Answer:
They complete the hill in 8 hours
Step-by-step explanation:
Equations:
Let's call the variables:
Aran can make build the ant hill in A hours
Beatrice can make build the ant hill in B hours
Charlie can make build the ant hill in C hours
In one hour, Aran makes 1/A of the ant hill.
In one hour, Beatrice makes 1/B of the ant hill.
In one hour, Charlie makes 1/C of the ant hill.
Aran and Beatrice build it in 10 hours, thus:
[tex]\displaystyle \frac{1}{A}+\frac{1}{B}=\frac{1}{10}\qquad\qquad[1][/tex]
Similarly:
[tex]\displaystyle \frac{1}{A}+\frac{1}{C}=\frac{1}{12}\qquad\qquad[2][/tex]
[tex]\displaystyle \frac{1}{B}+\frac{1}{C}=\frac{1}{15}\qquad\qquad[3][/tex]
We need to find the time taken for the three ants to build the anthill:
[tex]\displaystyle \frac{1}{A}+\frac{1}{B}+\frac{1}{C}=[/tex]
Adding [1], [2], and [3]:
[tex]\displaystyle \frac{2}{A}+\frac{2}{B}+\frac{2}{C}=\frac{1}{10}+\frac{1}{12}+\frac{1}{15}[/tex]
Adding the fractions (LCM=60):
[tex]\displaystyle \frac{2}{A}+\frac{2}{B}+\frac{2}{C}=\frac{6}{60}+\frac{5}{60}+\frac{4}{60}[/tex]
[tex]\displaystyle \frac{2}{A}+\frac{2}{B}+\frac{2}{C}=\frac{6+5+4}{60}=\frac{15}{60}=\frac{1}{4}[/tex]
Dividing by 2:
[tex]\displaystyle \frac{1}{A}+\frac{1}{B}+\frac{1}{C}=\frac{1}{8}[/tex]
All ants together make 1/8 of the hill, thus they complete the hill in 8 hours
Tennis star Rafael Nadal lost at the Australian Open. How many Grand Slams has he won?
Answer: 22
Step-by-step explanation:
Rahul made three Indian clay curry pots. He wants to see if he
can place them in the oven at the same time.
The diameter of the second pot is of the diameter of his first
pot.
cm wider than the diameter
The diameter of the third pot is
of his second pot.
The sum of the diameters of the three pots is 47.5 cm.
What equation represents the sum of the diameters of all three lord and what is the value of y?
Answer:2.234
Step-by-step explanation:
Write an
equivalent expression using the distributive property.
1/4(4x - 6)
Answer:
Step-by-step explanation:
Distributive property: a*(b + c)= (a*b) + (a*c)
[tex]\frac{1}{4}(4x - 6) = 4x*\frac{1}{4} - 6*\frac{1}{4}\\\\[/tex]
[tex]= x -3*\frac{1}{2}\\\\=x - \frac{3}{2}[/tex]
f(x) = ( - 3x² + 2 – 2)e". Find f'(x) and f''(x).
f'(2) =
f''(c)
=
Answer:
-3x²-5xeˣ-eˣ
-3eˣx²-11eˣx-6eˣ
Step-by-step explanation:
I'm going to go by the picture and not what you wrote in your title.
