Answer:
If we define W as the width:
12m ≤ W ≤ 22m
Step-by-step explanation:
We have a rectangle with length L and width W.
We know that:
"The length of a rectangle should be 9 meters longer than 7 times the width"
Then:
L = 9m + 7*W
We also know that the length must be between 93 and 163 meters long, so:
93m ≤ L ≤ 163m
Now we want to find the restrictions for the width W.
We start with:
93m ≤ L ≤ 163m
Now we know that L = 9m + 7*W, then we can replace that in the above inequality:
93m ≤ 9m + 7*W ≤ 163m
Now we need to isolate W.
First, we can subtract 9m in the 3 sides of the inequality
93m - 9m ≤ 9m + 7*W -9m ≤ 163m -9m
84m ≤ 7*W ≤ 154m
Now we can divide by 7 in the 3 sides, so we get:
84m/7 ≤ 7*W/7 ≤ 154m/7
12m ≤ W ≤ 22m
Then we can conclude that the width is between 12 and 22 meters long.
calculate the volume of each cone. Use 3.14 for π. Round answers to the nearest hundredth if necessary.
Answer:
πr of length
»» 3.14 x (5)²
»» 3.14 x 30 = 94.2cm²
πr of base
»» 3.14 x (4)²
»» 3.14 x 16 = 50.24cm²
Length x base
»» 94.2cm² x 50.25cm²
A= 4733.55cm²
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Problem 12
Given 12 consecutive integers, in how many ways can three of these integers
be selected to give a sum which divides by 4?
A step by step explanation.
9514 1404 393
Answer:
55
Step-by-step explanation:
Here's one way to count them.
12 consecutive integers will have 3 each of the integers whose value is 0, 1, 2, or 3 mod 4. To make a total that is 0 mod 4, any of these combinations of mod 4 values may be used:
000 -- 1 combination
013 -- 27 combinations, 3 each of mod 0, mod 1, and mod 3
022 -- 9 combinations, 3 of mod 0, and 3 ways to choose 2 of mod 2
112 -- 9 combinations, 3 of mod 2, and 3 ways to choose 2 of mod 1
233 -- 9 combinations, 3 of mod 2, and 3 ways to choose 2 of mod 3
__
Consider the set of 12 consecutive integers 1 .. 12. Then here are the 9 "233" combinations. Mod 2 integers are 2, 6, 10, and mod 3 integers are 3, 7, 11.
(2, 3, 7), (2, 3, 11), (2, 7, 11),
(3, 6, 7), (3, 6, 11), (6, 7, 11),
(3, 7, 10), (3, 10, 11), (7, 10, 11)
The total number of combinations that will be divisible by 4 is ...
1 + 27 + 9 + 9 + 9 = 55 . . . . combinations with a sum divisible by 4
__
Additional comment
The number of ways that 3 can be chosen from 12 is 220, so this is 1/4 of that total. It is perhaps not surprising that the remainders from division by 4 are uniformly distributed among the possibilities.
A computer program to list the 220 subsets and the mod 4 remainders of their totals confirms this is the correct number.
There are [tex]55[/tex] ways of these integers be selected to give a sum.
Given that:
It has consecutive integers .
Now,
Address the formula for [tex]C(n,r)[/tex],
[tex]C(n,r)=\frac{n!}{(n-r)!n!}[/tex]
Here,
[tex]n=12,r=3[/tex]
[tex]C(12,3)=\frac{12!}{(12-3)!3!} \\\\C(12,3)=\frac{12!}{9!3!} \\\\C(12,3)=\frac{12*11*10*9*8*7*6*5*4*3*2*1}{9*8*6*7*5*4*3*2*1*3*2*1} \\\\C(12,3)=\frac{12*11*10}{3*2*1} \\\\C(12,3)=4*5*11\\\\C(12,3)=220[/tex]
The sum [tex]mod 4[/tex] of any given subset increases by [tex]1[/tex] when the set is “slid” to the left.
Every subset gives rise to all four values [tex]mod 4[/tex] by sliding each of four places.
Since, The sum of the integer is divides by [tex]4[/tex].
