A triangle has three sides 35cm 54 cm and 61 cm find its area Also find the smallest of its altitude
Answers
Answer:
Area of given triangle is 939.15cm² and smallest altitude is 30.8cm
Solution:We are given three sides of a triangle, Let the sides be :
( a ) = 35 cm( b ) = 54 cm( c ) = 61 cmWe can find the area of the triangle with its three sides using Heron's Formula
Heron's FormulaHeron's formula was founded by hero of Alexandria, for finding the area of triangle in terms of the length of its sides. Heron's formula can be written as:
\( \sf{ \pmb { \longrightarrow \: \sqrt{s(s - a)(s - b)(s - c)} }}\)
where ( s ) :
\( \sf \longrightarrow s = \dfrac{a + b + c}{2} \)
Therefore, for the given triangle first we will calculate ( s )
\( \begin {aligned}\quad & \quad \longmapsto \sf s = \dfrac{a + b + c}{2} \\ & \quad \longmapsto \sf s = \dfrac{35 + 54 + 61}{2} \\ & \quad \longmapsto \sf s = \dfrac{150}{2} \\ & \quad \longmapsto \sf s = 75cm \end{aligned}\)
Now, Area of triangle will be:
\( \begin{aligned}&:\implies \sf\quad \sf \: A = \sqrt{s(s - a)(s - b)(s - c)} \\ &:\implies \sf\quad \sf \: A = \sqrt{75(75 - 35)(75 - 54)(75 - 61)} \\&:\implies \sf\quad \sf \: A = \sqrt{75 \times 40 \times 21 \times 14} \\ &:\implies \sf\quad \sf \: A = \sqrt{5 \times 5 \times 3 \times 3 \times 2 \times 2 \times 7 \times 7 \times 2 \times 2 \times 5} \\ &:\implies \sf\quad \sf \: A =5 \times 3 \times 2 \times 7 \times 2 \sqrt{5} \\ &:\implies \sf\quad \sf \: A =420 \times 2.23 \\ &:\implies \sf\quad \sf \boxed{ \pmb{ \sf A =939.15 {cm}^{2} }} \end{aligned}\)
Also, we have to find the smallest altitude, and the smallest altitude will be on the longest side. So,
\( \begin{aligned}&:\implies \sf\quad \sf \: Area =939.15 \\ &:\implies \sf\quad \sf \: \dfrac{1}{2} \times b \times h =939.15 \\ &:\implies \sf\quad \sf \: \dfrac{1}{2} \times 61 \times h = 939.15 \\&:\implies \sf\quad \sf \: h =939.15 \times \dfrac{2}{61} \\&:\implies \sf\quad \sf \: h = \dfrac{1818.3}{61} \\ &:\implies \sf\quad \boxed{ \pmb{\sf \: h =30.79 \: (approx)}} \end{aligned}\)
Answer:
Area = 939.15 cm² (2 d.p.)
Shortest Altitude = 30.79 cm (2 d.p.)
Step-by-step explanation:
Heron's Formula allows us to find the area of a triangle in terms its side lengths.
Heron's Formula
\(\sf Area = \sqrt{s(s-a)(s-b)(s-c)}\)
where:
a, b and c are the side lengths of the triangles is half the perimeterGiven values:
a = 35 cmb = 54 cmc = 61 cmFind the value of s:
\(\sf \implies s=\dfrac{a+b+c}{2}=\dfrac{35+54+61}{2}=75\:cm\)
Substitute the values into the formula and solve for area:
\(\begin{aligned}\implies \sf Area & =\sf \sqrt{75(75-35)(75-54)(75-61)}\\& = \sf \sqrt{75(40)(21)(14)}\\& = \sf \sqrt{882000}\\& = \sf \sqrt{176400 \cdot 5}\\& = \sf \sqrt{176400}\sqrt{5}\\& = \sf 420\sqrt{5}\\& = \sf 939.15\:\:cm^2\:\:(2\:d.p.)\end{aligned}\)
The altitude of a triangle is a perpendicular line segment drawn from a vertex of the triangle to the side opposite to it.
The shortest altitude of a triangle is drawn to the longest side.