To find the derivative of this we have to apply the product rule
(a*b)'=
a'*b+a*b'
We plug in our numbers and get
(-3x²+x-2)'*eˣ+(-3x²+x-2)*eˣ'
Now we can evaluate the derivatives and simplify
(-3x²+x-2)'= -6x+1
eˣ'=eˣ
which means we have
(-6x+1)*eˣ+(-3x²+x-2)*eˣ
Simplify
-6xeˣ+eˣ-3x²eˣ+xeˣ-2eˣ
Combine like terms
-3x²eˣ-5xeˣ-eˣ
Now we just need to find the derivative of this
We can apply the same product rule as we did before
(-3x²eˣ)'
Let's start by factoring out the -3 to get
-3(x²eˣ)'
which is equal to
-3(x²eˣ'+x²'eˣ)
Compute this and get
-3(x²eˣ+2xeˣ)= -3x²eˣ-6xeˣ
Now let's find the derivative of the second part
(-5xeˣ)'
-5(x'eˣ+xeˣ')
-5(eˣ+xeˣ)
-5eˣ-5xeˣ
Which means we have
(-3x²eˣ-6xeˣ)+(-5eˣ-5xeˣ)-eˣ
Combine like terms and get
-3eˣx²-11eˣx-6eˣ
Square ABCD is similar to square JKLM. AB = 10, BC = 10, CD = 10, DA = 10, and JK = 15. The area of square JKLM is ____u 2
Answer:
225 square units
Step-by-step explanation:
since they are similar, all sides of JKLM are 15 units so:
15x15=225
Gabby sells candy bars for $ 1 dollar each, and Twizzlers for 25 cents each. For every dollar she earns she gives 10 cents to charity. If She sells 42 candy bars and 45 Twizzlers, how much money will she have for herself after giving to charity? Write an expression and evaluate.
Answer:
$47.925 for herself.
Step-by-step explanation:
Answer:
Step-by-step explanation:
42+11.25 =52.35
52.35*.10
5.235$
I hope this is the right answer
Right Triangle ABC has its right angle at C, BC = 4, and AC= 8.
What is the value of the trigonometric ratio?
cos B
csc B
tan A
Drag a value to each box to match the trigonometric ratio?
9514 1404 393
Answer:
cos B = (√5)/5
csc B = (√5)/2
tan A = 1/2
Step-by-step explanation:
The length of hypotenuse AB is given by the Pythagorean theorem:
AB² = AC² +BC²
AB² = 8² +4² = 64 +16 = 80
AB = √80 = 4√5
The mnemonic SOH CAH TOA can help you remember the needed ratios.
Cos = Adjacent/Hypotenuse
cos B = BC/AB = 4/(4√5)
cos B = (√5)/5
__
Sin = Opposite/Hypotenuse
csc = 1/sin = Hypotenuse/Opposite
csc B = AB/AC = (4√5)/8
csc B = (√5)/2
__
Tan = Opposite/Adjacent
tan A = BC/AC = 4/8
tan A = 1/2
Answer:
tan A = 1/2
cos B = √5/5
csc B = √5/2
Step-by-step explanation: I took the test
Taylor completed 2/3 of her homework. Riian completed 7/8 of her homework. Taylor and Riian have the same amount of homework. Who completed a greater amount of homework?
Answer:
Riian completed a greater amount of homework.
Step-by-step explanation:
The fraction 7/8 is greater than the fraction 2/3.
ANSWER CORRECTLY OR I WILL REPORT AND DELETE YOUR ANSWER THANK YOU Classify the questions as statistical or not statistical. How many hours did Ryan study last Saturday? How many students in my class own 2 bags? How many bags do I own? How many hours do students in my class study every day? How many cars does each person in my neighborhood own? How many houseplants does each house on my block have?
The following are statistical questions:
How many hours do students in my class study every day? How many cars does each person in my neighborhood own? How many houseplants does each house on my block have?The following are not statistical questions:
How many hours did Ryan study last Saturday? How many students in my class own 2 bags? How many bags do I own?What is a statistical question?
A statistical question is a question that can be answered by collecting data that varies. For example, the hours studied by students in a class would vary. Some would study for 1 hour, others 2 hours or 5 hours or 10 hours.
To learn more about statistical questions. please check: https://brainly.com/question/11253919
#SPJ1
What is the probability of drawing an even numbered card from a standard deck of shuffled cards?
A) 20/52
B) 25/52
C) 30/52
D) 35/52
Answer:
Prob = 20/52
Step-by-step explanation:
There are 5 even number cards per suit: 2, 4, 6, 8, and 10.
and there are 4 suits in a deck, so the total of the even number card events is 5 * 4 = 20
Given that the deck has 52 cards total, then the probability of drawing an even numbered card is the number of successes (20) divided the number of total cards (52) This gives:
Prob = 20/52
which agrees with answer A) in your list.
