The area of the deck is 413 square feet
How to determine the area of the proposed deck?Start by calculating the area of the outer rectangle using:
Area = Length * Width
This gives
Area1 = (18 + 12) * (16 + 8)
Area1 = 720
Next, calculate the area of the inner rectangle using:
Area = Length * Width
This gives
Area2 = 16 * (18 + 8)
Area2 = 416
Subtract these areas
A1 = Area1 - Area2
A1 = 720 - 416
A1 = 304
Next, calculate the area of the outer semicircle using:
Area = 0.5πR²
This gives
Area1 = 0.5 * 3 * (12-1)²
Area1 = 181.5
Next, calculate the area of the inner semicircle using:
Area = 0.5πr²
This gives
Area2 = 0.5 * 3 * (7)²
Area2 = 73.5
Subtract these areas
A2 = Area1 - Area2
A2 = 181.5 - 73.5
A2 = 108
Add A1 and A2
A = 304 + 108
Evaluate the sum
A = 412
Hence, the area of the deck is 413 square feet
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Please help, math question below...
The value of x is 3.711 yd
What is Heron's Formula?area = √(s * (s - a) * (s - b) * (s - c))
where
s is the semi perimeter - half of triangle perimeter:
s = (a + b + c) / 2
Using Heron's Formula
area = √(s * (s - a) * (s - b) * (s - c))
area = √(14* (15- 6) * (15 - 14) * (15 - 10))
area = √(14* 9 * 1 * 5))
area = √ 630
area = 25.981 yd²
Now,
area of triangle= 1/2 * b * h
25.981 = 1/2 * 14 *h
51.962 = 14h
h= 3.711 yd
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Solve Triangle DEF. - Math
Answer:
[tex]p = 52.942259755149776[/tex]
Step-by-step explanation:
This is basic trigonometry.
[tex] \cos(39) = \frac{e}{22} [/tex]
[tex]e = \cos(39) \times 22[/tex]
[tex] \sin(39) = \frac{d}{22} [/tex]
[tex]d = \sin(39) \times 22[/tex]
And finally perimeter (p):
[tex]p = 22 + e+ d[/tex]
Dilate the figure by the scale factor. Then enter
the new coordinates.
(-3,-1)
A
(-1,-4) C
B(2,-2)
K = 5
A' ([?], [ ])
B' ([ ], [])
C' ([ ], [ ]) (pls help I will mark BRAINLIEST)
The triangle ABC was dilated with a scale factor of 5 to form a figure with new coordinates at A'(-15, -5), B'(10, -10) and C'(-5, -20).
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
The triangle ABC was dilated with a scale factor of 5 to form a figure with new coordinates at A'(-15, -5), B'(10, -10) and C'(-5, -20).
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These two figures shown are congruent. Which statement is true?
Answer:
The answer is C
Step-by-step explanation:
First if you look at the problem you will notice the triangles aren't the same size so if it's neither rotation nor translation then the shapes do not
there are 400 beads of the same size. 35% are red. 2/5 of the remaining are blue. the rest are white. what fraction are there white beads?
Answer:
84/400
Step-by-step explanation:
First, divide 35 by 100 to get the decimal, 0.35. Then, multiply 0.35 x 400. You should get 140. Now the question says 2/5 of the remaining are blue. You need to multiply 2/5 x 140 to get 56. 56 are blue. So now subtract 56 from 140 to get 84. The answer (not in simplest form) is 84/400.
how to solve this pleaseee
Answer:
if you divide 10 by 8 it should be 10/8 so a
Hope This Helps!!!
Answer: A
Step-by-step explanation: Step 3 is incorrect as it should be 10/8 (or 5/4 simplified.) When we have 8x = 10, we are looking at what number "x" multiplied by 8 gives 10. Meaning we need to have 8(?) = 10. So, to find out what x is, we just divide by 8 from both sides. Since 8x/8 cancels out and becomes just x, we get x = 10/8 since we are dividing 10 by 8. We get 5/4 simplified or 10/8 unsimplified.
Please mark my answer as brainliest if it was helpful!
