The height of the tree is 13.2 m.
What is proportional ?
The concept of proportionality in mathematics denotes the linear relationship between two quantities or variables. The size of one item increases by twofold, whereas the size of the other quantity decreases by one-tenth of the earlier amount.
We can set up a proportion comparing the height of each object to the length of the shadow.
Then , [tex]\frac{h}{s}[/tex].
=> [tex]\frac{3.8}{1.3} = \frac{h}{4.5}[/tex]
=> h = [tex]\frac{3.8*4.5}{1.3}[/tex]
=> 13.2 m.
Hence the height of the tree is 13.2 m.
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How many terms are in the given expression?5x - 2
The number of terms in the expression 5x - 2 is 2
What is number of terms in a mathematical expression ?The number of terms in an expression or equation refers to the values separated by a mathematical operator. A mathematical operator could be
AdditionSubtractionMultiplicationDivision and so onThe terms can be like terms or unlike terms
The two terms given is separated by the subtraction operator and are both unlike terms
The first term 5x consist of
coefficient = 5variable = xThe second term is just a constant which is 2
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The table below shows the energy of a 10 kg ball as a function of velocity. How much energy will the ball have at 10 m/s? velocity 0,2,3,6,10 energy 0,20,45,180,?
The amount of energy that the ball will have at 10 m/s is; 600 J
How to find the energy from velocity?From the given table, we see that when the velocity is 2 m/s, then the energy is 20 J.
If we take the square of the velocity, we get 2² = 4.
Thus, we need to multiply 4 by 6 to get the energy that is equal to 24 as 4 * 6 = 24.
Similarly;
For velocity equal to 3 m/s, the energy is given as:
E = 6 * 3²
E = 54 J
Thus, the general formula to find the energy is given as:
E = 6 * v²
where;
E is the energy
v is the velocity
Now, for velocity equal to 10 m/s, energy is given as;
E = 6 * 10
E = 60 J
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How to identify whether the word problem is about direct proportion, inverse proportion or partitive proportion?
The identification process of direct proportion, inverse proportion and partitive proportion is show below.
What is proportion?Proportion is comparison of things or magnitudes in terms of size, amount.
In direct proportion, when one quantity increase or decreases, the another quantity will also increase or decrease in the same ratio.
In inverse proportion, When one quantity increases, the another quantity decreases and vise versa.
Partitive proportion is when the division of a quantity into two or more equal or unequal parts.
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Hey, guys! How is your day? (°ω°)
Wilson paints 40% of a bookcase in 20 minutes.
Write an equation using equal fractions to represent this situation. Use a box to represent the time it takes to paint the whole bookcase.
The time taken for Wilson to paint the bookcase is 50 minutes.
What is percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, Wilson paints 40% of a bookcase in 20 minutes. It should be noted that 40% = 0.4
Therefore, the time taken to paint the whole bookcase will be:
= Number of minutes / Percentage painted
= 20 / 0.4
= 50
He'll use 50 minutes.
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On a typing test, Warren has 8 errors for every 2 minutes he spends typing. How many minutes has Warren typed if he has 64 errors?
Answer:16 minutes
Step-by-step explanation:
64 errors / 8 errors = 8
8 x 2 minutes = 16 minutes
How many times larger is 9 x 10^5 than 5 x 10^3?? PLSSSSS HELP
Answer:
[tex]1.8 \times {10}^{2} = 180[/tex]
Step-by-step explanation:
[tex] \frac{9 \times {10}^{5} }{5 \times {10}^{3} } = \frac{9}{5} \times \frac{ {10}^{5} }{ {10}^{3} } = 1.8 \times {10}^{2} = 1.8 \times 100 = 180[/tex]
Compute and expressed the result as a mixed fraction?
1) 2+ 3/4
Answer:
2 [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
2 + [tex]\frac{3}{4}[/tex]
= 2 [tex]\frac{3}{4}[/tex] ← as a mixed number
What’s is 3/20as a decimal I need HELP!
a frustum is made by removing a small cone from a similar large cone. The height of the small cone is quarter of the height of the large cone. Find the volume of the frustum.
