Faye can sort 22,200 recyclable items in 444 minutes, based on the ratio shown in the double number line.
To determine how many recyclable items Faye can sort in 444 minutes, we need to use the ratio shown in the double number line. We can do this by finding the slope of the line, which is the ratio of the change in items to the change in time.
To find the slope, we start at the point (0,0) on the number line and move to the point (150,3). The change in items is 150 - 0 = 150, and the change in time is 3 - 0 = 3. Therefore, the slope is:
slope = change in items / change in time
slope = 150 / 3
slope = 50
This means that Faye can sort 50 recyclable items in one minute. To find out how many items she can sort in 444 minutes, we simply multiply the number of minutes by the rate of 50 items per minute:
items sorted = rate x time
items sorted = 50 x 444
items sorted = 22,200
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A local company makes two types of soups, chicken and beef barley. Each batch of chicken soup takes 3 hours to prepare and 4 hours to package. Each batch of beef barley takes 3.5 hours to prepare but only 2 hours to package. There are 5 preparation workers and 6 packaging workers in the company. Each of them works 40 hours per week.
Part A:
Create a system of two inequalities that relates the number of batches of chicken soup, c, and the number of batches of beef barley soup, b, that can be made by the 5 preparation workers and the 6 packaging workers each week. Assume c≥0 and b≥0.
Part B:
Give two possible combinations of batches of chicken soup and beef barley soup that could be made in one week based on the constraints?
Answer:
Step-by-step explanation:
Part A:
Let's use the information given in the problem to create the inequalities:
Each batch of chicken soup takes 3 hours to prepare, so the total preparation time for c batches of chicken soup is 3c hours.
Each batch of beef barley takes 3.5 hours to prepare, so the total preparation time for b batches of beef barley soup is 3.5b hours.
Each batch of chicken soup takes 4 hours to package, so the total packaging time for c batches of chicken soup is 4c hours.
Each batch of beef barley takes 2 hours to package, so the total packaging time for b batches of beef barley soup is 2b hours.
There are 5 preparation workers who work 40 hours per week, so the total preparation time available is 5 workers x 40 hours/worker = 200 hours.
There are 6 packaging workers who work 40 hours per week, so the total packaging time available is 6 workers x 40 hours/worker = 240 hours.
To create the system of inequalities, we need to make sure that the total preparation and packaging times for both types of soup do not exceed the available time. Therefore:
3c + 3.5b ≤ 200 (total preparation time ≤ available preparation time)
4c + 2b ≤ 240 (total packaging time ≤ available packaging time)
Also, we have the non-negativity constraints:
c ≥ 0 (number of batches of chicken soup is non-negative)
b ≥ 0 (number of batches of beef barley soup is non-negative)
Therefore, the system of inequalities is:
3c + 3.5b ≤ 200
4c + 2b ≤ 240
c ≥ 0
b ≥ 0
Part B:
To find two possible combinations of batches of chicken soup and beef barley soup that could be made in one week based on the constraints, we can try different values for c and b that satisfy the inequalities from Part A. Here are two possible combinations:
Combination 1: c = 40, b = 0
Total preparation time: 3c + 3.5b = 3(40) + 3.5(0) = 120
Total packaging time: 4c + 2b = 4(40) + 2(0) = 160
Both inequalities are satisfied, and c and b are non-negative.
Therefore, in one week, the company can make 40 batches of chicken soup and 0 batches of beef barley soup.
Combination 2: c = 30, b = 20
Total preparation time: 3c + 3.5b = 3(30) + 3.5(20) = 135
Total packaging time: 4c + 2b = 4(30) + 2(20) = 160
Both inequalities are satisfied, and c and b are non-negative.
Therefore, in one week, the company can make 30 batches of chicken soup and 20 batches of beef barley soup.
I need some help with this.
Answer: 23
Step-by-step explanation:
The range of the data set is the same thing as subtracting the smallest value from the largest value.
Here, our smallest value is 8 and our largest value is 31.
31 - 8 = 23
This data set has a range of 23.
HELP PLEASE
A random sample of 100 customers at a local ice cream shop were asked what their favorite topping was. The following data was collected from the customers.