Thus,
[tex]220\div 4=55[/tex]
Hence, it has [tex]55[/tex] ways .
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Which best explains whether a triangle with side lengths 2 in., 5 in., and 4 in. is an acute triangle?
The triangle is acute because 22 + 52 > 42.
The triangle is acute because 2 + 4 > 5.
The triangle is not acute because 22 + 42 < 52.
The triangle is not acute because 22 < 42 + 52.
9514 1404 393
Answer:
The triangle is not acute because 2² + 4² < 5²
Step-by-step explanation:
The square of the hypotenuse of a right triangle with the given short sides would be 2² +4² = 20. So, that hypotenuse would be √20, about 4.47. The long side of this triangle is longer than that, so the angle opposite is larger than 90°. The triangle with sides 2, 4, 5 is an obtuse triangle.
The triangle is not acute because 2² + 4² < 5²
The triangle is not acute because 22 + 42 < 52.
Option C is the correct answer.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
To determine if a triangle is acute, we need to check whether all three angles of the triangle are acute angles (less than 90 degrees).
Pythagorean theorem,
- If the square of the length of the hypotenuse is greater than the sum of the squares of the other two sides, then the triangle is acute.
- If the square of the length of the hypotenuse is less than the sum of the squares of the other two sides, then the triangle is obtuse.
Now,
The triangle with side lengths 2 in., 5 in., and 4 in. is not a right triangle.
So we can't use the Pythagorean theorem directly.
Now,
We can check if the sum of the squares of the two shorter sides is greater than the square of the longest side.
2² + 4² = 4 + 16 = 20
5² = 25
Since 20 < 25, we know that the triangle is not acute.
Therefore,
The triangle is not acute because 22 + 42 < 52.
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HCF of the numbers divisible be
3 between 21 and 30 is ___
Answer:
3
Step-by-step explanation:
Numbers between 21 and 30 divisible by 3 are 24 and 27. so you get the HCF of the two.
Which expression are greater than 1/2? Choose all the apply
Answer:
25/30
5/8
Step-by-step explanation:
Which fraction is it out of all of these 6/14,5/8,25/30,or 3/6?
to determine which fractions are greater than 1/2, convert the fractions to decimals
to convert to decimals, divide the numerator by the denominator
1/2 = 0.5 less than half
6/14 = 0.43 less than half
5/8 = 0.625 greater than half
25 / 30 = 0.83 greater than half
3 / 6 = 0.5 equal to half
PLEASE HELP!! graph the circle whose equation is (x-6)^2 + (y+2)^2 =4
Answer:
Y= -x^2+12x-36
Step-by-step explanation:
the area of a tennis court is 2000m2 . a rugby pitch has a legnth of 45m and width of 45m . which has the biggest area?
Answer:
The area of a rugby pitch is more as compared to the area of the tennis court.
Step-by-step explanation:
Given that,
The area of a tennis court is 2000 m².
The length and width of a rugby pitch are 45 m and 45 m.
The area of a rugby pitch is given by :
A = lb
So,
A = 45×45
A = 2025 m²
So, it is clear that the area of a rugby pitch is more as compared to the area of the tennis court.
if a + b + c = 1, ab + bc + ca = -1 and abc = -1. find the value of a³+b³+c³
Answer:
1
Step-by-step explanation:
→ If we know that 3 numbers need to multiply to make -1, it must be
1, 1 and -1
→ Then we just substitute this into a³ + b³ + c³
1³ + 1³ + (-1)³ = 2 - 1 = 1
The figure below is made of 2 rectangular prisms.
What is the volume of this figure?
Answer:
6536 cubic in
Step-by-step explanation:
1. Split both the prisms apart- In doing so, you can simplify the problem.
2. Put in the #'s for the formula which in this case is V=L*W*H, we will start with the formula for the front one, V=7*8*1 or V=7*8
3. answer for the front is 56 cubic in, now we solve for the other half.
4. V=9*1*90 or V=9*90 which is 6480 cubic in.
5. add 6480 and 56 and your answer is 6536 cubic in as your answer.
