The answer is:
The first option:
[tex]Volumen_{max}=(8-2x)(6-2x)*x[/tex]
Why?From the statement, we know the dimensions of the box, and the length of the sides to be cut (x).
So,
Working with the length of the box, we have:
Let be 8 the length of the cardboard for the length of the box, so, if we cut out the side of length "x", we have:
[tex]Length=(8-(x+x))=(8-2x)[/tex]
Now,
Working with the width of the box, we have:
Let be 6 the length of the cardboard for the width of the box, so, if we cut out the side of length "x", we have:
[tex]Length=(6-(x+x))=(6-2x)[/tex]
Now that we already know the length and the width of the box, we know that the bottom of the box will have the same length "x", so, the greatest possible volume of the cardboard box will be:
[tex]Volumen_{max}=Length*Width*Bottom=(8-2x)(6-2x)*x[/tex]
Have a nice day!
Please help me out please
Answer:
[tex]\frac{8}{81}[/tex]
Step-by-step explanation:
Since the sequence is geometric there is a common ratio r between consecutive terms.
r = [tex]\frac{1}{3}[/tex] ÷ [tex]\frac{1}{2}[/tex]
= [tex]\frac{1}{3}[/tex] × [tex]\frac{2}{1}[/tex] = [tex]\frac{2}{3}[/tex]
Multiplying [tex]\frac{4}{27}[/tex] by r gives the next term in the sequence
[tex]\frac{4}{27}[/tex] × [tex]\frac{2}{3}[/tex] = [tex]\frac{8}{81}[/tex]
Find the volume of this figure.
Answer:
320 cubic units
Step-by-step explanation:
The volume of a pyramid is given by the formula ...
V = (1/3)Bh
where B is the area of the base, and h is the height.
Your pyramid has a rectangular base with edge lengths 8 units and 10 units. Hence the area of the base is ...
8×10 = 80 . . . . square units
The height is 12 units, so the volume formula gives the volume as ...
V = (1/3)(80)(12) = 320 . . . . cubic units
If the area of square 1 is 25 units square, and the area of square 2 is 16 units square, what is the perimeter of square 3
Answer:
12
Step-by-step explanation:
If square 1's area is 25, that must mean its side is 5
If square 2's area is 16, that must mean its side is 4
Since it looks like its going in order, square 3's side is 3, and since there's 4 sides to a square, the perimeter is 12.
Answer:
12 units²
Step-by-step explanation:
4^2+b^2=5^2
b=25-16
b^2=9
b=√9
b=3
there are 4 sides in a square so 3•4=12
Please help me out with this please
Intersecting Chord Theorem:
X = 1/2(78 + 76)
X = 1/2(154)
x = 77
The fish population of Lake Collins is decreasing at a rate of 5% per year. In 2004 there were about 1,350 fish. Write an exponential decay function that models this situation. Then find the population in 2010.
Answer:
Part 1) The exponential function is equal to [tex]y=1,350(0.95)^{x}[/tex]
Part 2) The population in 2010 was [tex]992\ fish[/tex]
Step-by-step explanation:
Part 1) Write an exponential decay function that models this situation
we know that
In this problem we have a exponential function of the form
[tex]y=a(b)^{x}[/tex]
where
y ----> the fish population of Lake Collins since 2004
x ----> the time in years
a is the initial value
b is the base
we have
[tex]a=1,350\ fish[/tex]
[tex]b=(100\%-5\%)=95\%=0.95[/tex]
substitute
[tex]y=1,350(0.95)^{x}[/tex] ----> exponential function that represent this scenario
Part 2) Find the population in 2010
we have
[tex]y=1,350(0.95)^{x}[/tex]
so
For [tex]x=(2010-2004)=6\ years[/tex]
substitute
[tex]y=1,350(0.95)^{6}=992\ fish[/tex]
Final answer:
The exponential decay function for the fish population in Lake Collins is P(t) = 1350 * e^(-0.05t). Using this, the estimated fish population in 2010 is about 1,000.
Explanation:
We need to write an exponential decay function to model the decreasing fish population in Lake Collins and then use it to find the population in 2010.