Height of large cone =12
radius of large cone =6
The volume of a frustum is equal to 445.3785 cubic units.
How to calculate the volume of a cone?Mathematically, the volume of a cone can be calculated by using this formula:
Volume of a cone = 1/3 × πr²h
Where:
h represents the height of a cone.r represents the radius of a cone.For the volume of the large cone, we have the following:
Volume of large cone = 1/3 × πr²h
Volume of large cone = 1/3 × 3.142 × 6² × 12
Volume of large cone = 3.142 × 36 × 4
Volume of large cone = 452.448 cubic units.
Since the height of the small cone is quarter of the height of the large cone, we have:
Height of small cone = 1/4 × 12 = 3 units.
Radius of small cone = 12/18 = 3/2 = 1.5 units (similar triangles by AAA).
For the volume of the small cone, we have the following:
Volume of small cone = 1/3 × πr²h
Volume of small cone = 1/3 × 3.142 × 1.5² × 3
Volume of small cone = 3.142 × 2.25
Volume of small cone = 7.0695 cubic units.
Mathematically, we know that the volume of a frustum is made by subtracting the volume of a small cone from the volume of a similar large cone cone:
Volume of the frustum = Volume of large cone - Volume of small cone
Volume of the frustum = 452.448 - 7.0695
Volume of the frustum = 445.3785 cubic units.
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1
Writing the function f(x) = 4x + 2, what does f(x) represent?
The phrase [tex]f (x)[/tex] denotes a formula with [tex]x[/tex] serving as its input variable. Not multiply f and x, though!
An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable .
The x in [tex]f(x)[/tex] is referred to the argument of the function or simply the argument in function notation. Therefore, the response is just 2 if they ask for a argument and give you the equation [tex]f(2)[/tex].
Hence, the phrase [tex]f (x)[/tex] represents a formula with [tex]x[/tex] serving as its input variable.
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what is 5(-4)+(-6)+2(-2)
Answer:
-30
Step-by-step explanation:
Distribute
5 x -4= -20 2 x -2= -4
-20+(-6)+(-4)
Add together
-20 + -6= -26
-26 + (-4)
Add again
-26 + -4= -30
-30
22. A box containing 40 marbles weighs 280 grams. When 30 marbles are added, the box weighs 430 grams. How many grams does the box weigh when empty? A 80 B 120 C 150 D 490 E 710
Answer:
A/ 80 grams
Step-by-step explanation:
We know that 430 - 280 = 150, so each marble weights 5 grams. Then we take 5 times 40 = 200 grams. Then we take 280 subtract 200 = 80 grams
The function y = f(x) is graphed below. What is the average rate of change of the function f(x) on the interval -9 ≤ x ≤ -4?
Answer:
2.4
Step-by-step explanation:
You want the average rate of change on the interval [-9, -4] for the graphed function.
Average rate of changeThe average rate of change (m) is the slope of the line between the points at the ends of the interval. For function f(x) on interval [a, b], this is ...
m = (f(b) -f(a))/(b -a)
ApplicationFor the function f(x) on the interval [-9, -4], the average rate of change is ...
m = (f(-4) -f(-9))/(-4 -(-9)) = (-4 -(-16))/5 = 12/5 = 2.4
The average rate of change of f(x) on [-9, -4] is 2.4.
Factor the expression using the GCF.
The expression $32z-48$ factored using the GCF is
The factor of the expression 32z - 48 will be 16 and (2z - 3). And the greatest common factor is 16.
What is the greatest common factor?Simply said, it is the biggest common element. The highest consistent element in the above example is 15, making 15 the greatest common factor amongst 15, 30, and 105. The biggest chunk of the common factors is called the "Greatest Common Factor" (of two or more numbers).
The expression is given below.
