Answer:
The area is changing at 2 m²/d.
Step-by-step explanation:
The area of a rectangle is given by:
[tex] A = l*w [/tex]
Where:
l is the length
w is the width
We have that the length is increasing at a rate:
[tex] \frac{dl}{dt} = 1 \frac{m}{d} [/tex]
And the width is decreasing at a rate:
[tex]\frac{dw}{dt} = -2 \frac{m}{d}[/tex]
The change in the rectangle's area is the following:
[tex] \frac{dA}{dt} = w\frac{dl}{dt} + l\frac{dw}{dt} [/tex]
When the length is 8 meters and the width is 18 meters we have:
[tex] \frac{dA}{dt} = 18 m*1\frac{m}{d} + 8 m(-2 \frac{m}{d}) [/tex]
[tex] \frac{dA}{dt} = 18 \frac{m^{2}}{d} - 16 \frac{m^{2}}{d} [/tex]
[tex] \frac{dA}{dt} = 2 \frac{m^{2}}{d} [/tex]
Therefore, the area is changing at 2 m² per day.
I hope it helps you!
How do I Evaluate f(5).
How many ways can a delegation of 55 Republicans, 22 Democrats, and 33 Independents be selected from a group of 99 Republicans, 33 Democrats, and 44 Independents?
Answer:
[tex]C(99,55)\,C(33,22)\,C(44,33)[/tex]
Step-by-step explanation:
A permutation refers to arrangement of the objects or numbers in order. Combinations refers to selecting the objects or numbers from a group of objects or collection such that the order of the objects does not matter.
A delegation of 55 Republicans, 22 Democrats, and 33 Independents is selected from a group of 99 Republicans, 33 Democrats, and 44 Independents.
So,
Number of ways [tex]=C(99,55)\,C(33,22)\,C(44,33)[/tex]
A supply of foods last for a week for 20 families. how long would the supply last for 3 more families.?
Given that,
A supply of foods last for a week for 20 families.
It is required to find the time that would the supply last for 3 more families.
20 families = 1 week = 7 days
If 3 more families joined, total no of families are now 23.
It means that,
1 family= (20/7) days
Now,
23 family =
[tex]\dfrac{20}{7}\times 23=65.71\ \text{days}\\\\\approx 66\ \text{days}[/tex]
So, the supply will last for 66 days.
Given the graph of h.
Solve for x: h(x) = -2 .
Answer:
{-3, -1}
Step-by-step explanation:
We want to find the value of x when the value of the graph is -2
h(x) = -2 when x=1 and x = -3
{-3, -1}
Please select the word from the list that best fits the definition
energy obtained from heat within the earth
Answer:
geothermal
Step-by-step explanation:
energy obtained from heat within the earth-geothermal
Plzzzzzzzzzzz helppppppp
Answer:
B
Step-by-step explanation:
B because it is the farthest away from 0.
What does reflecting over each axis do to a function algebra 2
The value of n is a distance of 3 units from 1 an 1/2 on a number line click on the number line to the possible values of n
Answer:
3
Step-by-step explanation:
Given the question :
The value of n is a distance of 3 units from 1 an 1/2 on a number line click on the number line to the possible values of n
From the context of the expression:
n is the distance which exists between 1 1/2 and 3 units from it;
Which may be ;
1 1/2 - - - - (1 1/2 + 3) = 4 1/2
1 1/2 - - - - - (3 - 1 1/2)
Either way, there exists a distance of 3 units between 1 1/2 and 3 units from it.
Hence, n = 3
Answer:
1 and 3 would both be correct
Solve -2(2x + 5) - 3 = -3(x - 1).
The solution for the equation -2(2x + 5) - 3 = -3(x - 1) is x = - 16 which can be solved by the use the distributive property.
What is distributive property?Distributive Property that when we multiply a number by a group of numbers that are added together, we can multiply each value in the group separately, then add the products of the multiplications.
-2(2x + 5) - 3 = -3(x - 1)
To solve this equation, we need to first use the distributive property to expand the left side of the equation.
We have:
-4x-10-3 = -3(x - 1)
-4x-13 = -3(x - 1)
Now, we can group the like terms on the left side and the right side of the equation.
On the left side, we have -4x - 13 and on the right side, we have -3x + 3.
-4x-13 = -3x + 3
To solve for x, we can add 3x to left side of the equation and add 13 to the right side.
This results in the equation:
-4x+ 3x = 13 + 3
Now, we can add 3x with -4x of the equation to isolate the x-term.
We have:
-x = 16
x = - 16
For more questions related to equation
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Cindy’s square garden has a side length of x ft. She will plant 5 tulip bulbs per square foot. Write a function g to model the number of bulbs she will plant. Use your function to determine how many bulbs will she plant if the garden has a side length of 8 feet?