To create an exponential decay function, we can use the formula P(t) = P0 * e^(rt), where:
P(t) is the population at time t,
P0 is the initial population,
r is the rate of decay (as a negative value), and
t is the time in years since the initial count.
Given the initial population of 1,350 fish in 2004 and a decay rate of 5% per year, we can write the function as:
P(t) = 1350 * e^(-0.05t)
To find the population in 2010, we first calculate the time passed since 2004, which is 6 years. Thus, t = 6:
P(6) = 1350 * e^(-0.05*6)
Calculating this gives us:
P(6) ≈ 1350 * e^(-0.3) ≈ 1350 * 0.740818 ≈ 1000 (rounded to the nearest whole number)
Therefore, the fish population in 2010 was approximately 1,000 individuals.
Please please help me
Answer:
131 m³
Step-by-step explanation:
The volume (V) of a cone is
V = [tex]\frac{1}{3}[/tex] area of base × height
= [tex]\frac{1}{3}[/tex] × π × 5² × 5
= [tex]\frac{1}{3}[/tex] π × 125 ≈ 131
Each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. Which ordered pair is a viable solution if x represents the number of days that a library book is late and y represents the total fee?
a. (–3, –0.90)
b. (–2.5, –0.75)
c.(4.5, 1.35)
d. (8, 2.40)
Answer:
The correct answer would be (8,2.40).
Step-by-step explanation:
Option one(-3, -0.9) and two (-2.5, -0.75) Would not be a viable solution because the value of number of days can not be negative and in option one and two, value of days -3 and -2.5 is negative.
Option three(4.5, 1.35) can not be correct because library charges fee for a full day so the number for days would be a whole number. Library would not charge for 4.5 days, they would either charge of 4 days or 5 days because 4.5 is not an whole number.
Option four(8, 2.40) is the correct answer because it satisfies our equation;
Y= 0.30 * X
2.40= 0.30 * 8
2.40 = 2.40
hope this helps :)
D is the right answer
If g(x)=f(x+1), then g(x) translates the function f(x) 1 unit _[blank]_.
Left
Right
Up
Down
answer: right
reason: because you are talking about the x axis so if you go left that would be a negative and you cant go up and down bc that's the y axis so the only way to go is right
hope this helped
How to write an exponential function from a table
Answer:
Step-by-step explanation:
I'll show you with an example. I'll make a table and then show you how to find the exponential equation, ok?
x y
0 3
1 12
2 48
3 192
The standard form of an exponential equation is
[tex]y=a(b)^x[/tex]
We will take 2 (x,y) coordinates from our table and fit them into the equations to solve for a and b. Using the point (0, 3):
[tex]3=a(b)^0[/tex]
b to the 0 power is equal to 1, so the equation then becomes a(1) = 3 so a = 3. We will use the other x, y coordinate along with that a value to now solve for b:
[tex]12=3(b)^1[/tex]
b to the first is b, so now that equation becomes 3b = 12 and b = 4. Filling that info back into the standard form:
[tex]y=3(4)^x[/tex]
There you go!
In this triangle, what is the value of x?
Enter your answer, rounded to the nearest tenth, in the box.
x =
To find x you can use cosine since you know the adjacent side and the hypotenuse. Remember that for cosine it is adjacent over hypotenuse
cos(x) = [tex]\frac{28}{72}[/tex]
cos(x) = [tex]\frac{7}{18}[/tex]
To find the x we must take the inverse of cosine:
[tex]cos^{-1}[/tex]([tex]\frac{7}{18}[/tex] = x
x = 67.1146...
x ≈ 67.1 degrees
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
67.1
Step-by-step explanation:
i took the test
Heo started to solve the quadratic equation (x + 2)2 – 9 = –5. He added 9 to both sides and the resulting equation was (x + 2)2 = 4. Next, he took the square root of each side. Which was the resulting equation of that step?
Step-by-step explanation:
After taking the square root:
x + 2 = ±2
Notice that x + 2 can also equal -2, because (-2)² = 4.
Find the 4th term of the expansion of (2a - b)^7.
a.
-560a^4b^3
c.
560a^4b^3
b.
-560a^3b^4
d.
