if a flagpole 12 feet tall casts a shadow that is 16 feet long, find the length of the shadow cast by an antenna which is 30 ft tall. round to the nearest tenth if necessary
The rectangles in the figure below are similar. Find the value of x
Answer:
C. 6
Step-by-step explanation:
It is given that the rectangles in the figure are similar.
Thus, the corresponding sides of the two rectangles will be equal.
So, we get,
[tex]\frac{3}{x}=\frac{5}{x+4}[/tex]
i.e. [tex]3(x+4)=5x[/tex]
i.e. [tex]3x+12=5x[/tex]
i.e. [tex]2x=12[/tex]
i.e. x = 6.
Hence, the value of x is 6.
Is 3/47 a rational number?
3/47= 0.06383 so it is RATIONAL
Answer:
Rational.
Step-by-step explanation:
We have been given a fraction [tex]\frac{3}{47}[/tex]. We are asked to determine whether our given number is rational or not.
We know that a number is rational number, when it can be represented as a fraction of form [tex]\frac{p}{q}[/tex], where q must be a non-zero number.
Upon looking at our given number, we can see that it is a fraction and numerator is equal to 47 that is a non-zero number.
Therefore, our given number is a rational number.
-2 1/2 = t/10 what is t?
Answer:
4
Step-by-step explanation:
What is the probability that a randomly chosen rod will fit into a randomly chosen ring?
The skeleton of acetonitrile is shown here. complete the structure
60÷5(7-5)=24 is that correct ? Thanks
Absolutely, it is correct.
[tex]\boxed{ \ 60 \div 5 (7 - 5) = 24 \ }[/tex]
Further explanationIn the 1500s the specific rules of the order of operation were promptly issued. The order of these workings states which processes take precedence (as a key priority) before which other operations.
Operation priorities are as follows.
Brackets (simplify in it)ExponentMultiplication or Division (from left to right)Addition or Subtraction (from left to right)Let's implement the rule.
[tex]\boxed{ \ 60 \div 5 (7 - 5) = \ ? \ }[/tex]
Subtract 7 by 5 in parentheses.
[tex]\boxed{ \ 60 \div 5 (2) = \ ? \ }[/tex]
Properly apply rule number 3 from the priority operation above. Initially, we have to divide 60 by 5.
[tex]\boxed{ \ 12(2) = \ ? \ }[/tex]
Continuing with multiplication 12 by 2 proves the exact result.
[tex]\boxed{ \ 12 \times 2 = 24 \ }[/tex]
Thus, this equation is correct.
[tex]\boxed{ \ 60 \div 5 (7 - 5) = 24 \ }[/tex]
Note:
What is the result if we don't follow operation priorities? Let's see.
At this crucial point.
[tex]\boxed{ \ 60 \div 5 (2) = \ ? \ }[/tex]
We decide to multiply 5 by 2, even though there are no parentheses from them, only parentheses for 2.
[tex]\boxed{ \ 60 \div 5 \times 2 = \ ? \ }[/tex]
[tex]\boxed{ \ 60 \div 10 = 6 \ }[/tex]
[tex]\boxed{ \ 60 \div 5 (7 - 5) = 6 \ }[/tex]
That's what happens if we don't follow operating priorities.
Unless the problem like this:
[tex]\boxed{ \ 60 \div (5 (7 - 5)) = 6 \ }[/tex]
[tex]\boxed{ \ 60 \div (5 (2)) = 6 \ }[/tex]
[tex]\boxed{ \ 60 \div 10 = 6 \ }[/tex]
Thus, the difference must be considered. Consequently, follow the priority of the operation and look at the problem in detail.
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The high school's lunch menu repeats every 6 school days. The middle school lunch menu repeats every 8 school days. On March 5th, both schools served chicken wraps. What is the next calendar date on which both schools will serve chicken wraps?
Final answer:
Both schools will serve chicken wraps again on March 29th.
Explanation:
The question involves finding the next calendar date when both the high school and middle school will serve chicken wraps again. To solve this problem, we need to find the Least Common Multiple (LCM) of the two repeating cycles, which are 6 days for the high school and 8 days for the middle school.
First, let's calculate the LCM of 6 and 8:
Multiple of 6: 6, 12, 18, 24, 30, 36, 42, 48, ...Multiple of 8: 8, 16, 24, 32, 40, 48, ...We find that the smallest common multiple is 24 days.
Since both schools served chicken wraps on March 5th, we simply add 24 days to that date. This gives us:
March 5th + 24 days = March 29thTherefore, both schools will serve chicken wraps again on March 29th.
what is the length of line segment AY?