⇒ 32z - 48
The expression can be rewritten as,
⇒ 32z - 48
⇒ 16 · 2z - 16 · 3
⇒ 16 (2z - 3)
The factor of the expression 32z - 48 will be 16 and (2z - 3). And the greatest common factor is 16.
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At a math convention, nine out of eleven people are bored by cable news. If there 122 at the convention who are not bored by cable news, then how many people at the convention are bored by cable news?
A total of 549 of people at the convention are bored by the cable news
How to determine the number of people at the convention that are bored?From the question, we have the following parameters that can be used in our computation:
Not bored = 122
Bored = 9/11 of the people
This means that
Not bored = 1 - Bored
So, we have
Not bored = 1 - 9/11
Evaluate
Not bored = 2/11
Recall that Not bored = 122
So, we have
2/11 * x = 122
Where x = the number of people
This gives
x = 122 * 11/2
Evaluate
x = 671
Recall that
Bored = 9/11 of the people
So, we have
Bored = 9/11 * 671
Evaluate
Bored = 549
Hence, the number of people at the convention that are bored is 549
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Shaq is climbing on the side of a mountain. From a spot on the
4
1/2 of
mountain, he climbs up of a kilometer. He then climbs down
5
a kilometer. How many kilometers is Shaq from his original starting
point?
In linear equation, 22.5 kilometer is Shaq from his original starting point.
What is linear equation?
The algebraic equation y=mx+b is known as a linear equation. m being the slope and b being the y-intercept, and just a constant and a first-order (linear) term are used. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.Shaq is he climbs up on the side of a mountain = 4 1/2 = 9/2
then he climbs down = 5 kilometer
Shaq from his original starting point = 9/2 * 5
= 45/2 = 22.5 kilometer
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Please help desperately I don’t know this. Burt keeps honeybees on his farm. When he first started, here’s a six room beehive that held 40 pounds of honey. Now he uses a 30 for a beehive. It has the same ratio and frames to Honey as a smaller beehive.
How much money does birds new beehive hold?
The ratio of frames to honey is the same as in a smaller beehive. 200 pounds of honey can be found in Bert's new beehive.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given data:
Number of frame beehives = 6
Pound of honey = 40
Current Frame beehive = 30
The first step is to formulate an equation and then use the formulated equation to find the number of honey
E = 40 × 30 ÷ 6
E = 40 × 5
E = 200 honey
Therefore the number of honey is 200.
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XR is tangent to circle O at point X. IfmXY = 110°, find m/YXR.
X
O
R
F
Y
D
The measure of ∠ YXR is 55 degrees.
Given that:-
m∠ XOY = 110 degrees
XR is a tangent to circle O at X.
We have to find the measure of ∠ YXR.
Draw the radii XO and OY to form the isosceles triangle XOY.
We know that the radius of the circle is perpendicular to the tangent.
Hence, ∠OXR = 90 degrees.
Consider the triangle XOR, we know that XO and OY are the radii of the triangle and hence equal.
Let, ∠ OXY = OYX = x
Hence,
110 + x + x = 180 degrees
2x = 70 degrees
x = 35 degrees
Now, we know that,
∠ OXR = ∠ OXY + ∠ YXR
90 = 35 + ∠ YXR
∠ YXR = 90 - 35 = 55 degrees.
∠ YXR = 55 degrees.
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(x-1)^2/x^2-1.
what is the x intercept
The x-intercept is 1 if the function is f(x) = (x-1)²/x²-1 after plugging f(x) = 0 or y = 0 the answer is 1.
What is a function?
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
The function is:
f(x) = (x-1)²/x²-1
To find the x-intercept where y = 0
or f(x) = 0
0 = (x-1)²/x²-1
x ≠ ±1
x - 1 = 0
x = 1
Thus, the x-intercept is 1 if the function is f(x) = (x-1)²/x²-1 after plugging f(x) = 0 or y = 0 the answer is 1.