What is the slope and y-intercept of the equation represented by the following graph
Answer: C slope= 1/2 y-intercept =2
Step-by-step explanation:
Find x.
special 17
A. 22
B. 113√2
C. 116√2
D. 33
The value of x in the triangle is (a) 22
How to solve for x?The complete question is in the attached image.
From the attached image of the triangle, we have:
[tex]\sin(45) = \frac{x}{22\sqrt 2}[/tex]
Evaluate sin(45)
[tex]\frac{1}{\sqrt 2} = \frac{x}{22\sqrt 2}[/tex]
Solve for x
[tex]x = \frac{22\sqrt 2}{\sqrt 2}[/tex]
Divide
x = 22
Hence, the value of x is (a) 22
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help me please ty ty
Answer:
A
Step-by-step explanation:
(f - g)(x)
= f(x) - g(x)
= 3x² + 4x - 6 - (6x³ - 5x² - 2) ← distribute parenthesis by - 1
= 3x² + 4x - 6 - 6x³ + 5x² + 2 ← collect like terms
= - 6x³ + 8x² + 4x - 4
Friar laurence: these violent delights have violent ends, and in their triumph die, like fire and powder, which, as they kiss consume: the sweetest honey is loathsome in his own deliciousness and in the taste confounds the appetite: therefore love moderately; long love doth so; too swift arrives as tardy as too slow. what do the oxymoron and paradox in this excerpt illustrate about love? only love has the ability to overcome obstacles. nothing good ever comes from truly loving another. loving with restraint is the key to long-lasting love. true love causes one to lose the ability to reason
Seriousness is what is being portrayed by the oxymoron and paradox in this excerpt.
Simply put, a serious relationship is one in which you are fully committed to your partner. You are completely open and honest with each other. You trust each other deeply. And you are on the same page together not only from your values and ethics perspective, but also from your future perspective.
Monks do not claim that "moderate" love is more wise than fleeting love, but they guide Romeo to understand the reason for his wisdom and explore their relationship.
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Find the value of x.
A) 71
B) 72
C) 73
D) 75
Answer:
The answer is c) 73
Step-by-step explanation:
The angle 146 and (-39 + x) lie on the same line, so that means their sum is 180 degrees because a straight line has 180 degrees.
180 = 149 - 39 + x
180 = 107 + x
180 - 107 = x
73 = x
Answer:
73
Step-by-step explanation:
The two angles form a straight line and a straight line is 180 degrees
-39+x + 146 = 180
Combine like terms
107 +x = 180
Subtract 107 from each side
107+x-107 = 180-107
x =73
A ladder is 7 feet 6 inches tall. How tall is it in inches?
Answer:
90 inches tall
Step-by-step explanation:
7x12=84
84+6=90
A normal score is the expected z-score of a data value, assuming the distribution of the random variable is normal. Is this statement true or false?.
The given statement about normal score that it is expected z score of a data value is true.
Given A statement that a normal z score is the expected z score of a data value, assuming the distribution of the random variable is normal.
We have to tell whether the given statement is true or false.
In z test the z score or standard score is the number of standard deviations by which the value of a raw score is above or below the mean value of what is observed or measured.
A normal distribution is arrangement of a data set in which most values cluster in the middle of the range and the rest taper off symmetrically toward either extreme.
A random variable is a variable which is identified without following any criteria.
A Z test is any statistical test for which the distribution of the test statistic under the null hypothesis ca be approximated by a normal distribution.
Hence the given statement about normal score is absolutely true.
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how to reduce this 25/35 please please help explain !!!!!!
Answer:
5/7
Step-by-step explanation:
Note that the highest common factor to the numbers are 5. Therefore, to simplify will be:
= 25/35
= 5/7
Draw a graph of the line that contains the given point and
(-3,0); m =
1
8
Answer:
Step-by-step explanation:
A ticket costs £656
Last year it cost £640
What percentage increase is this ?
Answer:
2.5%
Step-by-step explanation:
656 / 640 = 1.025
1.025 into percent is 102.5%
102.5% - 100% = 2.5
640 + 2.5% of 640 = 656
BOOM
The required value of increase in price is 2.5%.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
A percentage can be converted into a fraction or a decimal by dividing it by 100.
