[tex] \boxed{\Large {\mathcal {{{\color{orange}{Area \: of \: circle \: = \: πr²}}}}}}[/tex]
r = 7.15m[tex]\large \rm \pink{ \: Area \: of \: circle }\:\large\blue\implies \tt \large πr²\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large \rm \pink{ \: Area \: of \: circle }\:\large\blue\implies \tt \large \frac{22}{7} \: \times\:{7.15}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\\large \rm \pink{ \: Area \: of \: circle }\:\large\blue\implies \tt \large \frac{22}{7} \: \times\:51.1225 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large \rm \pink{ \: Area \: of \: circle }\:\large\blue\implies \tt \large \frac{22}{ \cancel7} \: \times\: \cancel{51.1225} \: \: ^{ \red{7.303} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large \rm \pink{ \:Area \: of \: circle }\:\large\blue\implies \tt \large {22} \: \times\:7.303 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large \rm \pink{ \: Area \: of \: circle }\:\large\blue\implies \tt \large \: 160.666 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Hence , the area of circle is 160.66 m²
Given :-
Radius of circle = 7.15mTo Find :-
Area of circleSolution :-
Area of Circle = πr²
putting the value of π and rArea = 3.14×(7.15)² m²
= 160.52465 , which rounded off to 2DP would be 160.52 m²
Solve the simultaneous equations
2
x
+
3
y
=
5
5
x
−
2
y
=
−
16
Answer:
x = -2, y = 3
Step-by-step explanation:
2x + 3y = 5
5x - 2y = -16
In order to find the value of a variable, we must eliminate the other variable by multiplying the equations to get the same coefficient.
We can multiply the first equation by 5 and the second one by 2 to get the same coefficient for x, the equations then become:
10x + 15y = 25
10x - 4y = -32
Now we can subtract:
19y = 57
y = 3
Since we know the value of y, we can substitute it into one of the original equations:
2x + 3(3) = 5
2x + 9 = 5
2x = -4
x = -2
Which is the graph of f(x) = (2)* ?
a graph
I assume you meant to type f(x)=2^x.
Which congruence theorem can be used to prove ?
Answer:
ASA
Step-by-step explanation:
by ASA congruence theorem
what is 3x+2y=6 ordered pair?
The ordered pair of the equation 3x +2y = 6 will be ( 0,3) and ( 2 , 0).
What is an equation?The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.
We have an equation 3x + 2y = 6 now the ordered pair of the equation will be found by the graph will be ( 0,3) and ( 2, 0). The graph is also attached with the answer below.
Therefore the ordered pair of the equation 3x +2y = 6 will be ( 0,3) and ( 2 , 0).
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someone please help me w this standard form question
Answer:
2.4 × 10⁶
Step-by-step explanation:
Given:
[tex]\sf x=3.8 \times 10^5[/tex][tex]\sf y=5.9 \times 10^4[/tex]To calculate the value of R, substitute the given values into the given formula:
[tex]\begin{aligned}\sf R & = \sf \dfrac{x^2}{y}\\\\ \implies \sf R& = \sf \dfrac{(3.8 \times 10^5)^2}{5.9 \times 10^4}\\\\& = \sf \dfrac{3.8^2 \times (10^5)^2}{5.9 \times 10^4}\\\\& = \sf \dfrac{14.44 \times 10^{10}}{5.9 \times 10^4}\\\\& = \sf \dfrac{14.44}{5.9} \times \dfrac{10^{10}}{10^4}\\\\& = \sf 2.4474... \times 10^{(10-4)}\\\\& = \sf 2.4474... \times 10^6\\\\\end{aligned}[/tex]
Therefore, the value of R to 1 decimal place is 2.4 × 10⁶
--------------------------------------------------------------------------
Exponent Rules used
[tex](a^b)^c=a^{bc}[/tex]
[tex]{a^b}{a^c}=a^{b-c}[/tex]
[tex]R = \frac{ {x}^{2} }{ y} \\ \\ R = \frac{ {(3.8 \times {10}^{5})}^{2} }{5.9 \times {10}^{4} } \\ \\ R = \frac{ ({3.8})^{2} \times ( { {10}^{5} )}^{2} }{5.9 \times {10}^{4} } \\ \\ R = \frac{14.44 \times {10}^{10} }{5.9 \times {10}^{4} } \\ \\ R = \frac{14.44 \times {10}^{10 - 4} }{5.9} \\ \\ R = 2.45 \times {10}^{6} [/tex]
HELP ASAP!
Consider right triangle DEF below.