Topping Sprinkles Nuts Hot Fudge Chocolate Chips
Number of Customers 17 12 27 44
Which of the following graphs correctly displays the data?
a bar graph titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled sprinkles going to a value of 17, the second bar labeled nuts going to a value of 12, the third bar labeled hot fudge going to a value of 27, and the fourth bar labeled chocolate chips going to a value of 44
a bar graph titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled nuts going to a value of 17, the second bar labeled sprinkles going to a value of 12, the third bar labeled chocolate chips going to a value of 27, and the fourth bar labeled hot fudge going to a value of 44
a histogram titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled sprinkles going to a value of 17, the second bar labeled nuts going to a value of 12, the third bar labeled hot fudge going to a value of 27 ,and the fourth bar labeled chocolate chips going to a value of 44
a histogram titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled nuts going to a value of 17, the second bar labeled sprinkles going to a value of 12, the third bar labeled chocolate chips going to a value of 27, and the fourth bar labeled hot fudge going to a value of 44
Option a. The graph that would correctly display the data that we have jere would be: a bar graph titled favorite topping with the x-axis labeled topping and the y-axis labeled number of customers, with the first bar labeled sprinkles going to a value of 17, the second bar labeled nuts going to a value of 12, the third bar labeled hot fudge going to a value of 27, and the fourth bar labeled chocolate chips going to a value of 44.
How to determine the correct graphThe correct graph to display this type of categorical data is a bar graph. The correct option should show the data with the correct number of customers for each topping as it is listed in the question we have :
Sprinkles: 17
Nuts: 12
Hot Fudge: 27
Chocolate Chips: 44
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7. The table top is a rectangular shape with length (5x - 2) metre and width (x + 2) metre. Mr. Phillip wants to put a piece of glass over the table top. The section of the table top not covered with the glass has a width of (x-3) metre. Determine the area of the table top that is not covered in the form of algebraic expressions.
Answer: The total area of the table top is given by the product of its length and width:
Area of table top = length × width
= (5x - 2)(x + 2)
The width of the section not covered by the glass is (x - 3) metre, which means that the width covered by the glass is (width of table top) - (width of section not covered):
Width covered by glass = (width of table top) - (width of section not covered)
= (x + 2) - (x - 3)
= 5
Therefore, the area of the table top not covered by the glass is:
Area not covered by glass = (length of table top) × (width not covered by glass)
= (5x - 2)(5)
= 25x - 10 square metres
Hence, the area of the table top that is not covered by the glass is 25x - 10 square metres.
Step-by-step explanation:
Right 804, 082 and expanded form two different ways
Expanded form of 804082 is 8 x 100000 + 0 x 10000 + 4 x 1000 + 0 x 100 + 8 x 10 + 2 x 1.
To write the number 804082 in expanded form, we need to break it down into its component parts based on place value.
Expanded form 1:
804082 = 8 x 100000 + 0 x 10000 + 4 x 1000 + 0 x 100 + 8 x 10 + 2 x 1
In this expanded form, we can see that the digit 8 is in the hundred thousands place, the digit 0 is in the ten thousands place, the digit 4 is in the thousands place, the digit 0 is in the hundreds place, the digit 8 is in the tens place, and the digit 2 is in the ones place.
Expanded form 2:
804082 = 8 x [tex]10^{5}[/tex] + 0 x [tex]10^{4}[/tex] + 4 x [tex]10^{3}[/tex] + 0 x [tex]10^{2}[/tex] + 8 x [tex]10^{1}[/tex] + 2 x [tex]10^{0}[/tex]
In this expanded form, we can see that each digit in the number is multiplied by its corresponding power of 10 based on its position in the number.
Both forms give us the same result, but they express the number in different ways based on the place value of each digit.
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Please can you explain the answer:
I got
1/2n^2 +n^2 - 7/2
but it says this is wrong
Answer:
an = 1/2n² -1/2n -2
Step-by-step explanation:
You want a formula for the n-th term of the quadratic sequence -2, -1, 1, 4.
Linear equationsUsing x = 1, 2, 3 and y = -2, -1, 1 we can write equations for the coefficients a, b, c of the quadratic expression ax² +bx +c.
a(1²) +b(1) +c = -2
a(2²) +b(2) +c = -1
a(3²) +b(3) +c = 1
SolutionSubtracting the first equation from the other two, we get ...