Nathan has $40 in a savings account. The interest rate is 5% per year and is not
compounded. How much interest will he earn in 1 year?
Use the formulai = prt, where / is the interest earned, p is the principal (starting amount),
is the interest rate expressed as a decimal, and is the time in years.
Submit
Money with Nathan in his savings account = $40
Rate of interest per annum = 5%
We know that :
[tex]\color{hotpink}\tt \: simple \: interest \color{plum}= \frac{principal \times rate \times time}{100} [/tex]
In this case :
Principal = $40
Rate = 5%
Time = 1 year
Simple interest he will earn in 1 year :
[tex] =\tt \frac{40 \times 5 \times 1}{100} [/tex]
[tex] = \tt \frac{200}{100} [/tex]
[tex]\color{plum} =\tt\$ \: 2[/tex]
Amount = Principal + Interest
Amount Nathan has to pay at the end of one year :
[tex] = \tt40 + 2[/tex]
[tex]\color{plum} =\tt \$42[/tex]
Thus, at the end of 1 year Nathan has to pay $42.
Therefore, simple interest Nathan will earn in 1 year = $2
I’ll give you 15 points if you know the answers to this question
It would be B)no.
Hope This Helps!
help me me me me pls
Answer:
"C" is the answer to that question
Answer:
C
Explanation:
Because I say so
7. Are the two triangles similar? How do you know? I need this answered quick plz
Answer:
Yes, by the angle angle rule.
Step-by-step explanation:
In the first triangle,
m<C=60 degrees, and m< D=53 degrees. You know that the sum of angles in a triangle add up to 180 degrees, so solve for E. m<E= 67 degrees.
In the second triangle,
m<F=60 degrees and m<H=67 degrees.
Since both triangle have two congruent angles, you can say that the two triangles are similiar by the AA rule.
Both triangle CDE and triangle FGH are similar to each other.
Similar figures
Two figures are said to be similar if they have the same shape and the ratio of their corresponding sides are in the same proportion. All the corresponding angles of similar figures are congruent.
∠C + ∠D + ∠E = 180° (angles in a triangle)
60 + 53 + ∠E = 180
∠E = 67°
∠C = ∠F, ∠D = ∠G, ∠E = ∠H, hence both triangles are similar.
Find out more on Similar figures at: https://brainly.com/question/2644832
Help ASAP I’ll mark brainliest
Answer:
C. 254
Step-by-step explanation:
There are 3 different types of engineers listed in the chart, Electrical, Chemical, and Mechanical. Under the first column of math, add together the numbers for all three engineers.
85+80+89= 254
Therefore, 254 engineers chose math as their favorite subject.
This month you make $3,881 from liquor salesfrom food, and from your gift shop. your monthly sales goal is $25,000, did you meet your goal?
Answer:
No
Step-by-step explanation:
If you add all the sales you do not meet your goal of $25,000
Answer from text book is given but I cant understand how they get this answer using these numbers?
This was the question:
Analia wants to know which school has higher academic achievements relative to the number of teachers per student.
a) What is the Graduation rate divided by teachers per student?
b) SAT average divided by teachers per student?
So I looked up the answer after getting it wrong and this is the calculations used to come to the answer. I cant figure out how they put these 3 numbers together to get 18,947 and 11,053
Answer:
The equation is
(students x points) / teachers
Can someone help me with this in
Answer:
Step-by-step explanation:
4
Jared has a collection of 90 movies on DVD. If
46 of the movies are comedies, 26 are drama,
and the rest are science fiction, what percent of
the movies are science fiction?