Therefore, the shortest altitude will be the height of the triangle when the longest side is the base:
\(\begin{aligned}\textsf{Area of a Triangle} & = \sf \dfrac{1}{2} \times base \times height\\\implies \sf 420\sqrt{5} & = \sf \dfrac{1}{2} \times 61 \times altitude \\\implies \sf Altitude & = \sf \frac{2 \cdot 420\sqrt{5}}{61}\\& = \sf \dfrac{840\sqrt{5}}{61}\\ & = \sf 30.79\:\:cm\:\:(2\:d.p.)\end{aligned}\)
Related Questions
If 400 x 300 = 120,000
And 40 x 30 is 1,200
Fill in the blanks and show your work
*_____ x ______ = 12,000?
Answers
Answer:
this list
Step-by-step explanation:
1×12000=12000
2×6000=12000
3×4000=12000
4×3000=12000
5×2400=12000
6×2000=12000
8×1500=12000
10 ×1200=12000
12 ×1000=12000
Find the value of 11/14 . Write fractions in the form a/b.
Answers
Answer:
10/14 = ? ... 12/14 = ?
Step-by-step explanation:
what is 3 3/8 as an improper fraction
Answers
Answer:
66/8
Explanation
8x8+2=66/8
66/8 simplafied is 33/8
Solve the following quadratic inequality x^2+x-6>0
Answers
Answer:
x < -3 or x > 2
Step-by-step explanation:
x² + x - 6 > 0
Convert the inequality to an equation.
x² + x - 6 = 0
Factor using the AC method and get:
(x - 2) (x + 3) = 0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
x - 2 = 0
x = 2
x + 3 = 0
x = -3
So, the solution is x < -3 or x > 2
Two glasses of milk and 4 snack bars have a total of 76 carbohydrates (carbs), and 4 glasses of milk and 3 snack bars have a total of 92 carbs.
Answers
Answer:
10 carbs in snack bars
14 carbs in milk
Step-by-step explanation:
Glasses of Milk = m
Snack Bars = s
I am going to make this a system of equations:
2m + 3s = 58
4m + 2s = 76
I am going to simplify one of them for a s:
4m + 2s = 76
2s = 76 - 4m
s = 38 - 2m
I am going to insert this into the other equation:
2m + 3s = 58
2m + 3(38 - 2m) = 58
2m + 114 - 6m = 58
(-4)m + 114 = 58
(-4)m = -56
m = 14 calories
I am going to plug this m into one of the equations (doesn't matter which):
2(14) + 3s = 58
28 + 3s = 58
3s = 30
s = 10
You can plug these values back into each of the equations to make sure they work.
Hope it helps! UvU
Factor: x(3y-5)+3(3y-15)
Answers
3xy-5x+9y-45
Step-by-step explanation:
Step by Step Solution
STEP1:STEP2:Pulling out like terms
2.1 Pull out like factors :
3y - 15 = 3 • (y - 5)
Equation at the end of step2: (x • (3y - 5)) + 9 • (y - 5) STEP3:Equation at the end of step 3 x • (3y - 5) + 9 • (y - 5) STEP4:Trying to factor a multi variable polynomial
4.1 Split 3xy-5x+9y-45
4.1 Split 3xy-5x+9y-45
into two 2-term polynomials
-5x+3xy and +9y-45
This partition did not result in a factorization. We'll try another one:
3xy-5x and +9y-45
This partition did not result in a factorization. We'll try another one:
3xy+9y and -5x-45
This partition did not result in a factorization. We'll try another one:
3xy-45 and +9y-5x
This partition did not result in a factorization. We'll try another one:
-45+3xy and +9y-5x
This partition did not result in a factorization. We'll try
\(\begin{gathered}\ \ \begin{gathered}\begin{gathered}\displaystyle \text{Let :}\\ \\\displaystyle f(x)=\int {\dfrac{dx}{e^x+8e^{-x}+4e^{-3x}}} \\ \\ \\\displaystyle \text{And} \\ \\\displaystyle g(x)=\int {\dfrac{dx}{e^{3x}+8e^{x}+4e^{-x}}} \\ \\ \\\displaystyle \text{Then find value of :} \\ \\\displaystyle \int {(f(x)-2g(x))dx} \, \quad \text{And} \\ \\ \\\displaystyle \int {(f(x)+2g(x))dx}\end{gathered}\end{gathered} \ \end{gathered} \ \textless \ br /\ \textgreater \ \ \textless \ br /\ \textgreater \ \)
Higher Class Question!
Ans if uk!!
asap
50 pts for this tough questions
Answers
Answer:
attachment
Step-by-step explanation:
see the attachment
![[tex]\begin{gathered}\ \ \begin{gathered}\begin{gathered}\displaystyle \text{Let :}\\ \\\displaystyle](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/sGCX1drsPEsvQeoT9EwhrUCAd3viqxbb.jpeg)
Given that.
