac{-5}{2}\)
We get y = -5/2
Solution (\(\mathbf{-\frac{1}{2},-\frac{5}{2}}\))
PLS HELP ASAP I DONT HAVE TIME FOR THIS, IT ALSO DETECTS IF ITS RIGHT IR WRONG
Answer:
120
Step-by-step explanation:
Add angle ABC and angle CBD together.
Consider the following sample data values. 7 4 6 12 8 15 1 9 13 a) Calculate the range. b) Calculate the sample variance. c) Calculate the sample standard deviation. a) The range is 14 b) The sample variance is (Round to two decimal places as needed.) c) The sample standard deviation is (Round to two decimal places as needed.)
a) The range is 14.
b) The sample variance is 20.78.
c) The sample standard deviation is 4.56.
a) Range
The range of a given set of data values is the difference between the maximum and minimum values in the set. In this case, the maximum value is 15 and the minimum value is 1. So, the range is:
Range = maximum value - minimum value
Range = 15 - 1
Range = 14
b) Sample variance
To calculate the sample variance, follow these steps:
1. Calculate the sample mean (X). To do this, add up all of the data values and divide by the total number of values:
n = 9
∑x = 7 + 4 + 6 + 12 + 8 + 15 + 1 + 9 + 13 = 75
X = ∑x/n = 75/9 = 8.33
2. Subtract the sample mean from each data value, square the result, and add up all of the squares:
(7 - 8.33)² + (4 - 8.33)² + (6 - 8.33)² + (12 - 8.33)² + (8 - 8.33)² + (15 - 8.33)² + (1 - 8.33)² + (9 - 8.33)² + (13 - 8.33)² = 166.23
3. Divide the sum of squares by one less than the total number of values to get the sample variance:
s² = ∑(x - X)²/(n - 1) = 166.23/8 = 20.78
Therefore, the sample variance is 20.78 (rounded to two decimal places).
c) Sample standard deviation
To calculate the sample standard deviation, take the square root of the sample variance:
s = √s² = √20.78 = 4.56
Therefore, the sample standard deviation is 4.56 (rounded to two decimal places).
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please help, the brainiest will go to the one with a good answer.
Reduce the following fraction: -36x^4y^4z^5/-12x^6y^3z
A. -3x^2yz^4
B. 3yz^4/1x^2
C. -9yz^5/-3x^2
D. 36yz^5/12x^2
Brian can iron 3 shirts in 5 minutes. If Brian irons at a constant rate, how many shirts can he iron in 30 minutes? WILL GIVE BRANLIEST
Answer:
18
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
30/5 = 6
6 * 3 = 18
A grocery store manager wanted to determine the wait times for customers in the express lines. He timed customers chosen at random.
What is the meaning of the interval in terms of wait times for customers?
The interval in terms of wait times for customers refers to the range of time periods within which the actual wait times for customers in the express lines are likely to fall.
To determine the interval, the grocery store manager timed customers chosen at random. Let's say the manager observed the following wait times for five randomly selected customers: 2 minutes, 4 minutes, 3 minutes, 5 minutes, and 2 minutes.
To calculate the interval, you can find the minimum and maximum values from the observed wait times. In this case, the minimum wait time is 2 minutes, and the maximum wait time is 5 minutes. Therefore, the interval in terms of wait times for customers is from 2 minutes to 5 minutes.
The interval in terms of wait times for customers, based on the observations, is 2 minutes to 5 minutes. This means that for future customers in the express lines, the expected wait time could range from a minimum of 2 minutes to a maximum of 5 minutes. The interval provides an estimate of the typical range of wait times, helping the grocery store manager understand the variability and plan accordingly to optimize customer service and minimize wait times. It is important to note that this interval is specific to the observed sample and may not necessarily represent the exact range for all customers in the express lines.
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At the start of 2014, Mike's car is worth 12000. the car depreciates by 30 percent every year. how much is his car worth in 2017
Answer:
$4,116
Step-by-step explanation:
Worth of Mike's car at the start of 2014 = $12,000
If the car is said to depreciates every year by 30% = 30/100 = 0.3
The worth of the car at the start of 2017 is what we are to determine.
This means that the car depreciated by 30% (0.3) for 3 years since 2014 (2017 - 2014 = 3 yrs)
The worth at the start of 2017 would be calculated as follows:
12,000 × (1 - 0.3)³
= 12,000 × (0.7)³
= 12,000 × 0.343
= 4,116
Worth of the car at the start of 2017 would be $4,116
Help ASAP will give brainiest
Answer:
39 in the filmmaking club
25 in the yearbook club
Step-by-step explanation:
X =14+y
14+y + y = 64
14 +2y = 64
2y=50
y=25
if y is 25 then subtract 25 from 64 to get x
64-25=39
if the cycle time is 2 minutes/customer then how many customers are served per hour? multiple choice question. 15 20 30 60
If the cycle time is 2 minutes per customer, 30 customers can be served per hour.