Given that,
The cost of ticket at present is £656.
Its cost last year was £640.
Then, the difference between the costs is given as,
656 - 640 = £16
Now, the increase in percentage can be found by taking the ratio of the difference to the last year price and multiplying it by 100 as below,
Percentage increase = 16/640 × 100%
= 2.5%
Hence, the percentage increase in price is 2.5%.
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what is the probability that a positive integer less than 100 picked at random has all distinct digits
the probability that a positive integer less than 100 picked at random has all distinct digits is 90.
He has 99 positive integers less than 100.
The integers that do not have all distinct digits have the same digit twice.
11, 22, 33, 44, 55, 66, 77, 88, 99
There are 9 integers that do not have distinct digits, therefore there are 99-9 integers that do.
Probability is without a doubt how probable something is to show up. whenever we are uncertain about the final results of an occasion, we can talk about the possibilities of sure outcomes and how probable they are. The analysis of events governed by opportunity is referred to as records.
A chain of moves in which the results are usually unsure. The tossing of a coin, selecting a card from a deck of playing cards, throwing a cube. occasion. it is a single final results of an experiment. Getting a Heads whilst tossing a coin is an event.
Simple probability is the calculation of an outcome or the chance of an event ever taking place. coverage companies use possibility statistics to determine the possibilities of having to pay out a declare. A simple chance is calculated by way of dividing a particular outcome through all of the feasible outcomes.
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The term at position n in a sequence is 3n
Work out the 4th term in this sequence.
(Hint: the 4th term is when n = 4)
Answer:
12
Step-by-step explanation:
3(4)=12
The 4th term of the sequence is 12.
What is Sequence?A grouping of numbers in a specific order is known as a sequence. On the other hand, a series is described as the accumulation of a sequence's constituent parts.
In the sequence 1, 3, 5, 7, 9, …, 1 is the first term, 3 is the second term, 5 is the third term, and so on.
Given:
sequence, S(n): 3n
Now, to find the 4th term of sequence we have to put n= 4.
So, the term of sequence
S(4) = 3(4)
s(4) = 12
Hence, the 4th term is 12.
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Expand and combine like terms. (5a^3 - 2)(5a^3+2)
Answer:
[tex]25a^6-4[/tex]
Step-by-step explanation:
So if you look at the equation, you'll notice it's being multiplied by it's conjugate which can be expressed as: x+a and x-a. See how only the sign changes? Well if remember the differences of squares, it looks like that, because it is. Essentially the difference of squares says that: [tex]a^2-b^2=(a-b)(a+b)[/tex]. So expanding this out will result in [tex](5a^3)^2-(2)^2[/tex] which simplifies to: [tex]25a^6-4[/tex]. If you're confused on how I got 25a^6. Try to think of a^3 as three a's rather than simply an exponent. and since it has a coefficient of 5. 5a^3 is the same as (5 * a * a * a). Now if you square this you have (5 * a * a * a) * (5 * a * a * a). So if you group like terms you'll end up with 6 a's being multiplied by each other (which can be expressed as a^6) and 5 * 5 which is 25.
The multiplication can be transformed into the difference of squares using the rule:(a−b)(a+b)=a²-b² . Gets the square of 2.
(5a³)²-4
Expand (5a³)².
5² (a³)² -4
To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.
5²a⁶-4
25a⁶-4 ====> Answer
{ Pisces04 }
URGENT: statistics: A researcher wishes to estimate the percentage of adults who support abolishing the penny what size sample should be obtained if he wishes the estimate to be within three percentage points with a 95% confidence if he:
A: uses a previous estimate of 26%?
B: he does not use any prior estimates?
Using the margin of error for the z-distribution, the sample sizes are given as follows:
a) 822.
b) 1068.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.We have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
Item a:
The estimate is of [tex]\pi = 0.26[/tex], hence we solve for n when M = 0.03.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.26(0.74)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.26(0.74)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.26(0.74)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.26(0.74)}}{0.03}\right)^2[/tex]
n = 821.2
A sample of 822 is needed.
Item b:
No prior estimate, hence [tex]\pi = 0.5[/tex].