\(\displaystyle f(x)=\int {\dfrac{dx}{e^x+8e^{-x}+4e^{-3x}}}\)
and,
\(\displaystyle g(x)=\int {\dfrac{dx}{e^{3x}+8e^{x}+4e^{-x}}}\)
To perform mathematical operations on f(x) and g(x), they should have the same denominator.
Multiplying & Dividing f(x) by e^2x,
\(\longrightarrow \: \displaystyle f(x)=\int {\dfrac{e {}^{2x} dx}{e^{3x}+8e^{x}+4e^{-x}}}\)
Now,
\(\begin{gathered} \longrightarrow \: \displaystyle \int \bigg( f(x) - 2g(x) \bigg)=\int {\dfrac{e {}^{2x} dx}{e^{3x}+8e^{x}+4e^{-x}}} - \int {\dfrac{dx}{e^{3x}+8e^{x}+4e^{-x}}} \\ \\ \longrightarrow \ \: \displaystyle \int \bigg( f(x) - 2g(x) \bigg)=\int {\dfrac{(e {}^{2x} - 2) dx}{e^{3x}+8e^{x}+4e^{-x}}}\end{gathered}
\)
Multiplying & Dividing by e^x,
\(\longrightarrow \ \: \displaystyle \int \bigg( f(x) - 2g(x) \bigg)=\int {\dfrac{ {e}^{x} (e {}^{2x} - 2) dx}{e^{4x}+8e^{2x}+4} }\)
Let's assume t = e^x
Differentiating on both sides w.r.t x,
\(dx = \dfrac{dt}{e {}^{x} }\)
Thus,
\(\longrightarrow \ \: \displaystyle \int \bigg( f(x) - 2g(x) \bigg)=\int {\dfrac{ {e}^{x} (t{}^{2} - 2)}{t^{4}+8t^{2}+4} } \times \dfrac{dt}{ {e}^{x} }\)
Dividing Numerator and Denominator by t²,
\(\longrightarrow \ \: \displaystyle \int \bigg( f(x) - 2g(x) \bigg)=\int {\dfrac{ (1 - \dfrac{2}{ {t}^{2} } )dt}{t^{2}+8+ \dfrac{4}{ {t}^{2} } } }\)
Consider t² + 8 + 4/t².
It can be rewritten as (t + 2/t)² + 4 = (t + 2/t)² + 2
\(\longrightarrow \ \: \displaystyle \int \bigg( f(x) - 2g(x) \bigg)=\int \dfrac{ (1 - \dfrac{2}{ {t}^{2} } )dt}{(t + \dfrac{2}{t} ) {}^{2} + {2}^{2} }\)
Here,
If y = t + 2/t and differentiating w.r.t t,
\(\implies dy = ( 1 - \dfrac{2}{t {}^{2} } )\)
Therefore,
\(\longrightarrow \ \: \displaystyle \int \bigg( f(x) - 2g(x) \bigg)=\int \dfrac{dy}{ {y}^{2} + {2}^{2} }\)
Of the form,
\(\boxed{ \boxed{ \sf \displaystyle \int \dfrac{dx}{ {x}^{2} + {a}^{2} } = \dfrac{1}{a}tan {}^{ - 1}( \dfrac{x}{a} ) }} \)
Further,
\(\begin{gathered} \longrightarrow \ \: \displaystyle \int \bigg( f(x) - 2g(x) \bigg) = \dfrac{1}{2} {tan}^{ - 1} \bigg( \dfrac{y}{2} \bigg) \\ \\ \longrightarrow \ \: \displaystyle \int \bigg( f(x) - 2g(x) \bigg) = \dfrac{1}{2} {tan}^{ - 1} \bigg( \dfrac{t {}^{2} + 2}{2t} \bigg) \\ \\ \longrightarrow \ \boxed{ \boxed{\displaystyle \int \bigg( f(x) - 2g(x) \bigg) = \dfrac{1}{2} {tan}^{ - 1} \bigg( \dfrac{ {e}^{2x} + 2 }{2 {e}^{x} } \bigg)}}\end{gathered} \)
Help me quick please:
6x8=50-2
Answers
Answer:
True
Step-by-step explanation:
6*8=50-2
48 = 48
Both sides are equal, so the statement is true.