3a +b = 1
8a +2b = 3
Subtracting twice the first from the second of these, we get ...
(8a +2b) -2(3a +b) = (3) -2(1)
2a = 1
a = 1/2
Then b can be found from ...
b = 1 -3a = 1 - 3/2 = -1/2
And c can be found from ...
-2 -b -a = c = -2 -(-1/2) -(1/2) = -2
The formula is ...
an = 1/2n² -1/2n -2
__
Additional comment
For systems of equations, the solver used in the second attachment works well. It tells us (a, b, c) = (1/2, -1/2, -2) as we found above.
Alternate solution
The first differences of the given terms are ...
1, 2, 3
And their differences are ...
1, 1
The coefficient of n² is half this second-difference value: 1/2.
If you subtract 1/2n² from the given terms, you get ...
-5/2, -3, -7/2, -4
This arithmetic sequence has the formula ...
a1 +d(n -1)
-5/2 +(-1/2)(n -1) = -1/2n -2
Adding this to the term we subtracted gives ...
an = 1/2n² -1/2n -2 . . . . . as above
If RQ and RS are midsegments of ANOP, what can you conclude about QR and NP? Verify your results by finding x
when QR = 3x + 2 and NP = 2x + 16.
A. QR-NP; x-3
B. QR=2NP; x-9
C. QR-NP:x-3
D. QR=-NP₁ x=9
The conclusion about QR and NP is 2QR = NP; x = 3
Making conclusion about QR and NP?From the question, we have the following parameters that can be used in our computation:
RQ and RS are midsegments of ANOP,
This means that
2QR = NP
So, we have
2 * (3x + 2) = 2x + 16
6x + 4 = 2x + 16
Evaluate the like terms
4x = 12
Divide
x = 3
Hence, the value of x is 3
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A right square pyramid is shown,the pyramid has a height of 24. The length of line segment DF is 7. Enter the length of segment AD.
The length of segment AD of the pyramid is approximately 4.95 units.
Since ACD is a right square pyramid, we know that triangle ACD is a right triangle, with DC as its hypotenuse.
Using the Pythagoras theorem, we can write:
AD² + AC² = DC²
Since AC is the length of one side of the square base of the pyramid, and all sides of a square are equal, we know that
AC = DC ÷ √2.
Substituting this into the equation above, we get:
AD² + (DC ÷ √2)² = DC²
Simplifying this equation, we get:
AD² = DC² - (DC ÷ √2)²
AD² = DC² - DC² ÷ 2
AD² = DC² ÷ 2
Now we can substitute the given value of DC into this equation and solve for AD:
AD² = 7² ÷ 2
AD² = 24.5
AD = 4.95
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The correct question is:
A right square pyramid ACD has a height of 24 units. The length of line segment DC is 7 units. Enter the length of segment AD.
Circle O has a circumference of 3677 cm.
What is the length of the radius ?
6 cm
18 cm
36 cm
72 cm
Answer:
585.14
Step-by-step explanation:
3677=2πr
r=3677÷44/7
=585.14
people drive an average of 12,000 miles per year with a standard deviation of 2,580 miles per year. what is the probability that a randomly selected sample of 36 drivers will drive, on average, more than 12,500 miles? does the central limit theorem apply? what is the sampling distribution of the mean?
The probability that a randomly selected sample of 36 drivers will drive, on average, more than 12,500 miles is approximately 0.123
This problem involves the sample mean of a set of data, and we can use the central limit theorem to approximate the distribution of sample means, even if the original distribution is not normal.
Let X be the number of miles driven by a single driver in a year. We know that the population mean µ = 12,000 miles and the population standard deviation σ = 2,580 miles. We also know that the sample size n = 36.
The sample mean X is an estimator of the population mean µ. The distribution of sample means is approximately normal with a mean of µ and a standard deviation of σ/√n, according to the central limit theorem
So, the distribution of sample means can be expressed as
X ~ N(µ, σ/√n)
Substituting the given values, we get
X ~ N(12,000, 2,580/√36) = N(12,000, 430)
Now we need to find the probability that a randomly selected sample of 36 drivers will drive, on average, more than 12,500 miles. This is equivalent to finding the probability that the sample mean is greater than 12,500
P(X > 12,500) = P(Z > (12,500 - 12,000) / 430)
where Z is a standard normal random variable.