Hope this helped ;D
In Act I, scene ii, Claudius’s mention of Fortinbras raises the issue of _____. the cause of King Hamlet’s death how Fortinbras is better than Hamlet an external threat to Denmark corruption in Denmark’s government
Answer:
the answer to this is D "an external threat to Denmark"
Step-by-step explanation: just did the assignment :)
Write the following comparison as a ratio reduced to lowest terms. 169 inches to 13 feet
Answer:
14.0833333333 feet | 13 feet
Step-by-step explanation:
169 Inches is 14.0833333333 feet on calculator compared to 13 feet
and 1.08333333333 is 14.0833333333 divided by 13
if is not it, then 13/14.0833333333 is 0.92307692307
i guess that is the lowest terms in ratio
Which function is a translation of the parent absolute value function?
f(x) = 2x1
f(x) = |x+6| f(x)=|x| f(x)=-4|x|
15 + 36 not-equals 41, so those lengths will not form a triangle.
15 squared + 36 squared = 1,521
41 squared = 1,681
Since a squared + b squared not-equals c squared, it will not be a right triangle.
15 squared + 36 squared = 297
41 squared = 82
Step-by-step explanation; did it on the website euphoria
The translation of the parent function is f ( x ) = | x + 6 | which is shifted 6 units to the left
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the transformation of the function be a translation , where
The parent function is f ( x ) = | x |
And , the translated function is f ( x ) = | x + 6 |
So , original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
And , the function is translated 6 units to the left
Hence , the translated function is f ( x ) = | x + 6 |
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whats the area of a rectangle
:)
Answer:
Baguette. :)
Step-by-step explanation:
Answer:
I don't know you lollollollll
Can you help me with this please (finals)
Answer:
around 90 cm because that measure is equal to 180 you divide into 2 so the answer is 90
Please help will mark BRAINLIEST! This is pt.1
Answer:
See below.
Step-by-step explanation:
Problem 1.
1. QU
2. QW
3. UW
Given
4. QUW
Problem 2.
1. CB
2. <1, <2
Given
3. BD, BE
Given
4. ABD, CBE
SAS
How much is six dimes, 8 nickels, and three one-dollar bills? *
Answer:
.60 + .40 + 3.00 = 4.00
Step-by-step explanation:
Answer:
$ 4
Step-by-step explanation:
six dimes (.10 each) = .60
8 nickels (.05 each)= .40
3 dollars (1.00 each) = 3.
Add together
Question:
The researcher wants to calculate the bacterial count in the dish after x hours of growth.
Fill in the values of A and b to write an exponential expression to model the number of bacteria in a colony that begins
with a single cell and doubles in size every hour
A(b)^x
Answer:
1(2)^x
Step-by-step explanation:
(^x means x is an exponent.)
Since the experiment begins with a single cell, the initial value, A, is 1. The population increases by a factor of 2 every hour, so the growth factor, b, is 2. Substitute the values of A and b in the general form of an exponential expression to create the expression modeling the number of bacteria in the colony after x hours.
A(b)^x=1(2)^x
=2^x
The exponential expression to model the number of bacteria in a colony that begins with a single cell and doubles in size every hour is [tex]1 * 2^{x}[/tex].
What is exponential expression?Exponential expressions are just a way to write powers in short form. The exponent indicates the number of times the base is used as a factor.
Let number of hours be x hours.
The bacterial count in the dish after x hours of growth is [tex]1 * 2^{x}[/tex].
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A card is picked from a standard deck of 52 cards. Determine the odds against and the odds in favor of selecting a 4.
Answer:
1 : 12
Step-by-step explanation:
P(4) = 4 cards out of 52 = 1/13
P(4') = 48 cards out of 52 = 12/13
Odds in favour of selecting a four
Probability "for" : Probability "against" = P(4) : P(4') = 1/13 : 12/13 = 1 : 12
Simplify ratio to the simplest integers.
a motor pumps out 6704.76 liters of water in 6 hours how many litres of water will it pump in one hour?