Answer:
True
Step-by-step explanation:
6x8=48
50-2=48
Hence, this equation is true
15 square meters is equivalent to how many square yards
Answers
Answer:
17.9399 square yards (hope it help)
Step-by-step explanation:
15 square meters is equivalent to 17.9399 square yards
Answer:
17.94 square yards
Step-by-step explanation:
FORMULA:
multiply the area value by 1.196
Now,
15 × 1.196 = 17.94
Convert each rate using dimensional analysis 44yds/s=?mi/h
Answers
Using dimensional analysis we have converted 44 yards/sec = 90 miles/hour.
What is dimensional analysis?Dimensional analysis is the study of how dimensions and units of measurement affect the relationship between physical quantities.
Dimensional analysis is crucial because it maintains the consistency of the units, which facilitates accurate mathematical computation.
As we use conversion factors to obtain the same units, dimensional analysis is also known as the Factor Label Method or Unit Factor Method.
We know that 1 yards/sec = 2.04545 miles/hour
Here given that 44yds/s = ? miles/hour
Lets solve
1 yards/sec = 2.04545 miles/hour
44 yards/sec = 44 × 2.04545 miles/hour
44 yards/sec = 89.9998 miles/hour
44 yards/sec = 90 miles/hour
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what statement require's proof before it's acceptable as a true statement? ...... A. defined terms B. postulate .C. undefined terms D. theorem...... hope your watching XxdeathshootxX
Answers
Answer:
D. Theorem
Step-by-step explanation:
Statements
1. WXYZ is a
parallelogram with
diagonals
XZ and WY
intersecting at
point V.
2. WX // ZY and
XY // WZ
3. ZWXYZYZW
ZWXZ = ZYZX
4.XYZW
5. AWZVAYXV
6. WV YV
7. XZ bisects WY
Given
Reasons
Definition of a parallelogram
Opposite sides of a
parallelogram are congruent
Corresponding parts of
congruent triangles are
congruent
Definition of segment bisector
Answers
1. ZX ≅WY; WXYZ is a parallelogram. 1. Given
2. ZY≅ WX 2. The opposite sides of the
parallelogram are ≅
what is parallelogram ?There are 4 different kinds of parallelograms, including 3 unique kinds. The four types are rhombuses, squares, parallelograms, and rectangles.
There are not equal sides on a parallelogram. A parallelogram only has equal sides on its opposite sides.
what is segment bisector ?A line segment bisector splits a line segment into two equally sized pieces. It passes through the segment's halfway.
The following justifications are given for the choice made above:
The following is how the two-column proof is presented.
Statement Motive
1. ZX ≅WY; WXYZ is a parallelogram. 1. Given
2. ZY≅ WX 2. The opposite sides of the parallelogram are ≅
3. YX ≅ YX 3. The reflexive quality
4. Δ ZYX ≅ΔWXY 4. The SSS thm.
5 . ∠ZYX ≅ ∠WXY 5 . CPCTC
6 . m∠ZYX ≅m∠WXY 6. Def. of ≅
7. m∠ZYX + mWXY equal 180° 7. Parallelograms with consecutive s are additional
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Select the correct answer.
It costs $480.00 to rent an apartment on the Gold Coast for a weekend. Last year it cost $400.00.
What method below shows how you would calculate the % increase?
Answers
The method is: Find the increase and find the ratio of the increase and the old price.
The percentage increase is 20%
What method below shows how you would calculate the percentage increase?A percentage is defined as the ratio that can be expressed as a fraction of 100.
The method below shows how you would calculate the % increase.
First step: Find the increase:
increase = 480 - 400 = $80
Second step: Find the ratio of the increase and the old price and multiply by 100 to express in percentage:
80/400 * 100 = 20%
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A house on the market was valued at $277.000. After several years, the value increased by 18%. By how much did the house's value increase in dollars? What is the current value of the house?
Answers
$49.86
Step-by-step explanation:
277x118=32686
32686 divided by 100 = 326.86 ( value after the increase )
326.86-277.00=$49.86
Answer this question please
Answers
All the functions which are bounded below and bounded above are,
⇒ Absolute value function.
⇒ sine function function
⇒ cosine function
We have to given that;
To check all the functions which are bounded below and bounded above.
Here, All the functions are,
⇒ Absolute value function.
⇒ sine function function
⇒ cosine function
⇒ Square root function
⇒ natural logarithmic function
Since, The Absolute value function is defined as;
⇒ | f (x) |
And,
⇒ | f (x) | ≤ M ; for M > 0
⇒ - M ≤ f (x) ≤ M
Hence, It is a bounded function.
Since, Sine and cosine function are defined in between 1 and - 1.
