a lawn can be mowed by 8 people in 6 hours. if 3 people take the day off and do not help mow the grass, how many hours will it take to mow the lawn?

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

The measurement of the angles are 95°, 120°, and 145°.

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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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:

Answer:

- 10

Step-by-step explanation:

Distribute the '+' into the '-' and simplify:  

-5+9+(-5)+(-10)+(1) =

-5 + 9 - 5 - 10 + 1 =

-10

Answer:

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!!

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

Answer:

120

Step-by-step explanation:

Add angle ABC and angle CBD together.

Answer:

18

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

30/5 = 6

6 * 3 = 18

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:

If Chris had to pay $249.21 when he returned the truck, it means that:

His total charge, C = $249.21

We conclude therefore that Chris drove the truck for 299 miles.

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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Answer:

A

Step-by-step explanation:

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 :)

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.

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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The closest probability of getting less than 21% seniors in a random sample of size 100 is A. 0. 241.

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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The slope of the line that passes through the points (9,8) and (2,3) is 5/7.

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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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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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

For the polynomial 9, 3x², 8x; the degree is 2 and the leading coefficient is 3

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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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

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Answer:division if you just use the derivative

Step-by-step explanation:

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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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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SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given expression

STEP 2: Multiply the constant with the leading term

STEP 3: Write the possible factors of the result in product form

STEP 4: Find the factors that will give the second term (-7x) when added

STEP 5: Substitute these factors for -7x in the expression in step 1

STEP 6: Factorize by grouping

Hence, the factors of the given expression are:

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!!

Answer:

m= 11/2

Step-by-step explanation:

Answer:

11/2

Step-by-step explanation:

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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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.

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 (\(\mathbf{-\frac{1}{2},-\frac{5}{2}}\))