560a^3b^4
Answer:
-560a^4b^3
Step-by-step explanation:
Given:
(2a - b)^7
By using Binomial theorem:
128a^7 - 448a^6b + 672a^5b^2 - 560a^4b^3 + 280a^3b^4 - 84a^2b^5 + 14ab^6-b^7
Here the fourth term is -560a^4b^3 !
Answer:
-560a^4 b^3.
Step-by-step explanation:
The (r + 1)th term of (a + x)^n = nCr a^(n-r) x^r.
So, the 4th term of (2a - b)^7 = 7C3 (2a)(7-3)x^3
= 35*16a^4(-b)^3
= -560a^4 b^3.
Which expression is equivalent to 7a^2b + 10a^2b^2 + 14a^2b^3?
ab(7a^2 + 10ab + 14b^2)
a^2b(7 + 10b + 14b^2)
7a^2(b + 3b^2 + 7b^3)
7a^2b^3(b^2 + 3b + 7)
Answer:
a^2b(7 + 10b + 14b^2)
Use wolframalpha for math questions, or photomath!
To solve this, factor out a^2b from the expression.
For this case we must indicate an expression equivalent to:
[tex]7a ^ 2b + 10a ^ 2b ^ 2 + 14a ^ 2b ^ 3[/tex]
We must draw the common term of the three terms, we have:
[tex]a ^ 2b (7 + 10b + 14b ^ 2)[/tex]
So:
[tex]7a ^ 2b + 10a ^ 2b ^ 2 + 14a ^ 2b ^ 3 = a ^ 2b (7 + 10b + 14b ^ 2)[/tex]
Answer:
[tex]a ^ 2b (7 + 10b + 14b ^ 2)[/tex]
Option B
Please answer this question CORRECTLY for 30 points and brainliest!
Answer:
22 quarters
Hope this helps! Correct me if im wrong.
.) The terms 4, t, 9 are the start of a sequence.
Part A: If the sequence is arithmetic, what is the value of t?
Part B: If the sequence is geometric, what is the value of t?
Answer:
see explanation
Step-by-step explanation:
A
If the sequence is arithmetic then the common difference d is
d = t - 4 = 9 -t, that is
t - 4 = 9 - t ( add t to both sides )
2t - 4 = 9 ( add 4 to both sides )
2t = 13 ( divide both sides by 2 )
t = [tex]\frac{13}{2}[/tex] = 6 [tex]\frac{1}{2}[/tex]
----------------------------------------------------------------------
B
If the sequence is geometric then the common ratio r is
r = [tex]\frac{t}{4}[/tex] = [tex]\frac{9}{t}[/tex] ( cross- multiply )
t² = 36 ( take the square root of both sides )
t = [tex]\sqrt{36}[/tex] = 6
A: If the sequence is arithmetic, what is the value of t is 6.5.
B: If the sequence is geometric, what is the value of t is 6.
If the sequence is arithmetic then the common difference d is,
What is the arithmetic sequence?An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms are the same.
d = t - 4
d= 9 -t,
that is,
t - 4 = 9 - t ( add t to both sides )
2t - 4 = 9 ( add 4 to both sides )
2t = 13 ( divide both sides by 2 )
t =[tex]\frac{13}{2}[/tex] = 6.5
If the sequence is geometric then the common ratio r is
r = [tex]\frac{t}{4} =\frac{9}{t}[/tex] = ( cross- multiply )
t² = 36 ( take the square root of both sides )
t = [tex]\sqrt{36}[/tex]= 6
Therefore we get,
A: If the sequence is arithmetic, what is the value of t is 6.5.
B: If the sequence is geometric, what is the value of t is 6
To learn more about the sequence visit:
https://brainly.com/question/6561461
#SPJ2
Help!
Assume that lines that appear tangent are tangent. Find the value of each variable.
It is so jard for me .
so by drawing construction i have done it.Value of x i haven't done.due to no perfect angle
Can you help me with these 2 questions?
Answer:
What school you go to
Step-by-step explanation:
step by step go catch friend and step by step friends
The diameter of the base of the cone measures 8 units.
The height measures 6 units.
What is the volume of the cone?
Answer: [tex]32\pi[/tex] cubic units.
