The perimeter of the decking area is 800cm.
How to determine the perimeterIt is important to note that the decking area takes the shape of a rectangle
The formula for determining the perimeter of the decking area is given as;
Perimeter = 2 multiplied by the sum of the length and width of the rectangle
It is mathematically written as;
Perimeter = 2 ( length + width)
Where;
length = 250cmwidth = 150 cmNow, let's substitute the values into the formula
Perimeter = 2 ( 150 + 250)
Sum the bracket
Perimeter = 2 ( 400 )
Perimeter = 2 × 400
Perimeter = 800 cm
Thus, the perimeter of the decking area is 800cm
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A car’s purchase for $27,000 after each year the resale value decreases by 35% what will the resale be after four years
The resale value of the car after four years is $4820
How to determine the resale value?The given parameters are:
initial value, a = $27,000
Rate, r = 35%
The value of the car each year is represented as:
Value = a *(1 - r)^t
So, we have:
Value = 27000 *(1 - 35%)^t
After four years, we have:
Value = 27000 *(1 - 35%)^4
Evaluate
Value = 4820
Hence, the resale value of the car after four years is $4820
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To fight a fire breathing dragon, a knight needs a sword made of Dragon Alloy #13, which contains 7% gold, 3% silver, and 90% magic steel. The dwarves promised to forge such a sword for the knight. At the moment, they have an alloy that contains magic steel, 21% gold, and 9% silver. How much of that alloy and how much magic steel do the dwarves have to combine to get 2.7 kg of Dragon Alloy #13?
Let [tex]x[/tex] and [tex]y[/tex] be the amounts of available alloy (AA) and pure magic steel that are used, so we also have
[tex]x + y = 2.7[/tex]
DA13 is supposed to contain 7% gold, 3% silver, and 90% steel, so that 2.7 kg of it is made up of
[tex]0.07 \times 2.7 \,\mathrm{kg} = 0.189 \,\mathrm{kg} \text{ gold}[/tex]
[tex]0.03 \times 2.7 \,\mathrm{kg} = 0.081 \,\mathrm{kg} \text{ silver}[/tex]
[tex]0.90 \times 2.7 \,\mathrm{kg} = 2.43 \,\mathrm{kg} \text{ magic steel}[/tex]
For each kg of the available alloy (AA), there is a contribution of 0.21 kg of gold, 0.09 kg of silver, and therefore 0.70 kg of steel; [tex]x[/tex] kg of it will contain [tex]0.21x[/tex] kg of gold, [tex]0.09x[/tex] kg of silver, and [tex]0.70x[/tex] kg of steel. Each kg of magic steel of course contributes 1 kg of steel; [tex]y[/tex] kg of it will contribute [tex]y[/tex] kg of steel.
Then the dwarves need
• total gold: [tex]0.21x = 0.189[/tex]
• total silver: [tex]0.09x = 0.081[/tex]
• total steel: [tex]0.70x + y = 2.43[/tex]
Solve for [tex]x[/tex] and [tex]y[/tex]. The first two equations are consistent and give [tex]x = 0.90[/tex], and substituting this into the third we find [tex]y = 1.80[/tex]. So the dwarves must combine 0.90 kg of AA and 1.80 kg of magic steel.
Identify the correct trigonometry formula to solve for x
The correct trigonometry formula to solve for x in the right angled triangle is sin(62°) = 18 / x
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
Hence:
sin(62°) = 18 / x
The correct trigonometry formula to solve for x in the right angled triangle is sin(62°) = 18 / x
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Ned and Sam are playing a game. Ned has -3 points. Sam has -8 points. How many more points does Ned have than Sam? Please provide an equation and an answer.
Answer:
5 points
Step-by-step explanation:
Subtracting their scores, we get (-3)-(-8)=5
What is the standard form equation of an ellipse that has vertices (−2,14) and (−2,−12) and co-vertices (9,1) and (−13,1)?
Answer:
[tex]\frac{(x+2)^2}{121} + \frac{(y-1)^2}{169} = 1[/tex]
Step-by-step explanation:
First, we identify that the vertices are vertical.
(an image below is attached if you want to see a visualization)
Therefore, the equation is such:
[tex]\frac{(x-h)^2}{b^2} + \frac{(y-k)^2}{a^2} = 1[/tex]
(h,k) is the center of the ellipse, which we could easily calculate by finding the midpoint between any pair of vertices.
This gets us (-2, 1)
Therefore, h = -2, k = 1
Now we want to find a,
we know the length of the major axis is 2a, and in this case, our length of the major axis is 26. So a = 13
Now we want to find b,
We know the length of the minor axis is 2b, and in this case, our length is 22, so b = 11
Now we will just plug in all the values and simplify to get our answer! B)
Olivia has made a pyramid model for her history project at school. The pyramid model has a square base. Each triangular side of the
model has a base length of 10 centimeters and a slant height of 8.9 centimeters. Olivia wants to wrap the pyramid in wrapping paper
before putting it into her school bag.