Answer:
The function that model the number of bulbs she will plant is g = 5x²
She will plant 320 bulbs in the garden
Step-by-step explanation:
∵ Cindy’s square garden has a side length of x ft
∵ Area of the square = side × side
∴ The area of the garden = x × x
∴ The area of the garden = x² ft²
∵ She will plant 5 tulip bulbs per square foot
→ That means there are 5 tulip bulbs in 1 foot²
∵ The area of the garden is x² ft²
→ Multiply the area of the garden by 5
∴ The number of tulip bulbs in the garden = 5 × x²
∴ The number of tulip bulbs in the garden = 5x²
∵ g represents the number of bulbs she will plant in her garden
∴ g = 5x²
∴ The function that model the number of bulbs she will plant is g = 5x²
∵ The garden has a side length of 8 feet
→ That means the value of x is 8 feet
∴ x = 8
→ Substitute the value of x in the function above
∴ g = 5(8)² = 5(64)
∴ g = 320
∴ She will plant 320 bulbs in the garden
Which equation represents a line that is perpendicular to the line on the graph ? O y = - 4x + 3 O O y = - 1/4 * x + 1 y = 1/4 * x - 2 O O y = 4x + 4
Answer:
D
Step-by-step explanation:
Answer
Its C notD!!!!!!
Step-by-step explanation:
The other person is wrong im right
hi I'm looking for the answers for my work I already did this agistment but failed it and need help getting my grade up
Answer:
amswer
Step-by-step explanation:
HURRY PLEASE 2020 2021 T-Math-Geo T1-CIT: Section 2 - Calculator Section
Which of these is defined as a part of a line that is bounded by two end points?
ray
angle
point
line segment
Answer:
the answer is a line segment :)
f(x) = x2. What is g(x)?
Answer:
B. g(x)=(2x)^2
Step-by-step explanation:
this is right
Can someone help me with this?
Answer:
1. Lines c and d
alternate exterior angles
Step-by-step explanation:
Answer:
3rd one
Step-by-step explanation:
You are buying fruit to make fruit baskets. Apples come in bags of 20. Oranges come in bags of 16, and bananas come in bags of 32. You have one bag of each fruit. Each fruit basket must be identical. What is the greatest number of fruit baskets that you can make using all of the fruit? *
Answer:
4 fruit baskets.
Step-by-step explanation:
Use GCF to find the answer. 20 divided by 4 is 5, 16 divided by 4 is 4, and 32 divided by 4 is 8.
Emilia wrote a total of 12 pages over 4 hours. After spending 6 hours writing this week, how
many pages will Emilia have written in total? Assume the relationship is directly proportional.
Answer:
30 pages
Step-by-step explanation:
Knowing she wrote 12 pages in 4 hours, we can do 12/4 to get 3 pages per hour. Multiply 3 pages by the 6 hours she spends writing and you get 18 pages in 6 hours. Add 12 pages and 18 pages and you have 30 pages.
Walter is helping to make cookies for a basketball tournament. He's made 15 cookies so far. His coach asked him to make at least 20 cookies but no more than 55. Solve the inequality and interpret the solution.
Answer:
[tex]5\leq x\leq 40[/tex]
Here, [tex]x[/tex] denotes the additional cookies that need to be made by Walter besides 15 cookies made by him so far
Step-by-step explanation:
Number of cookies made by Walter so far = 15
He is asked by his coach to make at least 20 cookies but no more than 55.
Let [tex]x[/tex] denotes the additional cookies that need to be made by Walter besides 15 cookies made by him so far.
The inequality is [tex]20\leq x+15\leq 55[/tex]
Now solve this inequality.
[tex]20\leq x+15\leq 55\\20-15\leq x\leq 55-15\\5\leq x\leq 40[/tex]
Answer: a
Step-by-step explanation: because its right
I NEED THIS ANSWER QUICK PLEASE!!!!!!!!!!
During the first hour of a snowstorm, 1 2/8 inches of snow fell. In the next hour, 4 3/8 inches fell. In the third hour, the snow stopped and 1 inch of snow melted. How much snow was on the ground at the end of the third hour?
Answer:
1 + 4 = 5
4/8 +3/8 = 7/8
5 7/8 - 7/8 = 5 inches left on the ground after 3 hours
Step-by-step explanation:
Does anyone know this question?
Which number has the lowest value?
A1/5B0.25C0.21D1/3
Answer:
A
Step-by-step explanation:
Answer:1/3 is bigger
Step-by-step explanation:
how do u write 2.25 in standard form?
9514 1404 393
Answer:
2.25
Step-by-step explanation:
The number 2.25 is already in standard form.
___
In the US (and other places), "standard form" is an ordinary decimal number, with the integer part to the left of the decimal point and the fractional part to the right of the decimal point: 2.25.
In the UK (and other places), "standard form" is a number written in scientific notation with a mantissa consisting of the leading non-zero digit to the left of the decimal point, the remaining significant digits to the right of the decimal point, and a multiplier that is 10 to the power appropriate to the place value of the leading digit. When the multiplier is 1, we need not write it.