Step-by-step explanation:
You can use this formula for calculate the volume of a cone:
[tex]V_{cone}=\frac{1}{3}\pi r^2h[/tex]
Where "r" is the radius and "h" is the height.
You know that the diameter of the base of the cone measures 8 units, then, the radius can be found by dividing the diameter by 2:
[tex]r=\frac{8units}{2}\\\\r=4units[/tex]
Since you already know that height and the radius, you can substitute them into the formula. Then, the volume of this cone is:
[tex]V_{cone}=\frac{1}{3}\pi (4units)^2(6units)[/tex]
[tex]V_{cone}=32\pi \ units^3[/tex]
Answer: 48
Step-by-step explanation:
What shape is the cross-section of the cylinder hone sliced perpendicular to its base?
A. Circle
B. Rectangle
C. Square
D. Triangle
Answer:
circle should be the answer
The answer is A. Circle
a small coin is thrown off the eiffel tower in paris. It lands 62.5m away from the centre of the base of the 320m- high structure. find the angle of elevation from the coin to the top of the tower
Answer:
78.9 degrees to the nearest tenth.
Step-by-step explanation:
This equals the angle whose tangent is 320/62.5 ( opposite side / adjacent side).
The angle of elevation from the coin to the top of the tower
What is angle of elevation?
The angle formed by the line of sight and the horizontal plane for an object above the horizontal.
Given that:
The coin lands 62.5m away from the center of the base of the 320m- high structure.
Height= 320 m
Base= 62.5 m
Now, tan [tex]\theta[/tex] = [tex]\frac{P}{B}[/tex]
=[tex]\frac{320}{62.5}[/tex]
= 5.12
[tex]\theta[/tex]= [tex]tan^{-1} (5.12)[/tex]
[tex]\theta[/tex]= [tex]78.94^{0}[/tex]
The angle of elevation is: 78.94 degrees.
Learn more about angle of elevation here:
https://brainly.com/question/14370377
#SPJ2
From net earnings of $740 per month, Lisa Jones must spend $200 for her portion of the rent on an apartment she shares with two friends. What percent of her net income is her rent payment? A. 73% B. 27% C. 32% D. 38%
Answer:
Step-by-step explanation:
the answer is 27%.
Answer:
27 %
Step-by-step explanation:
To find the percentage of which her net income is her rent payment you do
[tex]\frac{200}{740}[/tex] × 100 = 27.027027027
what is the length of the diagonal of a non-regulation tennis court with length 20 feet and width 15 feet?
Answer:
25 feet
Step-by-step explanation:
Basically that non-regulation tennis court is a rectangle. You want to know the length of the diagonal. If you draw it on paper, you'll see that this then become 2 triangles... of which you have 2 sides, and are seeking the hypotenuse. So....
H² = A² + B²
H² = 20² + 15² = 400 + 225 = 625
H = 25 feet.
Answer:
The diagonal of a non-regulation tennis court = 25 feet
Step-by-step explanation:
Pythagorean theorem
Hypotenuse² = Base² + Height²
The tennis court is like a rectangle.
We can consider the court as made of two right angled triangle
To find the length of diagonal of court
Here base = 15 feet and height = 20 feet
Diagonal or hypotenuse can be written as,
Diagonal ² = Base² + Height²
= 15² + 20²
= 225 + 400
= 625
Diagonal = √625 = 25 feet
Therefore the diagonal of a non-regulation tennis court = 25 feet
Sunny earns \$12$12dollar sign, 12 per hour delivering cakes. She worked for xxx hours this week. Unfortunately, she was charged \$15$15dollar sign, 15 for a late delivery on Tuesday. How much money did Sunny earn this week?
Answer:
12x - 15 dollars
Step-by-step explanation:
Sunny earns $12 per hour for delivering cakes.
She worked for x hours this week.