The trigonometric relation is solved and the length of side DE is given by the relation DE = 3.8 ( tan 40° )
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be represented as ΔEFD
Now , the measure of side EF = 5 units
The measure of side DF = 3.8 units
And , from the trigonometric relations , we get
tan θ = opposite / adjacent
On simplifying , we get
tan 40° = DE / DF
Multiply by DF on both sides , we get
DE = 3.8 ( tan 40° )
Hence , the trigonometric relation is solved
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4. Angles A and B are supplementary. If mA = 67, find mB
Answer:
113 degrees
Step-by-step explanation:
Two angles are called supplementary when they add up to 180 degrees
[tex]180 = x + y \\ 180 = 67 + y \\ y = 180 - 67 \\ y = 113 \\ therefore \: mB \: = 113[/tex]
What is the value of y?
Enter your answer in the box.
Answer:
5
Step-by-step explanation:
As seen in the figure, we know that because ΔABC is isosceles, ∠B = ∠C, so we know that 75 = 3x, x = 15. Next, following the rule that all angles in a triangle sum to 180°, we can set up this equation and solve it:
4y + 10 + 75 + 75 = 180
4y = 180 - 160
y = 20
∴ y = 5
Can someone answer this as soon as possible.
Please help me
Find the value of x
Answer:
52=x-15(being vertically opposite angle)
52+15=x
x=67
find the size of unknown angle
Answer:
x° = 75
(x + 30)° = 105°
Step-by-step explanation:
supplementary angle is two angles that sum is 180°
x° + (x + 30)° = 180°
2x + 30 = 180°
2x + 30 - 30 = 180 - 30
2x = 150
2x / 2 = 150 / 2
x° = 75
plug in 75,
75 + 30 = 105
check: 75 + 105 = 180
Answer: 75 degrees
Step-by-step explanation:
Do you see how both sides of the angle come together to form the straight line seen at the bottom? This means that these are supplementary angles.
Supplementary Angles: Both sides have to add up to a total of 180 degrees.
With this, form an equation: x+(x+30)= 180
Get rid of the parenthesis:
x+x+30= 180
Combine like terms.
2x+30= 180
2x= 180-30
2x= 150
x= 150÷2
x= 75
Checks:
x+x+30= 180
75+75+30= 180
You can also check using the equation in its simplified form: 2x+30= 180.
2x+30=180
2(75)+30=180
150+30=180
Hence x=75
a list of 8 numbers has a mean of 6. work out the total of the numbers.
Answer:
48
Step-by-step explanation:
The mean of a number is the sum of all the numbers divided by how many numbers there are. We can set up this formula: [tex]mean = \frac{sum}{amountnumbers}[/tex].
When we plug our values into this equation, we get: [tex]6 = \frac{sum}{8}[/tex]. Solving this equation gets us sum = 6 * 8 = 48
Need help
cnnbc recently reported that the mean annual cost of auto insurance is 959 dollars. assume the standard deviation is 263 dollars, and the cost is normally distributed. you take a simple random sample of 37 auto insurance policies. round your answers to 4 decimal places.
a what is the probability that one randomly selected auto insurance is more than $984?
b. a simple random sample of 37 auto insurance policies, find the probability that the average cost is more than $984.
Using the normal distribution, the probabilities are given as follows:
a. 0.4602 = 46.02%.
b. 0.281 = 28.1%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters are given as follows:
[tex]\mu = 959, \sigma = 263, n = 37, s = \frac{263}{\sqrt{37}} = 43.24[/tex]
Item a:
The probability is one subtracted by the p-value of Z when X = 984, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{984 - 959}{263}[/tex]
Z = 0.1
Z = 0.1 has a p-value of 0.5398.
1 - 0.5398 = 0.4602.
Item b:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{984 - 959}{43.24}[/tex]
Z = 0.58
Z = 0.58 has a p-value of 0.7190.
1 - 0.719 = 0.281.
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My square patio is tiled with square tiles, all the same size. All the tiles are gray, except the tiles along the two diagonals, which are all yellow. (The corners are yellow, the center is yellow, and all the tiles along the diagonal in between are yellow.) If there are $89$ yellow tiles, how many gray tiles are there
Answer:
1936
Step-by-step explanation:
We can start by removing the center tile, because all four diagonals over lap on that tile. We'll add it back later. 88/4=22. which means there are 22 tiles per half, 44+1(the center tile) total tiles per side, which means there are a total of 1936 tiles.