The given cycle time is 2 minutes per customer. To calculate how many customers can be served per hour, we need to calculate the number of minutes in an hour as follows: 60 minutes = 1 hour.
The time taken for each customer is 2 minutes. Therefore, the number of customers that can be served per hour can be calculated as follows:
Number of customers per hour = (60 minutes/hour) ÷ (2 minutes/customer)
Number of customers per hour = 30 customers.
Therefore, the number of customers that can be served per hour is 30, according to the given cycle time of 2 minutes per customer.
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INDEPENDENT PRACTICE
1. Angle 5 and 3 are vertical angles.
2. Angle 1 and 5 is a straight-line pair.
3. 4 and 3 are adjacent angles.
4. 4 and 1 are vertical angles.
5. 3 and 4 is a straight-line pair.
T or F
Tor F
Tor F
T or F
T or F
What is the slope of a line that passes through the points (9,8) and (2,3)?
The slope of the line that passes through the points (9,8) and (2,3) is 5/7.
What is a slope in a graph?The slope of a line in a graph is a measure of its steepness or slant. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. In mathematical terms, the slope of a line can be represented as the difference in the y-coordinates of two points on the line divided by the difference in the x-coordinates of the same two points.
The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:
slope = (y2 - y1) / (x2 - x1)
Plugging in the given points, we get:
slope = (3 - 8) / (2 - 9) = -5 / -7 = 5/7
So, the slope of the line that passes through the points (9,8) and (2,3) is 5/7.
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What is the slope that contains the points (-4, 7) and (-6, -4)?
Answer:
m= 11/2
Step-by-step explanation:
Answer:
11/2
Step-by-step explanation:
[Please help me on this- I will give you brainlist!!]
Write the terms in standard form. Then state the degree of the polynomial and the leading coefficient (LC).
For the polynomial 9, 3x², 8x; the degree is 2 and the leading coefficient is 3
What is an equation?An equation is used to show the relationship between numbers and variables.
Polynomial is an expression composed of variables, constants and exponents using mathematical operations such as addition, subtraction, multiplication and division
The degree is the highest exponent of variable for the polynomial. The polynomial with degree of 2 is known as a quadratic polynomial
Given the polynomial:
9, 3x², 8x
Writing in standard form is done by rearranging from highest exponent of variable to least. This is:
3x², 8x, 9
Hence the degree is 2 and the leading coefficient is 3
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First equation: y = -20x+800
third equation: y = -30x+800
how do the descent and landing time of the third balloon compare with that of the first balloon? What does this mean graphically
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10 The scatterplot shows the number of people in each of 8 different households and the average amount of money each household spent on groceries. Weekly Grocery Expenses y A v e r a g eA mountS p u n t o nG g r o c e r i e s( d o l l a r s )320 280 240 200 160 120 80 40 Number of People in Household x 0 2 4 6 8 Based on the scatterplot, what is the best prediction of the average amount of money spent on groceries for a household that has 7 people
The best prediction of the average amount of money spent on groceries for a household that has 7 people can be determined by examining the scatterplot and estimating the corresponding value on the y-axis.
Based on the scatterplot, the best prediction for the average amount of money spent on groceries for a household with 7 people would be around $160.
To arrive at this prediction, we observe the position on the x-axis where the number of people in the household is 7. Then, we look at the corresponding position on the y-axis to determine the average amount of money spent on groceries. In this case, the scatterplot suggests that households with 7 people tend to spend around $160 on groceries.
It's important to note that this prediction is based on the pattern observed in the given scatterplot, and there may be some variability or uncertainty in the actual amount spent on groceries for a specific household with 7 people.
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Determine which branch of statistics was used to make the following statement. In an online survey of 500 Virginia Tech students between spring 2010 and spring 2011, 3190 said that they had missed class because of alcohol consumption. A) differential statistics C) inferential statistics B) time series statistics D) descriptive statistics
The branch of statistics used to make the given statement is Option(D) Descriptive Statistics.
Which are the different branches of statistics?
The area of mathematics that deals with data is statistics. Data collection, descriptive statistics, and inferential statistics are the three main subfields of statistics.
The process of gathering data is what data collection is all about.The area of statistics known as descriptive statistics deals with how we present the data we have. Basically, this can be done in one of two ways: either visually (using graphs, charts, etc.) or quantitatively (via averages and so on).The part of statistics that deals with drawing inferences from the data is called inferential statistics.For the given question, we are presented with data quantitatively. The data shows out of 500 students, 31% missed class due to alcohol consumption.
Therefore the branch of statistics that was used to make the above statement is descriptive statistics.
Hence Option(d) is correct.
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how do i solve for x
Answer:division if you just use the derivative
Step-by-step explanation:
I don’t know how to find the value of x PLEASE HELP!!!
Answer:
the value of x is 8.
Step-by-step explanation:
\(x {}^{2} = 64\)
\(or \: x = \sqrt{64} \)
therefore x=8
is the answer...