Hence, Both are bounded below by - 1 and bounded above by 1.
So, Both function are bounded.
Since, Square root function is defined as,
⇒ √ f (x) ≥ 0
Hence, It is only bounded below.
Since, When the base of the logarithm is greater than 1, log(x) approaches negative infinity as x approaches 0.
Hence, It is not bounded.
Thus, All the functions which are bounded below and bounded above are,
⇒ Absolute value function.
⇒ sine function function
⇒ cosine function
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k^2 ; k = 4
pls help
Answers
An expression is given.
16
−
14
÷
2
+
(
3
+
2
)
2
What is the value of the expression?
46
46
34
34
26
26
16
Answers
9514 1404 393
Answer:
34
Step-by-step explanation:
Maybe you want to evaluate ...
16 - 14 ÷ 2 + (3 +2)²
The parentheses are evaluated first.
16 -14÷2 +5²
Then the exponential term.
16 -14÷2 +25
The division is evaluated next.
16 -7 +25
Finally, the sum is evaluated.
= 9 +25
= 34
____
Your calculator can do this arithmetic for you.
Tables of values represent continuous functions in which table do the values represent an exponential function
Answers
is there a pic to it? put the pic then i can answer
Answer:
You forgt to add picture
Step-by-step explanation:
The Venn diagram shows the number of customers who have purchased different types of pets from a pet store, where C represents customers who have purchased cats, D represents customers who have purchased dogs, and F represents customers who have purchased fish.
Circles C, D, and F overlap. Circle C contains 15, circle D contains 21, and circle F contains 12. The overlap of C and F contains 2, the overlap of F and D contains 0, and the overlap of D and C contains 3. The overlap of all 3 circles contains 1. Number 14 is outside of the circles.
How many people are in the set C ∩ D?
4
6
36
38
Answers
The number of people in the set C ∩ D (customers who purchased both cats and dogs) is obtained by adding the overlap of D and C (3) with the overlap of all 3 circles (1), resulting in a total of 4 individuals.
The correct answer is 4.
To determine the number of people in the set C ∩ D (customers who have purchased both cats and dogs), we need to analyze the overlapping regions in the Venn diagram.
Given information:
- Circle C (cats): 15
- Circle D (dogs): 21
- Circle F (fish): 12
- Overlap of C and F: 2
- Overlap of F and D: 0
- Overlap of D and C: 3
- Overlap of all 3 circles: 1
- Number outside of circles: 14
To determine the number of people in the set C ∩ D (customers who have purchased both cats and dogs), we need to consider the overlapping region between circles C and D.
From the information given, we know that the overlap of D and C is 3. Additionally, we have the overlap of all 3 circles, which is 1. The overlap of all 3 circles includes the region where customers have purchased cats, dogs, and fish.
To calculate the number of people in the set C ∩ D, we add the overlap of D and C (3) to the overlap of all 3 circles (1). This gives us 3 + 1 = 4.
Therefore, from the options given correct one is 4.
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Answer: 4
Step-by-step explanation:
trust me bro
An airplane can cruise at 640 mph how far can it take in 3/5 of an hour
Answers
Given:
An airplane can cruise at 640 mph.
To find the distance that can be covered in 3/5 of an hour:
In 3/5 of an hour, the distance would be,
\(\begin{gathered} 1\text{ hour=640 miles} \\ \frac{3}{5}\text{hour}=640\times\frac{3}{5} \\ =128\times3 \\ =384\text{ miles} \end{gathered}\)Hence, the distance that can be covered in 3/5 of an hour is 384 miles.
Kylee manages a small theme park and she has been analyzing the attendance data. Kylee finds that the number of visitors exponentially as the tempature increases, and this situation is represented by the function f(x) = 4 ^ x Kylee also finds a linear equation that no deals the number of people who leave the park early depending on the change in temperature , and it is represented by f(x) = - x + 5. The graph of the two functions is below. Find the solution to the two functions and explain what the solution represents.
Answers
suppose you are eating slices of pizza and after consuming the first slice you receive 14 utils of total utility, after the second you receive 22 utils of total utility, and after the third 25 utils of total utility. then group of answer choices the law of diminishing marginal utility is not applicable because your total utility is increasing instead of diminishing. your total utility is 61 utils. your total utility is 25 utils, and the marginal utility of the first slice is 8 utils (22 - 14). your total utility is 25 utils, and the marginal utility of the third slice is 3 utils.
Answers
The correct answer choice is the last one, your total utility is 61 utils, and the marginal utility of the first slice is 8 utils (22 - 14).