P(Z > 1.16) = 1 - P(Z < 1.16) = 1 - 0.877 = 0.123
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The given question is incomplete, the complete question is:
People drive an average of 12,000 miles per year with a standard deviation of 2,580 miles per year. what is the probability that a randomly selected sample of 36 drivers will drive, on average, more than 12,500 miles?
question 16
Estimate the sum by rounding each number to the nearest half or whole.
4 1/2 + 2 7/12
A. 6 1/2
B. 7
C. 7 1/2
D. 6
Answer:
The answer to your problem is, 12 1/2
Step-by-step explanation:
As shown to the problem we would need to add
4 1/2 + 2 7/12
Lets make them equivalent denominators:
1/2 & 7/12
= 24
1/2 = 12/24
7/12 = 14/24
Then make the new problem into;
4 12/24 + 7 14/24
= 12 1/2
Thus the answer to your problem is, 12 1/2
A line has a slope of -5 and a y-intercept
of 4
Write its equation in slope-intercept
form.
Write your answer using integers, proper
fractions, and improper fractions in
simplest form.
Answer:
y = -5x + 4.
Step-by-step explanation:
Slope-intercept formula: y = mx (m is slope) + B (y-intercept)
Plug in it:
y = 5x + 4.
A lighthouse casts a shadow that is 18 yards long. At the same time, a nearby house that is 9 yards tall casts a shadow that is 6 yards long. What is the height of the lighthouse?
The calculated height of the lighthouse, h will be yards
What will be the height of the lighthouseFrom the question, we have the following parameters that can be used in our computation:
Similar triangles of shadows and house
This means that
Ratio = Division or ratio of corresponding sides
So, we have
h : 9 = 18 : 6
So, we have the following representation
h/9 = 18/6
This gives
h = 9 * 18/6
By calculation, we have
height = 27 yards
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Frank sells lemonade in 500ml bottles, 6 bottles per carton, 4 cartons per case, and 96 cases per bakkie. How many litres of lemonade can he transport on a fully loaded bakkie?
Answer: yes he can transport them all
Step-by-step explanation: yes.
9.5 in. 2 in. 9.5 in. 2 in.
What's the area?
Answer:
it is 19 brainliest please
Step-by-step explanation:
Una chica mide 5 cm más que su mamá y 8 cm menos que su papá. Si entre los tres miden 3. 45 m. ¿Cuánto mide su papá?
If A girl is 5 cm taller than her mother and 8 cm less than her dad, the height of the girl's dad is 122 cm.
Let's assume that the height of the girl's mother is x cm. Then, according to the given information, the height of the girl would be (x + 5) cm and the height of her dad would be (x + 5 + 8) cm or (x + 13) cm.
Now, we know that the total height of the three individuals is 3.45 m or 345 cm (since 1 m = 100 cm). Therefore, we can write an equation as follows:
x + (x + 5) + (x + 13) = 345
Simplifying the equation, we get:
3x + 18 = 345
Subtracting 18 from both sides, we get:
3x = 327
Dividing both sides by 3, we get:
x = 109
Therefore, the height of the girl's mother is 109 cm, the height of the girl is (109 + 5) cm or 114 cm, and the height of the girl's dad is (109 + 13) cm or 122 cm.
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Question content area top Part 1 A salesperson at a jewelry store earns 3% commission each week. Last week, Jarrod sold $530 worth of jewelry. How much did he make in commission? How much did the jewelry store make from his sales?
The commission made by Jarrod and total sales done by Jewelry store is equals to $15.90 and $514.10 respectively.
Percent of commission rate earned = 3%
Amount of Jewelry sold last week = $530
Commission Jarrod made last week
= multiply the amount of his sales by the commission rate.
⇒ Commission Jarrod made last week = 3% of $530
⇒ Commission Jarrod made last week = 0.03 x $530
⇒ Commission Jarrod made last week = $15.90
Jarrod made $15.90 in commission last week.
The jewelry store made from Jarrod's sales
= subtract the commission from the total amount of sales.
⇒Store's profit = $530 - $15.90
⇒ Store's profit = $514.10
The jewelry store made $514.10 from Jarrod's sales last week.