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.5(0.5)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.03}\right)^2[/tex]
n = 1067.11
A sample of 1068 is needed.
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The ratio of vina's age to jill is 7:6.if vina is 4 years older than jill,how old is jill
jill is 24 years old.
What is ratio ?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls).The ratio of vina's age to jill is 7:6 .
Let vina's age =7x
let jill's age = 6x
If vina is 4 years older than jill.
Then , 7x - 6x = 4
x = 4
Now vina's age = 7x = 7 * 4 = 28 years
jill's age = 6x = 6 * 4 = 24 years.
Therefore, jill is 24years old.
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For f(x) = x^2 and g(x) = x^2 + 2, find the following composite functions and state the domain of each
Answer:
[tex]composite \: function \: is \: given \: as \: in \: two \: forms \\ \\ f(g(x))and \: g(f(x)) \: therefore \: f(g(x)) =( x {}^{2} ) {}^{2} + 2 \\ whereas \: g(f(x)) = (x {}^{2} + 2) {}^{2} \\ domain of \: f(x) = x {}^{2} is( \infty - \infty ) \: and \: domain \: of \: g(x) = x {}^{2} + 2 \: is \: also \: ( \infty - \infty )[/tex]
An English teacher has equal numbers of fiction, literature, and poetry books.
Each day, she randomly selects one book to read from. She designs a
simulation to estimate the probability that the next three books she selects
are all literature.
Which simulation design could she use to estimate the probability?
The simulation design regarding the probability is:
Let 1, 3 = fiction.
Let 2, 4 = non fiction.
Let 5,6 = poetry
What is a simulation design?It should be noted that a simulation design us used to make a particular prediction.
In this case, a number cube can be used to estimate the probability.
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Samuel bought presents for 40 cents, 50 cents, 60 cents, and 70 cents. How much money did he spend in all?
Answer:
$2.20
Step-by-step explanation:
100 cents= $1
70+60= 130. Move the decimal to the left twice to get $1.30.
50+40= 90 cents
90+30= $1.20+ the 1 dollar from before and you get $2.20
Answer: 220
Step-by-step explanation:
40+50+60+70= 220
Because the questions says in all we have to add it all together.
I don’t know how to start to go about this. Any suggestions would be greatly appreciated. How do I go about finding X?
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:x = 7° [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Since the two triangles are congruent, their corresponding sides and angles should be equal to one another too.
That means : Angle ADB = Angle CDB.
[tex]\large \textsf{Solve for x } [/tex]
[tex]\qquad \tt \rightarrow \:7x = 49 \degree[/tex]
[tex]\qquad \tt \rightarrow \:x = \cfrac{ 49 \degree}{7}[/tex]
[tex]\qquad \tt \rightarrow \:x = { 7 \degree}{}[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
You keep track of the daily hot chocolate sales and the outside temperature each day. The data you gathered is shown in the data table below.
Hot Chocolate Sales and Outside Temperatures
Sales ($) $100 $213 $830 $679 $209 $189 $1,110 $456 $422 $235 $199
Temperature (°F) 92° 88° 54° 62° 85° 16° 52° 65° 68° 89° 91°
how would you describe the correlation in the data? Explain your reasoning
Answer:
There is a negative correlation.
Step-by-step explanation:
The point on the scatter plot are downwards sloping. This implies that there is a negative relationship between the variables temperature and sales. Thus, there is a negative correlation.
The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary Prove that the height of the tower is 6 m.
Kindly help!
Answer:
Proof explained below
Step-by-step explanation:
Tan trigonometric ratio
[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleDraw a diagram to help visualize the scenario (see attached).
If the angles are complementary, their sum is 90°.
Therefore, let one of the angles be [tex]x[/tex] and the other angle be [tex]90^{\circ}-x[/tex].
Use the tan trig ratio to create two equations with the missing side length.