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1. (a) What does probability convey about an event's
occurrence? (b) What is the probability of a
random event based on?
a) In any given experiment or trial, there is a probability that either an event occurs or it does not. The probability of the occurrence of an event lies between 0 and 1.
The event E of a sample space S is said to have occurred if the outcome ω of the experiment is such that ω ∈ E. However if the outcome ω is such that, ω ∉ E we say that the event has not occurred.
Let us take the example of playing cards. Here the event E is drawing a face card. If you draw a king of spades, we say the event E has occurred. However, if you draw an eight of clubs, we say the event E has not occurred.
b) The probability of an event is equal to the events relative frequency in the population of possible events that can occur.
An event’s relative frequency is a number between 0 and 1, so the event’s probability is from 0 to 1.
For example, when someone says that the probability it raining today is high, you understand that they mean that there is a high chance that it will rain.
But what if someone says that the probability of something happening is very low? You understand that the person means that the event may not occur at all. In mathematics, we define probability in a similar sense.
What is Probability?
Probability is the measure of uncertainty of any event (any phenomenon happened or bound to happen).
What is event?
In probability, the set of outcomes from an experiment is known as an Event.
What is random events?
An event with a probability of occurrence determined by some probability distribution.
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2x-84=108
x=?
please help
Answer:
X=
Step-by-step explanation:
Let's solve your equation step-by-step.
2x−84=108x
Step 1: Subtract 108x from both sides.
2x−84−108x=108x−108x
−106x−84=0
Step 2: Add 84 to both sides.
−106x−84+84=0+84
−106x=84
Step 3: Divide both sides by -106.
−106x
−106
=
84/−106x=−42/53
please help
2/5÷2 3/4
2/5÷2 3/4
0.4 / 2.75
= 0.14545...
a shipment of 12 television sets contains 3 defective sets. in how many ways can a hotel purchase 5 of these sets and receive at least 2 of the defective sets?
The hotel can acquire 5 of these sets in 119/792 different ways and still expect to receive 2 of the defective sets.
Define the term combination?Combinations are mathematical operations that count the total number of possible configurations for a set of elements is when order of said selection is irrelevant.As per the stated question.
You can select five television from a possible twelve in the sample space.
To acquire at least 2 faulty, therefore:
¹²C₅ = 12!/(7!)(5!) =12*11*10*9*8/(5*4*3*2*1)
¹²C₅ = 11*9*8
Obtaining two or three defective items. (At least 2).
2 defective items are-
(³C₂)(⁹C₄) = 3*9*8*7*6/(4!)
(³C₂)(⁹C₄) =9*7 =63
Three defective items equal -
(³C₃)(⁸C₂) = 1*8*7/2!
(³C₃)(⁸C₂) = 56
Total defective items is 63+56= 119 ways.
Probability = 119/(11*9*8)
Probability = 119/792
Thus, a hotel can acquire 5 of these sets in 119/792 different ways and still expect to receive 2 of the flawed sets.
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What do you need to multiply the subtotal by in order to get the total?
Given: Subtotal: 42.00
Total: 45.99
Tax rate: 9.5%
Sales tax: $3.99
The sum of 3 and four times a number
Answer:
-7
Step-by-step explanation:
tickets for a community theater cost $11 for each main floor seat and $6 for each balcony seat. there are 400 seats on the main floor, and these seats were sold out for the evening performance. the total revenue from ticket sales was $5060. how many balcony seats were sold?
The number of balcony seats sold is 110
Finding Unknown quantity using Linear equation:
The linear equation is an equation that is used to find an unknown quantity or an unknown number. In this, we will represent the Uknown value with a variable like x, y, z, etc.
Here we have
Tickets for a community theater cost $11 for each main-floor seat
and $6 for each balcony seat.
There are 400 seats on the main floor, which are sold out for the evening performance
The total revenue from ticket sales was $5060.
Here we don't know the number of balcony seats.