Therefore, the amount of commission and sales made by jewelry store is equal to $15.90 and $514.10 respectively.
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PLEASE HELP!!! URGENT!!!!
Pictured are curves y=p(x) and y=q(x), together with tangents for x = 2. Let r(x)=p(x)*q(x) and determine r'(2).
Slope Formula:
[tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Simply plug in the 2 coordinates into the slope formula to find slope mCalculusDifferentiation
DerivativesDerivative NotationDerivative Rule [Product Rule]:
[tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Let's identify what the problem initially gives us:
We are given the graphs of the curves [tex]\displaystyle y = p(x)[/tex] and [tex]\displaystyle y = q(x)[/tex] along with their tangents for x = 2.This means that they give us the derivative of each respective curve at x = 2, since the definition of a derivative is the slope of the tangent line.
We are also given that some function [tex]\displaystyle r(x)[/tex] is equal to [tex]\displaystyle p(x)q(x)[/tex], where the functions are multiplied by each other.
[tex]\displaystyle r(x) = p(x)q(x)[/tex]We are then asked to find [tex]\displaystyle r'(2)[/tex], which is the derivative of the [tex]\displaystyle r(x)[/tex] function at x = 2.
Step 2: WorkIn order to find the derivative of [tex]\displaystyle r(x)[/tex], we will need to use the Product Rule, which states how to find a derivative of 2 functions being multiplied by each other. Note the equation given under "General Formulas and Concepts":
[tex]\displaystyle \begin{aligned}r(x) & = p(x)q(x) \\r'(x) & = \boxed{ p'(x)q(x) + p(x)q'(x) }\\\end{aligned}[/tex]
∴ the derivative of [tex]\displaystyle r(x)[/tex] is equal to [tex]\displaystyle \boxed{ r'(x) = p'(x)q(x) + p(x)q'(x) }[/tex]
To find the derivative evaluated at x = 2, we substitute in x = 2 into our derivative:
[tex]\displaystyle\begin{aligned}r'(x) & = p'(x)q(x) + p(x)q'(x) \\r'(2) & = p'(2)q(2) + p(2)q'(2) \\\end{aligned}[/tex]
This is where the graphs and their tangent lines come into play.
To find [tex]\displaystyle q(2)[/tex] and [tex]\displaystyle p(2)[/tex], we simply refer to the [tex]\displaystyle y = q(x)[/tex] and [tex]\displaystyle y = p(x)[/tex] graphs, respectively:
[tex]\displaystyle q(2) = \boxed{ -1 }[/tex][tex]\displaystyle p(2) = \boxed{ 3 }[/tex][tex]\displaystyle \begin{aligned}\implies r'(2) & = p'(2)(-1) + 3q'(2) \\& = \boxed{ -p'(2) + 3q'(2) }\end{aligned}[/tex]
We have now simplified our derivative equation [tex]\displaystyle r'(2)[/tex] to be:
[tex]\displaystyle\begin{aligned}r'(x) & = p'(x)q(x) + p(x)q'(x) \\r'(2) & = p'(2)q(2) + p(2)q'(2) \\& = -p'(2) + 3q'(2) \\\end{aligned}[/tex]
To find [tex]\displaystyle p'(2)[/tex] and [tex]\displaystyle q'(2)[/tex], we refer to the tangent lines of the graphs [tex]\displaystyle y = p(x)[/tex] and [tex]\displaystyle y = q(x)[/tex], respectively. We will have to find their slopes (by the definition of a derivative) using the Slope Formula:
[tex]\displaystyle p'(2) = \frac{5 - 1}{3 - 1} = \frac{4}{2} = \boxed{ 2 }[/tex][tex]\displaystyle q'(2) = \frac{-1 - 0}{2 - -1} = \boxed{ \frac{-1}{3} }[/tex][tex]\displaystyle\begin{aligned}\therefore r'(2) & = -p'(2) + 3q'(2) \\ r'(2) & = -2 + 3 \bigg( \frac{-1}{3} \bigg) \\& = -2 - 1 \\& = \boxed{ -3 }\end{aligned}[/tex]
Answer[tex]\displaystyle \therefore \boxed{ r'(2) = -3 }[/tex]
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Topic: Calculus
Unit: Derivatives
Preferred Products has issued preferred stock with an annual dividend of $6. 50 that will be paid in perpetuity. If the discount rate is 10%, at what price should the preferred sell? Note: Round your answer to 2 decimal places
members of the stony creek bluebird club monitor nest boxes they've hung for local bluebirds. without disturbing the nest, they keep track of how long it takes the bluebird eggs to hatch after being laid. the table below shows the outcomes they record.days to hatchnumber of eggs122133146154161based on the data, what is the probability that the next bluebird egg laid will take more than 14 days to hatch?write your answer as a fraction or whole number.