Answer:
x=8
Step-by-step explanation:
\(8^{2} =64\)
8·8·8·8·8·8·8·8=64
hope this helps
good luck!!
At a high school 24% of the students are seniors. Which of the following is closest to the probability of getting less than 21% seniors in a random sample of size 100?
A 0.241
B 0.769
C 0.759
D 0.231
The closest probability of getting less than 21% seniors in a random sample of size 100 is A. 0. 241.
How to find the probability ?The normal approximation to the binomial distribution can be used to find the probability.
First, find the mean :
= sample size x probability of success
= 100 x 0. 24
= 24
Then the standard deviation :
= √ ( 100 x 0. 24 x ( 1 - 0. 24 ))
= 4. 278
Using the standard normal distribution (Z) , we have:
Z = (X - μ) / σ
Z = ( 21 - 24 ) / 4.278
= - 0. 702
From the Z - table, we have:
P ( Z < -0.702 ) = 0.2417
In conclusion, option A is correct.
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1. Express the following measurements in standard notation.
9.322 x 104 m
Scientific notation is built upon the idea of moving the decimal place to the left or right so many places.
A foundational background concept is that multiplying by 10 makes a number bigger and moves the decimal to the right.
For example: 3.4 x 10 = 34
The counterpart for that is that dividing by 10 makes a number smaller and moves the decimal to the left.
For example: 3.4 ÷ 10 = 0.34
So, when you see 3.4 x 10^5, this means you’re multiplying by 10 fives times, so that will move the decimal point five places to the right.
3.4 x 10^5 = 340 000
On the other hand, when you see a negative exponent on the 10, then that means you’re actually dividing by that many 10s and will move the decimal point that many places to the left. (to make the number smaller)
3.4 x 10^-5 = 0.000034
So, you need to first identify if you’ll make the number bigger or smaller (is the power of 10 postive or negative?) and then how many places the decimal point will need to move.
help pls D:
9. The table represents some points on a linear
function. Which situation can be modeled by this
function?
X
3
5
7
11
Y
228
380
532
836
A. The cost of buying number of concert tickets for
$76 each.
B. The number of pages y that can be read in 76
minutes.
C. The number of gallons of fuel xthat can be used to
travel 228 miles.
D. The amount of money spent from a savings
account with y dollars.
Answer:
A
Step-by-step explanation:
Chris rented a truck for one day. There was a base fee of $15.99, and there was an additional charge of 78 cents for each mile driven. Chris had to pay $249.21when he returned the truck. For how many miles did he drive the truck?
Answer:
299 miles
Explanation:
Base Fee for the truck = $15.99
Charge per mile driven = 78 cents =$0.78
Let the number of miles driven = x
Therefore, for x miles, Chris would be expected to pay a total charge, C defined by the equation below:
\(C=15.99+0.78x\)If Chris had to pay $249.21 when he returned the truck, it means that:
His total charge, C = $249.21
\(\begin{gathered} $249.21$=15.99+0.78x \\ 0.78x=$249.21$-15.99 \\ 0.78x=233.22 \\ \text{Divide both sides by 0.78} \\ x=299 \end{gathered}\)We conclude therefore that Chris drove the truck for 299 miles.
How to factor 2x^2 - 7x +6
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given expression
\(2x^2-7x+6\)STEP 2: Multiply the constant with the leading term
\(6\times2x^2=12x^2\)STEP 3: Write the possible factors of the result in product form
\(\begin{gathered} 12x^2 \\ x\cdot12x,-x\cdot-12x \\ 2x\cdot6x,-2x\cdot-6x \\ 3x\cdot4x,-3x\cdot-4x \end{gathered}\)STEP 4: Find the factors that will give the second term (-7x) when added
\(\begin{gathered} -7x \\ -3x+(-4x)=-3x-4x=-7x \end{gathered}\)STEP 5: Substitute these factors for -7x in the expression in step 1
\(2x^2-4x-3x+6\)STEP 6: Factorize by grouping
\(\begin{gathered} 2x(x-2)-3(x-2) \\ (2x-3)(x-2) \end{gathered}\)Hence, the factors of the given expression are:
\((2x-3)(x-2)\)If two fair dice are rolled, find the probability that the sum of the dice is 9, given that the sum is greater than 3.
The probability is
The probability that the sum of the dice is 9 is, 4/33.
What is dice?
Dice are little, thrown-away devices with marked sides that can rest in various locations. They are frequently employed in tabletop games including dice games, board games, role-playing games, and games of chance to provide random values.
Let two fair dice are rolled.
So the possible number of outcomes are,
(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4,6)
(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)
There are total 36 outcomes.
There are 33 outcomes with sum greater than 3.
The outcomes with sum greater than 9 are, 4 which are (3, 6), (4, 5), (5, 4) and (6, 3).
Hence, the probability that the sum of the dice is 9 is, 4/33.
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