Let us assume that number of balcony seats = x
Then total revenue = 400(11) + 6x = 5060
=> 4400 + 6x = 5060
=> 6x = 5060 - 4400
=> 6x = 660
=> x = 110
Therefore,
The number of balcony seats sold = 110
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PLEASE HELP QUICK!!!!
Determine the length of the line segment shown.
line segment from negative 3 comma 10 to 4 comma negative 1
13 units
12 units
7 units
3 units
The length of the line segment defined by two endpoints; negative 3 comma 10 to 4 comma negative 1 as required in the task content is; 13.04.
What is the length of the line segment?It follows from the task content that the length of the line segment whose endpoints are as given in the task content is to be determined.
Recall; The length of a line segment whose endpoints are defined by; (x1, y1) and (x2, y2) is given as;
Length = √{ (y2 - y1)² + (x2 - x1)² }
Therefore, since the given endpoints are; (-3, 10) and (4, -1), it follows that the length of the line segment in discuss is;
Length = √{ (-1 - 10)² + (4 - (-3))² }
Length = √(121 + 49)
Length = √170
Length = 13.04.
Ultimately, the length of the line segment as required is; 13.04.
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If $3000 is invested at tan interest rate if 4.8%, compounded hourly for two years what is the ending balance?
The final balance is $97,920.
Compound interest is calculated on the principal as well as the interest accumulated over the previous period. It differs from simple interest in that interest is not added to the principal when calculating interest for the following period.
Given this, The principal is $3000.
Interest rate = 4.8%
Time = 2 years We must find the final balance.
The end balance formula is
C = P[ 〖(1+r)〗^n – 1]
C = 3000[ 〖(1+4.8)〗^2 – 1]
C = 3000 [ 〖(5.8)〗^2 – 1]
C = 3000 [ 33.64 – 1]
C = 3000 ( 32.64)
C = 97,920
Therefore the ending balance is $97,920
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Write an equation in point-slope form for the line that passes through each point
with the given slope. Then graph the equation.
1. (-6, -3), m = -1
2. (-7, 6), m = 0
3. (-2, 11), m=4/3
The equation of the line passing through
(1) point (-6, -3) and m = -1 is y = -x -9 .
(2) point (-7 , 6) and m = 0 is y = 6 ,
(3) point (-2 , 11) and m = 4/3 is y = (4/3)x + 41/3 .
the graph of the line is shown below .
In the question ,
point on the line and slope of the line is given
So , equation will be
Part(1)
(-6, -3), m = -1
(y -(-3)) = -1(x -(-6))
y + 3 = -1(x + 6)
y + 3 = -x - 6
y = -x -6 -3
y = -x -9
the equation is y = -x -9 .
Part(2)
(-7, 6), m = 0
(y - 6) = 0(x -(-7))
y - 6 = 0(x + 7)
y - 6 = 0
y = 6
the equation is y = 6
Part(3)
(-2, 11), m=4/3
(y - 11) = (4/3)(x -(-2))
y - 11 = (4/3)x + 8/3
y = (4/3)x + 8/3 + 11
y = (4/3)x + 41/3
the equation is y = (4/3)x + 41/3
the graph of all the three equations are shown below .
Therefore , The equation of the line passing through
(1) point (-6, -3) and m = -1 is y = -x -9 .
(2) point (-7 , 6) and m = 0 is y = 6 ,
(3) point (-2 , 11) and m = 4/3 is y = (4/3)x + 41/3 .
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Can anyone write the equation of the graph?
The equation of the graph is f(x) = |x - 3| + 5
How to find the equation of the graph line?Given that the graph is an absolute value graph
We start by calculating the vertex of the graph
In this case, the graph has it minimum point located at the coordinate (3, 5)
This coordinate can then be interpreted as
(h, k) = (3, 5)
As a general rule, the general representation of the equation of an absolute value function is f(x) = |x - h| + k
Substitute the known values in the above equation
So, we have the following equation
f(x) = |x - 3| + 5
Hence, the equation of the graph represented by the figure is f(x) = |x - 3| + 5
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