The probability of a bluebird egg taking more than 14 days to hatch, based on the data provided, is 6/7 or approximately 0.86.
Probability is a measure of the likelihood of an event occurring. It is represented by a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
In this case, the event we are interested in is the probability of a bluebird egg taking more than 14 days to hatch. We can calculate this probability by dividing the number of eggs that took more than 14 days to hatch by the total number of eggs.
According to the data provided, there were 6 eggs that took more than 14 days to hatch, out of a total of 7 eggs. Therefore, the probability of a bluebird egg taking more than 14 days to hatch, based on this data, is 6/7 or approximately 0.86.
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HELP ASAP PLEASE!!! I need help
Answer:
5.6 miles
Second answer option
Step-by-step explanation:
From the tables we see that 1 mile ≈ 1.61 km
Therefore 1 km ≈ 1/1.61 mile
9 km ≈ 9 x 1/1.61 ≈ 9/1.61 ≈ 5.592341 miles
Rounded to first decimal(tenth) that would be 5.6 miles
This is the second answer option
answer the statistical measures and create a box and whiskers plot for the following set of data
The statistical measures are: Min: 6 Q1: 7 Med: 11.5 Q3: 13 Max: 15.
The box and whiskers plot is given below.
How to Create a Box and Whiskers Plot?To create a box and whiskers plot, we have to first derive the statistical measures of the data set given, which is the five number summary that include, the mina nd max values, the median, and the quartiles.
Given the data set, 6, 7, 7, 8, 10, 13, 13, 13, 15, 15, the five number summary which are the statistical measures are:
Minimum: 6 (lowest value)
First Quartile: 7 (middle of the first half of the data)
Median: 11.5 (center of the data set)
Third Quartile: 13 (middle of the second half of the data)
Maximum: 15 (largest value).
The box and whiskers plot of the data set, 6, 7, 7, 8, 10, 13, 13, 13, 15, 15, is shown in the diagram attached below.
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please help 30 points
Answer: =[tex]\frac{a}{4(a+2)}[/tex]
Step-by-step explanation:
Let's find common denominator of the the other side first
we have:
2a-4= 2(a-2)
2a²-8 = 2(a²-4) = 2(a-2)(a+2)
a²+2a = a(a+2)
common denominator is 2a(a-2)(a+2)
combine right side:
[tex]\frac{a^{2}(a+2)-a(a^{2}+4)-4(a-2) }{2a(a-2)(a+2}[/tex]
combine like terms on top:
[tex]\frac{a^{3}+2a^{2}-a^{3}-4a-4a+8 }{2a(a-2)(a+2}[/tex]
[tex]\frac{2a^{2}-8x+8 }{2a(a-2)(a+2}[/tex]
lets put the whole problem together.
[tex]\frac{a-2}{4(a^{2}+4a+4) }[/tex] / [tex]\frac{2a^{2}-8x+8 }{2a(a-2)(a+2}[/tex]
When dividing fractions, keep the first, change the sign, flip the 2nd fraction
[tex]\frac{a-2}{4(a^{2}+4a+4) }[/tex] * [tex]\frac{2a(a-2)(a+2}{2(a^{2}-4x+4) }[/tex] simplify more and then reduce
[tex]\frac{a-2}{4(a+2)(a+2) }[/tex] * [tex]\frac{2a(a-2)(a+2}{2(a-2)(a-2) }[/tex]
=[tex]\frac{a}{4(a+2)}[/tex]
excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 36 kmph. for how many minutes does the bus stop per hour?
When excluding stoppages, the speed of a bus is 54 km/h, and including stoppages, it is 36 km/h. the bus stop is 20 minutes per hour
We have to Calculate the distance traveled by bus in 1 hour excluding stoppages and calculate the distance traveled by bus in 1 hour including stoppages. Then we have to calculate the time taken to cover that difference between the distances and convert the calculated time into minutes.