Right triangle ACD
Given:
[tex]\theta = x[/tex]O = CD (tower)A = 9 mSubstituting the given values into the tan trig ratio:
[tex]\implies \tan (x)= \dfrac{\textsf{CD}}{9}[/tex]
Right triangle BCD
Given:
[tex]\theta = 90^{\circ} - x[/tex]O = CD (tower)A = 4 mSubstituting the given values into the tan trig ratio:
[tex]\implies \tan (90^{\circ} - x)= \dfrac{\textsf{CD}}{4}[/tex]
[tex]\textsf{As }\:\tan(90^{\circ} - x)= \cot (x):[/tex]
[tex]\implies \cot(x)= \dfrac{\textsf{CD}}{4}[/tex]
[tex]\implies \dfrac{1}{\tan(x)}= \dfrac{\textsf{CD}}{4}[/tex]
[tex]\implies \tan(x)= \dfrac{4}{\textsf{CD}}[/tex]
Therefore, the two equations are:
[tex]\textsf{Equation 1}: \quad \tan (x)= \dfrac{\textsf{CD}}{9}[/tex]
[tex]\textsf{Equation 2}: \quad \tan(x)= \dfrac{4}{\textsf{CD}}[/tex]
Substitute one equation into the other and solve for CD:
[tex]\implies \sf \dfrac{CD}{9}=\dfrac{4}{CD}[/tex]
[tex]\implies \sf CD \cdot CD= 4 \cdot 9[/tex]
[tex]\implies \sf CD^2=36[/tex]
[tex]\implies \sf CD=\sqrt{36}[/tex]
[tex]\implies \sf CD= \pm 6[/tex]
As distance cannot be negative, CD = 6 m only, thus proving that the height of the tower is 6 m.
Please help! If Paul's average speed is 5 km per hour, how long would it take Paul to walk 6.25 km?
a.)
An hour and 30 minutes
b.)
An hour and 15 minutes
c.)
An hour and 10 minutes
d.)
An hour and 25 minutes
Write the equation of the line that passes through the points (-9,-9)(−9,−9) and (6,-7)(6,−7). Put your answer in fully simplified form, unless it is a vertical or horizontal line.
2x-15y = 117 is the simplified form of the equation.
Equation : In a mathematical sentence, if two expressions are present in left and right side of an equal sign, then the mathematical sentence is called an equation.
If, a, b, c be integers and x is x-intercept & y is y-intercept, then ax+by=c is called equation of line.
Given that, the equation of the line that passes through the points (-9,-9)(−9,−9) and (6,-7)(6,−7).
Now, (-9,-9) & (6, -7) have a line through them with slope = (-9+7)/(-9-6) = 2/15
Therefore, (y+7) = 2/15×(x-6)
⇒ y+7 = 2x/15 - 4/5
⇒ y = 2x/15 - 4/5 - 7
⇒ y = 2x/15 -39/5
This is the equation in slope intercept form.
Multiplying the equation with 15, we get,
⇒ 15y = 2x-117
⇒ 2x-15y = 117 , which is the simplified form of the equation.
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slope of [3,5] and [0,11]
\[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{What is the formula for finding slope?}[/tex]
[tex]\mathbf{\dfrac{y_2 - y_1}{x_2 - x_1} = slope}[/tex]
[tex]\huge\textbf{Often people understand it better by:}[/tex]
[tex]\mathbf{\dfrac{rise}{run} = slope}[/tex]
[tex]\huge\textbf{Answering the given question:}[/tex]
[tex]\mathbf{y_2 \rightarrow 11}\\\\\\\mathbf{y_1 \rightarrow 5}\\\\\\\mathbf{x_2 \rightarrow 0}\\\\\\\mathbf{x_1 \rightarrow 3}[/tex]
[tex]\huge\textbf{Now, that we have that information out}\\\huge\textbf{the way, we can answer the question.}[/tex]
[tex]\huge\textbf{Your equation should look like this:}[/tex]
[tex]\mathbf{\dfrac{11 - 5}{0 - 3} = slope}[/tex]
[tex]\huge\textbf{Solving for the answer:}[/tex]
[tex]\mathbf{\dfrac{11 - 5}{0 - 3} = slope}[/tex]
[tex]\mathbf{\rightarrow \dfrac{6}{-3} = slope}[/tex]
[tex]\mathbf{\rightarrow 6 \div -3 = slope}[/tex]
[tex]\mathbf{\rightarrow -2}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\textsf{S}\frak{lope \rightarrow -2}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]