2.25 = 2.25×10⁰ (full form) = 2.25 (with superfluous 10⁰ removed)
In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where 0 represents the worst possible life and 10 represents the best possible life. The responses were normally distributed, with a mean of
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
[tex]P(X < 4) = 0.4141 [/tex]
b
[tex]P(4 < X < 6) = 0.32876[/tex]
c
[tex]P(X >8) = 0.064037 [/tex]
d
The correct option is B
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 4.5[/tex]
The standard deviation is [tex]\sigma = 2.3[/tex]
Generally the probability that a randomly selected study participant's response was less than 4 is mathematically represented as
[tex]P(X < 4) = P(\frac{X - \mu }{\sigma} < \frac{4 - 4.5}{ 2.3} )[/tex]
[tex]\frac{X -\mu}{\sigma} = Z (The \ standardized \ value \ of\ X )[/tex]
So
[tex]P(X < 4) = P(Z < -0.217 )[/tex]
From the z-table [tex]P(Z < -0.217 ) = 0.4141[/tex]
So
[tex]P(X < 4) = 0.4141 [/tex]
Generally the probability that a randomly selected study participant's response was between 4 and 6 is mathematically represented as
[tex]P(4 < X < 6) = P( < \frac{4 - 4.5}{ 2.3} < \frac{X - \mu }{\sigma} < \frac{6 - 4.5}{2.3})[/tex]
=> [tex]P(4 < X < 6) = P( \frac{4 - 4.5}{ 2.3} < \frac{X - \mu }{\sigma} < \frac{6 - 4.5}{2.3})[/tex]
=> [tex]P(4 < X < 6) = P( -0.217 < Z< 0.6522[/tex]
=> [tex]P(4 < X < 6) = (Z< 0.6522) -P( Z < -0.217) [/tex]
From the z-table
[tex](Z< 0.6522) = 0.74286 [/tex]
So
[tex]P(4 < X < 6) = 0.74286 -0.4141[/tex]
=> [tex]P(4 < X < 6) = 0.74286 -0.4141[/tex]
=> [tex]P(4 < X < 6) = 0.32876[/tex]
Generally the probability that a randomly selected study participant's response was more than 8 is mathematically represented as
[tex]P(X > 8) = P(\frac{X - \mu }{\sigma} > \frac{8 - 4.5}{ 2.3} )[/tex]
[tex]P(X > 8) = P(Z > 1.52174 )[/tex]
From the z-table [tex]P(Z > 1.52174 ) = 0.064037[/tex]
So
[tex]P(X >8) = 0.064037 [/tex]
1.6.PS-21 Question Help Challenge A gold mine has two elevators, one for equipment and another for the miners. The equipment elevator descends 5 feet per second. The elevator for the miners descends 17 feet per second. One day, the equipment elevator begins to descend. After 29 seconds, the elevator for the miners begins to descend. What is the position of each elevator relative to the surface after another 16 seconds? At that time, which elevator is deeper? The position of the equipment elevator relative to the surface is feet
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
Equipment elevator :
Descent rate = 5 ft/s
Miner's elevator :
Descent rate = 17 ft/s
Position of elevator after 16 seconds
Total descent time of equipment elevator = (29 + 16) = 45 seconds
Position after 45 Seconds :
Descent rate * time
5ft/s * 45s = 225 ft
Descent time of Miner's elevator = 16 seconds
Position after 16 Seconds :
Descent rate * time
17ft/s * 16s = 272 fts
Miner's elevator is deeper = 272 feets > 225 fts
Position of equipment elevator relative to the surface = - 225fts
The number of students in a chess club decreased from 16 to 12. What is the percent decrease ? Round to the nearest percent.
Answer:
25% decrease
- Trust me it's right
A bathtub can hold 30 gallons of water.
How many quarts of water can it hold?
Enter your answer as a number, like this: 42
Answer:
120 quarts
Step-by-step explanation:
1 gallon=4 quarts
30x4= 120
On average, Carson saves about 53% of his allowance each month. When creating a circle graph of what Carson does
with his money, which of the following fractions would be the best to represent how much he saves?
1/2 1/4 3/10. 3/4
Answer:
1/2
Step-by-step explanation:
1/2 would be the best fraction to represent how much he saves.
Why did karen take the kids (;´༎ຶД༎ຶ`)
Wait Jimmy what are you doing here I didn't expect this
so we meet again, brother.
Answer:
Because Karen found your briefcase of $1 bills and some crusty socks.
Get over the divorce Jimmy, she doesn't like fax machines.
Jefferson Elementary School is sending 8 of its students to a drumming contest in Orlando, Florida. The cost will be $588 per person. How much will it cost for the entire group of 8 students to attend?
Answer:
4704
Step-by-step explanation:
8*588=4704
Kim's rectangle measures 4ft by 6ft. What are the dimensions of a rectangle that is similar to Kim's rectangle?
Answer: 24ft by 36
Step-by-step explanation:
It is asking which dimension of a rectangle is similar. 24 divided by 6 is 4 and if you do the same to 6 then 36 divided by 6 is also 6 which makes it similar