2 units
3 units
4 units
6 units
Answer:
Option C. 4 Units
Step-by-step explanation:
From the intersecting chords theorem we know that if two chords are intersecting each other in a circle then the products of the lengths of the line segments of each chord are equal.
Therefore AY.YC =YB.YD
Here AY = x, BY = 3, YC = 6, YD = 8
So x.6 = 3.8
6x = 24
x = 24/6 = 4 Units
Option C 4 units is the correct option.
In the number 514,482,441, how is the relationship between the first pair of 4s the same as the relationship between the second pair of 4s? How is it different?
A square field has an area of 479 ft what is the approximate length of a size of the field
Answer:
21.9 ft
Step-by-step explanation:
The area of a square is the square of the side length, so the side length is the square root of the area:
... s = √(479 ft²) ≈ 21.886 ft
This is approximately 21.9 ft.
Since there are 20 standard amino acids, the number of possible linear polypeptides of length n can be expressed as:
Since there are 20 standard amino acids, the number of possible linear polypeptides of length n can be expressed as [tex]20^n[/tex].
What are Amino acids?Amino acids may be defined as compounds that significantly contain carbon, hydrogen, oxygen, and nitrogen. These compounds serve as the monomers or the building blocks of proteins that are composed of an amino group, a carboxyl group, a hydrogen atom, and a specific side chain.
Two amino acids are held together by a linkage known as peptide linkage. When a number of peptide linkages are present in the structure of the protein, it is known as polypeptides.
If any polypeptide chain is derived from 20 amino acids. So, the possibility of a combination for any polypeptide chain will be [tex]20^n[/tex], where n = the number of amino acid residues in the polypeptide chain.
Therefore, since there are 20 standard amino acids, the number of possible linear polypeptides of length n can be expressed as [tex]20^n[/tex].
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Why -4 x (-4) = 16 not -16? Simple...
Surface area of a right cone.
Solve for P S=2b+ph
Answer:
P=S-2b/h
Step-by-step explanation:
To solve this equation the first thing we do is subtract 2B from both sides of the equation. S-2b=ph+2b-2b which would give us S-2B=PH. next, we divide H from both sides of the equation which would give us the answer: S-2B/h=p
Find the domain of the function. (enter your answer using interval notation.) f(x) = 5 x 3 − 1 x2 + 2x − 24
Choose the word phrase (greater than, less than, or equal to) to make the statements true.
Each paper clip can be traded for three matches.
Each pencil can be traded for six paper clips.
Three pencils are worth [less than, greater than, or equal to] seventeen paper clips.
which one pls
Answer:
Three pencils are worth greater than seventeen paper clips.
Step-by-step explanation:
Each paper clip can be traded for three matches.
Each pencil can be traded for six paper clips.
Three pencils are worth [tex]3\times6=18[/tex] paper clips.
So, the correct statement is - Three pencils are worth greater than seventeen paper clips.
A completely filled 20 gallon tank originally contains 10 pounds of salt dissolved in water. pure water enters the tank at the rate of 5 gallons/minute, and the well-stirred mixture leaves the tank at the same rate. find the amount of salt in the tank at any time t .
To find the amount of salt in the tank at any time t, we can use the equation S(t) = 10 - 10(W(t)/20), where W(t) represents the amount of water in the tank at time t. Substituting the given values, we can calculate the amount of salt in the tank.
Explanation:To find the amount of salt in the tank at any time t, we need to consider the rate at which pure water enters and leaves the tank. Since water enters the tank at a rate of 5 gallons/minute, the amount of water in the tank at any time t can be represented by the equation: W(t) = 5t, where t represents time in minutes. The concentration of salt in the tank remains constant, so the amount of salt in the tank at any time t can be represented by the equation: S(t) = 10 - 10(W(t)/20), where S(t) represents the amount of salt in pounds and W(t) represents the amount of water in gallons.
Let's solve for S(t) when t = 10 minutes:
S(10) = 10 - 10(5/20) = 10 - 10(1/4) = 10 - 10/4 = 10 - 2.5 = 7.5 pounds of salt.
The simplified expression e2t + 2 + e−2t inside the radical can be re-written as
The expression [tex]e^{2t} + 2 + e^{-2t[/tex] is a quadratic equation in terms of exponentials. Without additional information, simplification beyond this stage is not generally feasible. This concept is a typical part of high school algebra, with applications in several fields.