Unfortunately, she was charged $15 for a late delivery on Tuesday
She was supposed to earn $12 × x = $12x this week
But she was charged $15 for late delivery on Tuesday
So her net earning this week is; $12x - $15
Answer:
12x-15
Step-by-step explanation:
compete the square to determine minum or maxuim value of function define by -x2+10x+5
Answer:
maximum value y = 30
Step-by-step explanation:
Given
- x² + 10x + 5
To complete the square the coefficient of the x² term must be 1
factor out - 1
= - (x² - 10x) + 5
To complete the square
add/subtract ( half the coefficient of the x- term )² to x² - 10x
= - (x² + 2(- 5)x + 25 - 25) + 5
= - (x - 5)² + 25 + 5
= - (x - 5)² + 30 ← in vertex form
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Hence vertex = (5, 30)
The max/ min occurs at the vertex
Since a < 0 then vertex is a maximum
Hence maximum value is y = 30
А
Subtotal
Male
11
20
Female
13 T 22 TOT 10 us
24 27 20 26
Subtotal
a. Fill in the blank cells by computing subtotals. In the last call of the bottom
5pts
place the sum of all the interior cells. What is the total number of the
participated in the survey?
b. P(male)
Answer:
a)
The total number of students who participated in the survey is 97
b)
P(male) = 0.5361
c)
P(A) = 0.2474
d)
The events male and TV show B are not mutually exclusive since 5 males prefer TV show B.
e)
The events female and TV show C are mutually exclusive since no female participant prefers TV show C
Step-by-step explanation:
a)
The total number of students who participated in the survey is obtained as;
Number of male participants + number of female participants
52 + 45 = 97
b)
P(male)
This is the probability that a randomly selected individual would be a male;
P(male) = ( number of male participants) / ( total participants)
= 52/97 = 0.5361
c)
P(A)
This is the probability that a randomly selected participant would prefer TV show A;
P(A) = ( participants who prefer TV show A) / (total participants)
= 24/97 = 0.2474
d)
Two events are said to be mutually exclusive if they cannot happen at the same time. Another word that means mutually exclusive is disjoint. If two events A and B are disjoint, then the probability of them both occurring at the same time is 0.
The events male and TV show B are not mutually exclusive since 5 males prefer TV show B. The probability is thus not 0.
e)
Two events are said to be mutually exclusive if they cannot happen at the same time. Another word that means mutually exclusive is disjoint. If two events A and B are disjoint, then the probability of them both occurring at the same time is 0.
The events female and TV show C are mutually exclusive since no female participant prefers TV show C. The probability is thus 0.
According to the diagram below, which similarity statements are true?
it can be concluded that [tex]\( \angle BAD = \angle CBD \) and \( \angle ABD = \angle BCD \).[/tex] So, all three angles are equal.
From the given information:
[tex]\( \angle BAD + \angle ABD = 90^\circ \)[/tex]
[tex]\( \angle CBD + \angle BCD = 90^\circ \)[/tex]
[tex]\( \angle ABD + \angle DBC = 90^\circ \)[/tex]
[tex]\( \angle BAD + \angle BCD = 90^\circ \)[/tex]
We can see that:
[tex]\( \angle BAD + \angle ABD = \angle CBD + \angle BCD \)[/tex]
[tex]\( \angle BAD + \angle BCD = \angle ABD + \angle DBC \)[/tex]
[tex]\( \angle BAD + \angle BCD = \angle BAD + \angle BCD \)[/tex]
From equations (1) and (2), we can conclude that:
[tex]\[ \angle BAD + \angle ABD = \angle CBD + \angle BCD = \angle ABD + \angle DBC \][/tex]
This implies that [tex]\( \angle ABD = \angle CBD \) and \( \angle BCD = \angle DBC \).[/tex]
Therefore, it can be concluded that [tex]\( \angle BAD = \angle CBD \) and \( \angle ABD = \angle BCD \).[/tex] So, all three angles are equal.
The complete question is:
According to the diagram below, which similarity statements are true? Check all that apply.