AOPS ANSWER:
Suppose that we have a square with dimensions [tex]$e \times e$[/tex]. The diagonals each have [tex]$e$\\[/tex] tiles. If [tex]$e$\\[/tex] is even, the number of yellow tiles is [tex]$2e$[/tex], because the [tex]2[/tex] diagonals don't intersect. If [tex]$e$[/tex] is odd, then the number of yellow tiles is [tex]$e+e-1=2e-1$[/tex]. (We have to subtract [tex]1[/tex] because the center tile is counted [tex]2[/tex] times). We know that there are [tex]89[/tex] yellow tiles, which is an odd number, so [tex]$89=2e-1$[/tex]. This implies that [tex]$e = 45$[/tex]. So the dimensions of the floor are [tex]$45 \times 45$[/tex], or [tex]2025\\[/tex] square units. Since all of the other tiles are gray, there are [tex]$2025-89=\boxed{1936}$[/tex] gray tiles.
What remainder is represented by the synthetic division below?
A vertical line and horizontal line combine to make a L shape. There are two rows of entries within the shape. Row 1 has entries 2, 10, 1, 5. Row 2 has entries blank, negative 10, 0, negative 5. Entry negative 5 is on the outside to the left of the shape, and a third row of entries is outside and below the shape. Row 3 has entries 2, 0, 1, 0.
The remainder represented by synthetic division is -5.
What is synthetic division?
Synthetic division can be defined as a simplified way of dividing a polynomial with another polynomial equation of degree 1.
Given
A vertical line and a horizontal line combine to make an L shape.
There are two rows of entries within the shape.
Row 1 has entries 2, 10, 1, 5.
Row 2 has entries blank, -10, 0, -5.
Entry -5 is on the outside to the left of the shape. The entry represents the zero of the divisor. This entry to the variable (assume the variable is x) is;
x + 5 = 0
x = -5
Hence, the divisor of the synthetic division is -5.
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Answer:
its a) -5
Step-by-step explanation:
Select all numbers that are a solution of the inequality.
Every month a salesperson adds 7 new accounts. The algebraic expression that represents the number of new accounts that he will add in m months is _____.
The algebraic expression that represents the number of new accounts that he will add in m months is x ≥ 7m.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Every month, a salesperson adds 7 new accounts.
Let m be the number of the month and x be the number of the accounts.
Then the inequality equation will be
x ≥ 7m
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Is this pattern a net for the three-dimensional figure?
no
yes
Answer:
yes
Step-by-step explanation:
2 bases 3 rectangles, folds properly.
Determine the Angle Measures
The angles are p=67°, q=15°, x=82°, y=81°, s=28° and m=72.5°.
For the given figures we need to find the unknown angles.
In the first figure to find angle p first apply the angle sum property to the triangle.
That is, 82°+31°+p=180° (∵ Sum of interior angles of a triangle is 180°)
⇒p=67°.
p=67° is a vertically opposite angle to the other triangle.
To find q:
67°+98°+q=180°
⇒q=15°.
In the second figure to find angles x and y apply the angle sum property to the triangle.
That is, 28°+(53°+x)+17°=180°
⇒98°+x=180°
⇒x=82°.
To find y:
x+y+17°=180°
⇒82°+y+17°=180°
⇒y=81°
In the third figure to find angles x and y apply the angle sum property to the triangle.
That is, 100-x+30+4x+7x=180°
⇒10x=80°⇒x=10°.
Now the angles of the triangle are 100-10=90°, 30+4x=70°
y=90°+70°=160° (∵Exterior angle is equal to the sum of two opposite interior angles).
In the 4th figure, to find angle 's' use the isosceles triangle concept.
That is, s+76°+76°=180° (∵In isosceles triangle base angles are equal)
⇒s=28°
In the 5th figure, to find angle 'm' use the isosceles triangle concept.
That is, 35°+m+m=180° (∵In isosceles triangle base angles are equal)
⇒2m=145°
⇒m=72.5°
Hence, the angles are p=67°, q=15°, x=82°, y=81°, s=28° and m=72.5°.
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Someone help me as fast as possible!!
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: length = 11 \: \: in[/tex]
[tex]\qquad \tt \rightarrow \: width = 4 \: \: in[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Let the measures be :
width = xlength = x + 7[tex] \textsf{\large Area of rectangle :} [/tex]
[tex]\qquad \tt \rightarrow \: Area = length \sdot width [/tex]
[tex]\qquad \tt \rightarrow \: 44 = x \sdot(x + 7)[/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + 7x = 44[/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + 7x - 44 = 0[/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + 11x - 4x - 44 = 0[/tex]
[tex]\qquad \tt \rightarrow \: x(x + 11) - 4(x + 11) = 0[/tex]
[tex]\qquad \tt \rightarrow \: (x + 11)(x - 4) = 0[/tex]
possible values of x = -11 and 4
[tex] \textsf{But the acceptable value of x = 4} [/tex]
[ length or width of rectangle can't be negative ]
[tex]\qquad \tt \rightarrow \: length = x + 7 = 4 + 7 = 11 \: \: in[/tex]
[tex]\qquad \tt \rightarrow \: width = x = 4 \: \: in[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
A swimming pool is 50 metres long and 25 metres wide. How many lengths of the pool will a competitor in a 1500 metre race have to swim?