Answer:
Amount of water pumped out by the motor = 1117.46 liters
Step-by-step explanation:
Amount of water pumped out by the motor pump = 6704.76 liters
Time taken by the motor to pump the water = 6 hours
Rate at which the motor pumps out the water = [tex]\frac{\text{Amount of water pumped out}}{\text{Time taken to pump the water}}[/tex]
= [tex]\frac{6704.76}{6}[/tex]
= 1117.46 liters per hour
Therefore, amount of water pumped out by the motor = 1117.46 liters
d) The Princess was allowed to climb trees.
e)
Hector lived a lonely life in the King's castle.
Answer these questions in one or two words only.
a) Who first discovered that the Princess had climbed up a tree?
Hector is the one who discovered
Solve for x. 8x = 35
Answer:
[tex]x = \frac{35}{8} [/tex]
Step-by-step explanation:
Divide both sides by 8:
[tex] \frac{8x}{8} = \frac{35}{8} \\x= \frac{35}{8} [/tex]
Analyze the graph below and complete the instructions as follows.
Answer:
Option A:
x^2 + (y - 2)^2 = 9
Step-by-step explanation:
We know that the equation for a circle centered in the point (a, b) and of radius R is given by:
(x - a)^2 + (y - b)^2 = R^2
So the first thing we need to find is the center of the circle.
We can see that the center is at:
x = 0
y = 2
Then the center is at the point (0, 2)
Now we want our circle to pass through point 2, located at a distance of 2 units from the radius of the first circle.
So the distance between the center and point 2 is 2 units plus the radius of the smaller circle:
And the radius of the smaller circle is one unit.
Then, the radius of a circle centered at (0, 2) that passes through point 2 is:
R = 1 + 2 = 3
Then we have a circle centered at (0, 2) and of radius R = 3
Replacing these in the equation for a circle we get:
(x - 0)^2 + (y - 2)^2 = 3^2
x^2 + (y - 2)^2 = 9
The correct option is A
A motor boat travels 60 miles down a river in 3 hours but takes 5 hours to return upstream. Find the rate of the boat in still water and the rate of the current.
Step-by-step explanation:
Given that,
A motor boat travels 60 miles down a river in 3 hours but takes 5 hours to return upstream,
We know that,
Speed = distance/time
The rate while moving downstream[tex]=\dfrac{60}{3}=20\ mph[/tex]
The rate while moving upstream [tex]=\dfrac{60}{5}=12\ mph[/tex]
The rate of the boat in still water is the average of these:
[tex]v_s=\dfrac{20+12}{2}=16\ mph[/tex]
The rate of the current is the difference between the boat speed and actual speed = 16 mph - 12 mph = 4 mph
Hence, this is the required solution.
john had a bag of 10 marbles (2 Green, 4 Blue, 1 Yellow, 2 Red) What is the probability that john selects a green marble, replaced it, and then selects a green marble?
Answer:
2/9
Step-by-step explanation:
the question didnt say replaced it with another colour
A 15-day supply of vitamins costs $1.74, what is the price in cents per day?
Answer:
it costs 12 cents per day.
Step-by-step explanation:
15 days cost $1.74
1 day then costs 1.74/15 = $0.116 ≈ $0.12
Joseph borrows $10000 from his sister Katie at an annual interest rate of 10%. If the
interest is compounded twice a year, how much does he owe after 12 months? Give your answer in dollars.
Answer:
A = P ( 1 + r / n) ^( t * n)
where
A = the amt owed
P = amt borrowed
r = the interest rate as a decimal
n = the number of compoundings per year
t = the number of years
A = 10000 ( 1 + .10 / 2)^(2 *1) = 10000 ( 1.05)^2 = $11025
Step-by-step explanation:
Given F ( x ) = -2/3 x - 4 What is the zero of this function?
Answer:
-4
Step-by-step explanation:
f(0)=(-2/3)(0) - 4
= - 4
Sea grass grows on a lake. The rate of growth of the grass is ????????/???????? = ????????, where ???? is a constant.
a. Find an expression for ????, the amount of grass in the lake (in tons), in terms of ????, the number of years, if the amount of grass is 100 tons initially, and 120 tons after one year.
b. In how many years will the amount of grass available be 300 tons?
c. If fish are now introduced into the lake and consume a consistent 80 tons/year of sea grass, how long will it take for the lake to be completely free of sea grass?