A. △ ABDsim △ BCD
B. △ ABCsim △ BDC
C. △ ABCsim △ ADB
D. △ ABDsim △ ADC
The similarity statements that are true are:
A. [tex]\(\triangle ABD \sim \triangle BCD\)[/tex]C. [tex]\(\triangle ABC \sim \triangle ADB\)[/tex]D. [tex]\(\triangle ABC \sim \triangle BDC\)[/tex][tex]\(\triangle ABD \sim \triangle BCD\):[/tex]
- Since D lies on AC and [tex]\( \angle ADB = \angle BDC = 90^\circ \),[/tex] both [tex]\(\triangle ABD\)[/tex]and \[tex](\triangle BCD\)[/tex]share [tex]\( \angle ADB = \angle BDC \).[/tex]
- They both share the common angle [tex]\( \angle B \).[/tex]
- Therefore, [tex]\(\triangle ABD \sim \triangle BCD\).[/tex]
[tex]\(\triangle ABC \sim \triangle ADB\):[/tex]
- Both triangles share the angle [tex]\( \angle A \).[/tex]
- They both have right angles at [tex]\( \angle ABC = \angle ADB = 90^\circ \).[/tex]
- Therefore, [tex]\(\triangle ABC \sim \triangle ADB\).[/tex]
[tex]\(\triangle ABC \sim \triangle BDC\):[/tex]
- Both triangles share the angle [tex]\( \angle C \).[/tex]
- They both have right angles at [tex]\( \angle ABC = \angle BDC = 90^\circ \).[/tex]
- Therefore, [tex]\(\triangle ABC \sim \triangle BDC\).[/tex]
What is x? Help please
Answer: [tex]x=\frac{8}{3}[/tex]
Step-by-step explanation:
By the Intersecting secants theorem, we know that:
[tex]EC*ED=EB*EA[/tex]
Then, substituting, we get:
[tex](x+4)(x+4+1)=(x+1)(x+1+11)\\\\(x+4)(x+5)=(x+1)(x+12)[/tex]
Now we need to expand the expression:
[tex]x^2+5x+4x+20=x^2+12x+x+12[/tex]
Simplifying, we get that the value of "x" is:
[tex]x^2+9x+20=x^2+12x+12\\\\9x+20=12x+12\\\\20-12=12x-9x\\\\8=3x\\\\x=\frac{8}{3}[/tex]
The ShowMe Theater is showing 12 movies. Each movie is shown at five different times during during the day. How many choices of movies and showtime does Bart have?
bart has a choice of twelve different movies at 5 different times each so you just multiply twelve and five to get 60 choices
Answer:
Bart has 60 choices.Step-by-step explanation:
Givens
The theater is showing 12 movies.Each movie is shown at five different times.To find the total number of choices of movies and showtime that Bart have, we just need to multiply. Because, if each movie is shown at five different times, and there are 12 movies, then the total number of choices are
[tex]12 \times 5 = 60[/tex]
Therefore, Bart has 60 choices to watch a movie.
Tammy mixes the letters s, c, h, o, o, and l thoroughly. without looking, allen draws one letter. expressed as a fraction, decimal, and percentage, what is the probability that allen will not select a consonant? (1 point)
There are 6 letters: (4 consonants, 2 vowels)
The probability that Allen will not select a consonant is: (2/6 which simplifies to 1/3) because there are only 2 letters out of the 6 that are not consonants
Fraction: 1/3
Decimal: 0.3333
Percentage: 33.33%
The probability that Allen does not select a consonant is 1/3 as a fraction, 0.3333 as a decimal, and 33.33% as a percentage.
You've asked what the probability is that Allen will not select a consonant when drawing one letter from the mix of letters 's, c, h, o, o, l'. First, let's determine how many vowels and consonants there are in the selection. We have two vowels ('o', 'o') and four consonants ('s', 'c', 'h', 'l'). This gives us a total of six letters.
To find the probability of not selecting a consonant, we look at the likelihood of selecting a vowel instead, since those are the only two types of letters available. There are 2 vowels out of a total of 6 letters. The probability as a fraction is thus 2/6, which simplifies to 1/3.
To express this probability as a decimal, divide the numerator by the denominator: 1 divided by 3 equals approximately 0.3333. Finally, to express this as a percentage, multiply the decimal by 100 to get 33.33%.
In summary:
Fraction: 1/3Decimal: 0.3333Percentage: 33.33%Can someone help me out?
Answer:
see below
Step-by-step explanation:
If you haven't memorized it so you know it already, it takes about 10 seconds with your calculator to discover that ...
arccos((√3)/2) = β = 30°
This fact matches only one answer choice.