Reason:
I'm assuming that the swimmer travels along the 50 meter side
Divide 1500 over 50 to get 1500/50 = 30, which tells us that the swimmer must make 30 trips.
Find y
y
A.4
B. 4√2
C. 8
D. 2√2
X
30°
4√3
Step-by-step explanation:
z = 4√3
y = ?
Z° = 90° - 30° = 60°
Y° = 30°
• Find y.
y/sin(Y) = z/sin(Z)
y/sin(30°) = 4√3/sin(60°)
y/(1/2) = 4√3/(1/2 √3)
y . 1/2 √3 = 4√3 . 1/2
y . 1/2 √3 = 2√3
y = 2√3 . 2/√3
y = 4√3/√3
y = 4
The answer is A.
An object is moved at a constant speed of 20m/s for 4s
Answer:
80 m is distance traveled
Step-by-step explanation:
if object moves at 20m/s, then in 4 seconds the expression 20 x 4 is used to get 80. 80 m traveled
Convert 203 yards into meters.
Hint: 1 yard=0.91 meters
203 yards=[blank]−−−−−− meters
Enter your answer as a number that correctly fills in the blank.
Round the answer to two decimal places, like this: 45.53
Answer:
184.73
Step-by-step explanation:
1 yard = 0.91m
203 yard=?
(203x0.91)/1=184.73.
+1(415) 450-6164
find the arc length of a sector with a radius of 4 feet and a central angle of 6°
Answer:
24 ft.
Step-by-step explanation:
Radius = 4 ft
Central angle = 6°
Arc length = radius × central angle
= 4 × 6°
= 24 ft.
Find all solutions to the equation x3 + 100x + 8x2 = –800. –10, –8, 10 –10, 8, 10 8, –10i, 10i –8, –10i, 10i
All the solution of the equation x³ + 8x² + 100x + 800 = 0 will be 10i, -10i, and -8. Then the correct option is D.
What is a factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The equation is given below.
x³ + 8x² + 100x = -800
x³ + 8x² + 100x + 800 = 0
Then the factor of the equation will be
x³ + 8x² + 100x + 800 = 0
x² (x + 8) + 100(x + 8) = 0
(x² + 100)(x + 8) = 0
Then all the solution of the equation will be
x = 10i, -10i, and -8.
Then the correct option is D.
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Answer:
d
Step-by-step explanation:
The largest bubblegum bubble ever blown was 23 inches in diameter. What was its circumference?.
Answer:
[tex]C=23\pi[/tex] inches
or as a decimal
72.26 inches
Step-by-step explanation:
Formula for circumference: [tex]C=2\pi r[/tex]
Radius = [tex]\frac{d}{2}[/tex]
Altogether we get: [tex]C=2*\pi*\frac{d}{2}[/tex]
Which simplifies to: [tex]C=\pi d[/tex]
So now we can plug in 23 for [tex]d[/tex].
[tex]C=\pi*23[/tex]
Our final answer is:
[tex]C=23\pi[/tex] inches
or as a decimal
72.26 inches
Mr. Hann is trying to decide how many new copies of a book to order for his students. Each book weighs 6 ounces.
The equation will be given as y = 6x for the given information in the question.
The complete question is as below:-
Mr Hann is trying to decide how many new copies of a book to order for his students. Each book weighs 6 ounces Which ordered pair is a viable solution if x represents the number of books he orders and y represents the total weight of the books, in ounces?
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Here we are given that the weight of each book is 6 ounces. If there are x number of books, the weight of x books will be 6 times x.
And if y represents the total weight, we can form an equation describing the relation between a number of books and their net weight. The equation can be
y = 6x
Hence all the ordered pairs satisfying the above equation will represent the number of books and the total weight.
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Tara has a box of 908 beads for making bracelets. She wants to put 15 beads on each bracelet she makes. What is the greatest number of bracelets Tara can make with these beads? Tara has a box of 908 beads for making bracelets . She wants to put 15 beads on each bracelet she makes . What is the greatest number of bracelets Tara can make with these beads ?
Answer:
Tara can make 60 bracelets.
Step-by-step explanation:
908 / 15 = 60.5
decrease 2155.45 by 18.5 round 2dp
The solution is 1756.69
What is number system?A number system is defined as a system of writing to express numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner.
We have to find the 18.5% of 2155.45.
So,
2155.45 * 0.185 = 398.75825
Now, subtract
21.55.45 - 398.75825
= 1756.69175
Hence, the value is 1756.69
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help please fast grade 5 math help extra points to thooese who explain marking brainliest