Given data:
The speed of a bus while excluding stoppages = 54 km/h.
the speed of the bus while including stoppages = 36 km/hr.
From the given data we can say that:
The Distance traveled by bus in 1 hour, excluding stoppages is = 54 km.
The Distance traveled by bus in 1 hour, including stoppages, is = 36 km.
Distance traveled = Distance traveled by bus in 1 hour excluding stoppages – distance traveled by bus in 1 hour including stoppages
= 54km − 36km = 18km
The bus covers 18 km less due to stoppages.
the time taken to cover18 km, = distance traveled / speed of the bus
= 18km / 54km/hour
= 1 / 3 hour
Time taken in minutes = ( 1 / 3×60 )minutes
=20minutes
Therefore, the bus stops per hour for 20 minutes.
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If one zero of the quadratic polynomial x ^ 2 + kx + 2 is 1, then what is the value of k?
Answer: -3
Step-by-step explanation:
by puggin in 1 to the equation, you get 1^2 + k + 2 = 0, which equals 3 + k; to solve, bring 3 to the other side to get k = -3.
a data analyst performs a correlation analysis between two quantities. the result of the analysis is an r value of 0. what does this mean?
An r value of 0 in a correlation analysis indicates that there is no linear relationship between the two quantities being analyzed.
This means that there is no correlation between the two variables, and any observed pattern or association between them is likely due to chance. In other words, the values of one variable do not predict the values of the other variable. However, it is important to note that a correlation analysis only measures linear relationships, and there may still be other types of relationships between the variables that are not captured by the r value.
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A water sample shows 0.034 grams of some trace element for every cubic centimeter of water. Abdoulaye uses a container in the shape of a right cylinder with a diameter of 13.4 cm and a height of 10.3 cm to collect a second sample, filling the container all the way. Assuming the sample contains the same proportion of the trace element, approximately how much trace element has Abdoulaye collected? Round your answer to the nearest tenth.
Answer:49.4g
Step-by-step explanation:
After considering the given data we conclude that the total amount of trace element collected by Abdoulaye is 4 grams.
Formula for volume of a cylinder
[tex]V = \pi r^2 h[/tex]
Here,
Radius = 13.4 / 2 = 6.7 cm
Height = 10.3
Then
V = 3.14 × (6.7)² × 10.3
V = 1,451.8 cubic centimeters
Volume of cylinder is approximately 1,451.8 cubic centimeters.
In the event a water sample shows 0.034 grams of some trace element for every cubic centimeter of water, then the amount of trace element in the sample can be evaluated by multiplying the volume of the sample by the concentration of the trace element in the water sample.
1.451.8 × 0.034 = 49.36 grams
Then , approximately 49.36 grams of trace element has Abdoulaye collected rounding the value to the nearest tenth which is 4 grams.
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One rectangle is "framed" within another. Find the area of the shaded region if the "frame" is 3 units wide.
Answer: 84 square inches.
Step-by-step explanation:
Side A of shaded: 5+3+3 = 11
Side B of shaded: 3+3+3= 9
11x9= 99
99-(3x5{normal rectangle area})= 84
Please help me with this questions , I think that they are not really hard , but I don’t know how to do them
The percentage of values and the z-scores are listed below
Calculating the percentage of valuesHere, we have
Between z = 0.53 and 2.67
This is represented as
Percentage = (0.53 < z < 2.67)
Using a graphing calculator, we have
Percentage = 29.43%
Next, we have
To the right of z = 1.61
This is represented as
Percentage = x > 1.61
Using a graphing calculator, we have
Percentage = 5.40%
Calculating the z-scoresHere, we have
Percentage = 35% to the left of the z-score
This means that
P(z < z) = 0.35
Using a graphing calculator, we have
z = -0.385
Next, we have
Percentage = 18% to the right of the z-score
This means that
P(z > z) = 0.18
Using a graphing calculator, we have
z = 0.915
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Solve negative a minus six sevenths equals two thirds for a.
a equals negative 32 over 21
a equals 32 over 21
a equals negative 8 over 21
a equals 8 over 21