How much wrapping paper will Olivia need to cover the pyramid?
OA. 178 square centimeters
OB. 89 square centimeters
OC. 456 square centimeters
OD. 278 square centimeters
Answer:
278 square centimeters
Step-by-step explanation:
You need to use the Pythagorean Theorm. If you're pyramid is a perfect square, then to the middle the length is 5. Because 10/2 is 5. You then use the Pythagorean Theorm (a^2 + b^2 =c^2) to find the side length of the traingle. When you square the hypotenuse and subtract the bottom leg sqaured, you are left with 3.46274054 after square rooting it. (c^2-a^2=b^2) Plug these into the equation for a right, rectangluar pyramid. You then get 277.9, rounded, is 278.
Hope this helps!
Name a pair of complementary angles in this figure.
a protractor, with segment DEF along the bottom, EH point to the 55 degree on the left, EJ to 90 degrees, EK to the 30 degrees on the right
angles DEH and HEJ
angles DEH and DEJ
angles DEH and DEK
angles DEF and DEH
The answer choice which represents a pair of complementary angles in the task content is; angles DEH and DEJ.
Which pair of angles represent complementary angles?It follows from the concept of angle geometry that two or more angles are said to be complementary when the sum of their measures is 90°.
It follows from the task content therefore that since, DEJ = 90° and the sum of the measures of angles DEH and DEJ amounts to 90°.
Hence, the pair of angles are complementary.
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Ivy is running errands for her mother. She bikes along straight paths to the supermarket, the bank, and then back home.Find the distance between Ivy's house and the supermarket and the distance between the supermarket and the bank. Each distance is rounded to the nearest meter.
The distance between Ivy's house and the supermarket and the distance between the supermarket and the bank:
H&S = 1,014 M; and S&B = 854m. This is resolved using the Sine Theorem.
Notice that the Angles of a Triangle add up to 180° That is
∠A + ∠B + ∠C = 180°
Thus,
∠C = 180° - 32° - 109°
= 39°
Recall the Sine Theorem which indicates;
a/SinA = b/SinB = c/SinC
thus given that
AC = 1,523m
We have
AC/SinB = BC/SinA
BC = AC/SinB * SinA
= 1523/Sin109° * Sin32°
BC =854m
Therefore
AC/SinB = AB/SinC
Thus,
AB = AC/SinB * SinC
= 1523/Sin109° * Sin39°
AB ≈ 1,014m
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How many full cases and additional items are needed to fulfill the order? 50 8
The computation illustrate that there'll be 13 cases and 2 additional units.
How to illustrate the information?From the information given, it was stated that 80 units are needed, 6. units per case.
Therefore, the number of cases will be:
= 80/6
= 13 remainder 2.
Therefore, there'll be 13 cases and 2 additional units
Complete information
80 units are needed, 6. units per case. What is the number of cases and the number of additional units?
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The arrival times of geese to a gaggle were recorded (in seconds) and given in the stemplot below.
Stem&Leaf
What is the 12th fastest time a goose took to join the gaggle? Make sure to use labels and avoid the use of abbreviations.
The 12th fastest time a goose took to join the gaggle is 49 seconds.
What is the 12th fastest time a goose took to join the gaggle?
A Stem and Leaf Plot is a type of graph where the data is divided into a stem (the first digit or digits) and a leaf (usually the last digit).
The data in the stem plot arranged from the first fastest time it takes a goose to join the gaggle is: 13, 14, 15, 19, 19, 21, 27, 27, 28, 32, 45, 49, 49, 62, 62.
The 12th fastest time is 49
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The following statements are all incorrect. Explain the statements and the errors fully using the probability rules discussed in topic two. 1.The number 7 is a lucky number so you are more likely to win raffles with ticket number 7 than with a different number. 2.I roll two dice and add the results. The probability of getting a total of 8 is 1/12 because there are 12 different possibilities and 8 is one of them. 3.Mr. Verde has to have a major operation. Ninety-three percent of the people who have this operation make a complete recovery. There is a 93% chance that Mr. Verde will make a complete recovery if he has this operation.4.The Ramblers play the Chargers. The Ramblers can win, loose, or draw, so the probability that they win is 1/3. 5.I have flipped an unbiased coin four times and got heads. It is more likely to get tails the next time I flip it.6.Thirty random college students are asked if they study during the week. Since 60% said yes, a statement can be made that 40% of students only study on the weekend.
The probability is illustrated below.
How to illustrate the probability?1) Raffles game is a gambling competition in which people get numbered tickets and each number has an equal chance of winning.