Answer:
[tex](a)\ G(t) = 100 *e^{0.1823t}[/tex]
[tex](b)\ t = 6[/tex]
[tex](c)\ t = 1.7[/tex]
Step-by-step explanation:
Given
[tex]G_0 = 100[/tex] --- initial
[tex]G(1) = 120[/tex] --- after 1 year
[tex]r \to rate[/tex]
Solving (a): The expression for g
Since the rate is constant, the distribution of G follows:
[tex]G(t) = G_0 * e^{rt}[/tex]
[tex]G(1) = 120[/tex] implies that:
[tex]G(t) = G_0 * e^{rt}[/tex]
[tex]120 = G_0 * e^{r*1}[/tex]
Substitute [tex]G_0 = 100[/tex]
[tex]120 = 100 * e^{r[/tex]
Divide both sides by 100
[tex]1.2 = e^{r[/tex]
Take natural logarithm of both sides
[tex]\ln(1.2) = \ln(e^r)[/tex]
[tex]0.1823 = r[/tex]
[tex]r = 0.1823[/tex]
So, the expression for G is:
[tex]G(t) = G_0 * e^{rt}[/tex]
[tex]G(t) = 100 *e^{0.1823t}[/tex]
Solving (b): t when G(t) = 300
We have:
[tex]G(t) = 100 *e^{0.1823t}[/tex]
[tex]300 = 100 *e^{0.1823t}[/tex]
Divide both sides by 100
[tex]3 = e^{0.1823t}[/tex]
Take natural logarithm
[tex]\ln(3) = \ln(e^{0.1823t})[/tex]
[tex]1.099 = 0.1823t[/tex]
Solve for t
[tex]t = \frac{1.099}{0.1823}[/tex]
[tex]t = 6[/tex] --- approximated
Solving (c): When there will be no grass
Reduction at a rate of 80 tons per year implies that:
[tex]G(t) = 100 *e^{0.1823t}- 80t[/tex]
To solve for t, we set G(t) = 0
[tex]0 = 100 *e^{0.1823t}- 80t\\[/tex]
Rewrite as
[tex]80t = 100 *e^{0.1823t}[/tex]
Divide both sides by 100
[tex]0.8t = e^{0.1823t}[/tex]
Take natural logarithm of both sides
[tex]\ln( 0.8t) = \ln(e^{0.1823t})[/tex]
[tex]\ln( 0.8t) = 0.1823t[/tex]
Plot the graph of: [tex]\ln( 0.8t) = 0.1823t[/tex]
[tex]t = 1.7[/tex]
A brick staircase has a total of 17 steps The bottom step requires 131 bricks. Each successive step requires 5 less bricks than the prior one. How many bricks are required to build the staircase?
Answer: 1547 bricks are required to build the staircase.
Step-by-step explanation:
We are given:
Number of bricks in the first step, [tex]a_1[/tex] = 131
Number of bricks in the second step, [tex]a_2[/tex] = 131 - 5 = 126
Number of bricks in the third step, [tex]a_3[/tex] = 126 - 5 = 121
Sequence become:
131, 126, 121, .....
These are in arithmetic progression where a = 131 and d (common difference) = -5
To calculate the sum of an AP, we use the formula:
[tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex]
where,
n = number of terms = 17
Putting values in above equation, we get:
[tex]S_n=\frac{17}{2}[2(131)+(17-1)(-5)]\\\\S_n=\frac{17\times 182}{2}=1547[/tex]
Hence, 1547 bricks are required to build the staircase.
The perimeter of a rectangle is 58 inches and the area is 180 square inches. Find the dimensions of the rectangle.
Answer:
width = 9 inches
length= 20 inches
perimeter of the rectangle=2(9+20)
2w +2L= 2×29
=58 inches
area of the rectangle=w×L
=9×20=180 inch²