What is marginal utility?
Marginal utility refers to the additional satisfaction or benefit that a consumer derives from consuming one more unit of a good or service. It is the change in total utility resulting from a change in the quantity consumed. It is a way to measure the additional benefit a consumer receives from consuming one more unit of a good or service.
your total utility is 61 utils, and the marginal utility of the first slice is 8 utils (22 - 14). The law of diminishing marginal utility states that as the consumption of a good or service increases, the additional satisfaction or utility from consuming one more unit of the good or service will decline. In this example, as you consume more slices of pizza, the marginal utility of each slice decreases (8 utils for the first slice, 3 utils for the third slice). This is consistent with the law of diminishing marginal utility. Therefore, choice A is incorrect.
Hence, The correct answer choice is the last one, your total utility is 61 utils, and the marginal utility of the first slice is 8 utils (22 - 14).
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Can any of the experts help me on my new question for math? PLEASE!!!
Answers
Answer:
yes I can
but wheres the question
why dont you type it in the comments
PLEASE HELP I WILL GIVE BRAINLIEST
Answers
Answer:
Do it in this order
Step-by-step explanation:
5 3 1 2 4 6
Simplify 46 - 2x) - 3(3 - 4x)
Answers
I think the answer is 10x +37.
I hope this helps!
A population consisting of an unlimited number of unit is termed as
Answers
Answer:
Infinite population
Step-by-step explanation:
Population refers to an entire set of people or objects present for the purpose of gathering data and when the population is unlimited in size i.e. it cannot be ascertained easily, it is known as infinite population.
hope it helps you a follow would be appreciated
Answer:
The answer is infinite population.
Find the shaded area. Choose the letter for the best answer.
I’m checking if I’m correct
Answers
Answer:
H. 36 sq inches
Step-by-step explanation:
area of rectangle
= 4 x 6
= 24
area of triangle
= 1/2 x (10-6) x (4+2)
= 12
total shaded area
= 24 + 12
= 36 sq inches
so answer is H
hope this helps!
For any positive integer n, the value of n! is the product of the first n positive integers. For example, 4! = 4 * 3 * 2 * 1 =24. What is the greatest common divisor of 5! and 7! ?
Answers
The GCD of 5! and 7! is 2^3 * 3^1 * 5^1 = 120.
the greatest common divisor of 5! and 7! is 120.
To find the greatest common divisor (GCD) of 5! and 7!, we need to factorize both numbers and identify the common factors.
First, let's calculate the values of 5! and 7!:
5! = 5 * 4 * 3 * 2 * 1 = 120
7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040
Now, let's factorize both numbers:
Factorizing 120:
120 = 2^3 * 3 * 5
Factorizing 5,040:
5,040 = 2^4 * 3^2 * 5 * 7
To find the GCD, we need to consider the common factors raised to the lowest power. In this case, the common factors are 2, 3, and 5. The lowest power for 2 is 3 (from 120), the lowest power for 3 is 1 (from 120), and the lowest power for 5 is 1 (from both numbers).
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The cooler at a picnic contained 4 apple juice boxes, 8 orange juice boxes, and 6 fruit punch juice boxes. A juice box is selected at random. What is the probability of the complement of choosing an orange juice box? (first answer will get brainliest)
1/18
4/9
5/9
17/18
Answers
Answer:
\( p(O)=\frac{8}{18}=\frac{4}{9}\)
And since we want the complement of choosing an orange juice box the answer would be:
\( P(O') =1 - P(O) = 1-\frac{4}{9}= \frac{5}{9}\)
And the nest answer for this case is:
5/9
Step-by-step explanation:
For this case we know that we have 4 apple juice boxes, 8 orange juice boxes, and 6 fruit punch juice boxes, so then the size of the sample space is:
\( 8+4+6= 18\)
Then we can find the probability of selecting an orange juice box with the definition of Laplace given by:
\( p =\frac{possible}{total}\)
And for this case the possible cases are 4 and the total 18 so then the probability is given by:
\( p(O)=\frac{8}{18}=\frac{4}{9}\)
And since we want the complement of choosing an orange juice box the answer would be:
\( P(O') =1 - P(O) = 1-\frac{4}{9}= \frac{5}{9}\)
And the nest answer for this case is:
5/9
A boy who is 3 feet tall can cast a shadow on the ground that is 7 feet
long. How tall is a man who can cast a shadow that is 14 feet long?
Answers
Don’t forget a brainliest if it’s correct ;)