A) 18
B) 20
C) 28
D) 32
PLEASE HELP!!!! What is the slope of the line that passes through the points (2, 3) and (6, 8)
Answer:
[tex]\frac{5}{4}[/tex]
Step-by-step explanation:
to find the slope (m) of a line:
[tex]m= \frac{y_2 - y_1}{x_2 - x_1}[/tex]
where y₁ = 3
y₂ = 8
x₁ = 2
x₂ = 6
plug into the equation:
[tex]m = \frac{8 - 3}{6 - 2} \\m = \frac{5}{4}[/tex]
so the slope is [tex]\frac{5}{4}[/tex]
The height of a building is 956 feet, which is about 479 feet higher than another building. What is the height of the second building?
The second building has a height of feet
At 8p.m., the temperature was -9 degrees Fahrenheit. Over the next five hours, the temperature dropped by 18 degrees. What is the temperature after five hours?
Answer:
-27 if im reading the question right.
Step-by-step explanation
HELP ASAPPPPP I WILL GIVE BRAINLIST
Answer:
Step-by-step explanation:
Count all writing utensils which is 16, then jus count the number of pencils
Answer:
5:16 because she has 5 pencils and a total of 16 writing utensils
Step-by-step explanation:
3. Jalen is a lifeguard at a public swimming pool and is planning to string
flags across both diagonals of the rectangular pool. He knows the
dimensions of the pool are 50 meters by 25 meters.
What value represents the length of flag string Jalen will need to reach
across the diagonals of the pool?
Answer:
[tex]Flag = 55.90m[/tex]
Step-by-step explanation:
Given
[tex]Length = 50m[/tex]
[tex]Width = 25m[/tex]
Required
Determine the length of the flag
Because the flag crosses through opposite diagonals of the pool. Its length is the length of the diagonal of the pool.
This is calculated using Pythagoras theorem.
[tex]Flag^2 = Length^2 + Width^2[/tex]
Substitute values for Length and Width
[tex]Flag^2 = 50^2 + 25^2[/tex]
[tex]Flag^2 = 2500 + 625[/tex]
[tex]Flag^2 = 3125[/tex]
Take positive square root of both sides
[tex]Flag = \sqrt{3125[/tex]
[tex]Flag = 55.90m[/tex]
Hence, the length of the flag is approximately 55.90m
(9/8) to the power of 2; can some give me the answer quick please.
Answer:
(9/8)²=
81/64.
...........................
y = - 4x y = 2x - 1
which method is the best to solve this
Answer:
get all the varibles on one side
Step-by-step explanation:
mark me as brainliest plz thx
. Which expression represents the phrase below? 4 less than the product of 8 and a number, x *
A. 8 - 7x
B. (8 + 4) - 3
C. 4 - 8x
D. 8x - 4
Answer:
8x-4
Step-by-step explanation:
4 is less meaning it is subtraction and product of 8 and x is 8x
What is the slope of a line that passes through the points (-2, 4) and (-6, 12)?
O-2
○
0
열
2
02
Answer:
[tex]\displaystyle m=-2[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Slope Formula: [tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (-2, 4)
Point (-6, 12)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [Slope Formula]: [tex]\displaystyle m=\frac{12-4}{-6+2}[/tex][Slope] [Fraction] Subtract/Add: [tex]\displaystyle m=\frac{8}{-4}[/tex][Slope] [Fraction] Divide: [tex]\displaystyle m=-2[/tex]5
Which equation will solve the following word problem? The professor has 390 books that he wants to display in his office. Each shelf can hold 65 books. How many shelves will he need?
390s = 65
390(65) = s
s/390 = 65
390 = 65s
Answer:
6 shelves
Step-by-step explanation:
Let the number of shelves needed be s
If the total number of books to be displayed is 390books
If Each shelf can hold 65 books, then;
1 shelf = 65books
To know the total shelf needed;
s = 390 books
Divide both expressions
1/s = 65/390
65s = 390
Divide through by 65
65s/65 = 390/65
s = 390/65
s = 6
Hence 6 shelves will be needed
si un punto está sobre el eje x cual es su valor de la ordenada
Answer:
si un punto esta sobre el eje x cual es su valor de cordenada
Step-by-step explanation:
360