Explanation:The provided expression [tex]e2t + 2 + e-2t[/tex] belongs to a class of mathematical problems often seen in high school algebra. It involves exponentials, which introduces the concept of exponential functions.
The expression is in a form of a quadratic equation in terms of exponentials, which can be solved via appropriate methods such as factoring, quadratic formula, or completing the square. However, without additional information or context like an equation being set to zero, simplification beyond this stage is not generally feasible. Exponential functions often have applications in fields like physics, economics, and engineering, especially in phenomena that exhibit growth or decay properties.
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Solve for x: u= kx + yx
Answer:
The value of the equation for x is [tex]x=\frac{u}{k+y}[/tex].
Step-by-step explanation:
Consider the provided equation.
[tex]u= kx + yx[/tex]
We need to solve the equation for x.
Take x common from right side as shown below:
[tex]u= x(k + y)[/tex]
Divide both the sides by k+y.
[tex]\frac{u}{k+y}=\frac{x(k + y)}{k+y}[/tex]
[tex]x=\frac{u}{k+y}[/tex]
Hence, the value of the equation for x is [tex]x=\frac{u}{k+y}[/tex].
Jim walks 3.5km every day. How far does he walk in 5 days?
Suppose that 10 of the 30 freshmen, 40 of the 60 sophomores, 5 of the 20 juniors and 40 of the 50 seniors were in favor of multiple choice exams. what is the overall estimate of the proportion of students in favor of multiple choice exams?
What is the size of the largest and smallest numbers of vertices of degree 1 possible in an n-vertex tree, for n > 2?
Maria has 3/4 pound of cheese to use making sandwiches. she's used about 1/32 pound of cheese on each sandwich. how many sandwiches can she make
Graph the solution of this inequality 4\9x -10>x\3-12
Answer:
I'm terrible at explaining so here's a ss
- Ripper
Step-by-step explanation:
One number is 3 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 500, find the numbers
Need help with math problem
The temperature of a lake drops by the same amount each day for 10 days. The temperature drops by a total of 5 degrees.
Drag the numbers to form the equation that represents the change in the lake's temperature each day.
( ? ) ( ? ) = ( ? )
5, -5, 10, -10, 1/2, -1/2, 1/10, -1/10
Thanks
Ratio Conversion Table mile : yard 1 : 1,760 yard : foot 1 : 3 foot : inch 1 : 12 Using the conversion table, match the equivalent measurements. Tiles 29 feet 352 yards 372 feet 124 yards 2 miles 0.2 miles 1,016 yards 10,560 feet 348 inches Pairs What would all the pairs be HELP 52 points
29 feet = 348 inches
352 yards = 0.2 miles
372 feet = 124 yards
2 miles = 10560 feet
you can actually just google for the answers lol
29 feet = 348 inches
352 yards = 0.2 miles
372 feet = 124 yards
2 miles = 10560 feet
A tee-ball team for 5 year-olds has half as many girls as boys. If there are 15 children on the team, how many are boys and how many are girls?
As the has half as many females as males, the number of males in the team is 10, and the number of females in the team is 5.
What is the number of males and females in the team?Given the parameter:
A team for 5-year-olds has half as many females as males.
There are 15 children on the team.
There are half as many females as males, this can be expressed as:
Let G represents females and B represents males.
G = 0.5B
Also, there are 15 children on the team, so we can write an equation based on the total number of children:
B + G = 15
Now, we solve the system of equations:
G = 0.5B
B + G = 15
First, substitute the expression for females from the first equation into the second equation:
B + 0.5B = 15
1.5B = 15
B = 15/1.5
B = 10
Plug B = 10 into the first equation and solve for females:
B + G = 15
10 + G = 15
G = 15 - 10
G = 5
So, there are 10 males and 5 females on the team.
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A mural inspired by photo graph measures 107 inches by 180 inches.the scale factor is 12.what are the dimensions of the photograph
For the straight line defined by the points (3, 59) and (5, 87), determine the slope and y-intercept. do not round the answers.
The slope of the given line is 14 and y intercept is 17.
What is the equation of a line ?The equation of a line is y = mx + b.Where m is slope and b is y intercept.
According to the given question a straight line defined by the points (3, 59) and (5, 87).
We know slope (m) = (y₂ -y₁)/(x₂ - x₁)
∴ m = (87 - 59)/(5 - 3)
m = 28/2
m = 14.
Now the equation of the line will be of the form y = 14x + b.
Now we will put any of the values of the given pair of points.
∴ 59 = 14(3) + b
b = 59 - 42
b = 17.
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