2) When two dice are rolled then there will be totally 36 outcomes. Of those the outcomes with sum 8 are (2,6),(3,5),(4,4),(5,3),(6,2).
These are 5 in number.
So,P( sum =8)= 5/36.
3)This is a true statement.
4) Here win, lose, or tie is just the outcomes where their probabilities are different from each other and those values depend upon different situations.
5) Tossing a coin is a random experiment which means that the result of the experiment (ie head or tail) cannot be predicted.
6) If 60% said yes to " study during the week" then 40% will say yes to "either won't study or study at weekend".
7) When two coins are tossed, the outcomes are as follows
H,H
H,T
T,H
T,T.
So, P( head, tail ) =2/4 =1/2
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The reasons for each incorrect statement are as follows;
The error in the statement is that, there might be other luckier numbers compared to number 7 and hence, the statement does not hold true for all numbers.The statement is incorrect because, there are 36 different possibilities and there are 5 possibilities of getting an 8.The statement is incorrect because, 93% does not necessarily represent a 93% chance of complete recovery as this is subject to other variables.The probability that they win is not 1/3 as it is subject to what the results have been over the years and not just the possible results.Since, the coin is unbiased, it follows that upon flipping the coin for the fifth time, it is not likely to have tails the next time it is flipped.The statement is incorrect because some students study during the week and weekends, hence, the conclusion is not correct.What is Probability?The term probability put simply is the ratio of the desired outcome to the possible outcomes. It therefore follows that probability as the name implies is used to predict the chance of an occurrence.
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Describe the function over each part of its domain. State whether it is constant, increasing, or decreasing, and state the slope over each part.
The function is illustrated below based on the information.
How to describe the function?When x <= 8000
The cost remains constant at 0.35 when x increases from 0 to 8000. The slope of the cost function over this part is 0
When 8000 < x <= 20000
The cost remains constant at 0.75 when x increases from 8000 to 20000 and the slope of the cost function over this part is 0.
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would anyone be able to help me with this?
This graph has its maximum at 4. There is no minimum while the inflection is at 2, 10/3.
How to solve for the maximum of the graphWe have ( x-2²) (x-4)
x-2²) = 0, or x - 4
x - 2 = 0, x = 2
Hence we can see that the graph has its minimum at x = 4
b. The graph here does not have a local maximum
c. Next we have to find the point of inflectionTo do this you have to differentiate the equation
Use the product rule of differentiation in order to solve for the solution.
(x-2)²[ (x-4) 2 (x-2)]
This would then give us
x -2, 3x -10
In both equations we have to make x the subject of the equation
X = 2, x = 10/3
Hence the point of inflection is 2 and 10/3
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Select the statement that best describes √ 1 5
Two angles in a triangle have measures of 42 and 82. (Degrees)
What is the measure of the third angle?
Answer:
angles of the triangle are equal 180
so 42+82=124
180-124=56
so the answer is 56
Step-by-step explanation:
Geometry Question!! PLEASE HELp
The difference between the distance travelled by any point on the record and it's label is; 27.57cm.
What is the difference between the distance travelled in each case?According to the task content, it follows from observation that the quantity required is the difference between the circumference in each case and can be evaluated as follows;
Difference = π(17.78 - 9)
Difference = (22/7) × 8.78
Difference = 27.57cm.
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During an unusual storm, the temperature fell 8° C, rose 5° C, fell 4° C,
and then rose 6° C. If the temperature was 32° C at the outset of the storm,
what was it after the storm was over?
Find the integral
∫(cos(1/x)) /x^2 dx
Answer:
Step-by-step explanation:
∫(cos(1/x)/x² dx
[tex]put~\frac{1}{x} =t\\diff.\\\frac{-1}{x^2} dx=dt\\\int(- cos~t~)dt=-sin~t+c\\=-sin (\frac{1}{x} )+c[/tex]
The following table shows the cost of 4 party favor packs. For example, the Slinky costs $9 for a pack of 5. Which toy pack has a cost of $2.50 per toy
Answer:
yo-yo cost 2.50 dollar because if we divide 15 and 6 the answer will be 2.50
1 Austin has found that both(13,17) and (24,61) are solutions to a system of linear equations how are the two lines related? explain
Considering that the graphs have two intersection points, the two lines are equal.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In a graph, the solution of two linear equations is the intersection of the two lines. Hence, if there are two solutions, as is the case in this problem, the two lines are equal.
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43 POINTS!!,!,!!,!,!!
Alex went to a furniture shop to buy chairs and tables for his cafe. Find the maximum numbers of chairs he can buy if, he spent $300 for 3 tables cost of 1 chair is $30 and, he cannot spend more than $800 on the furniture.
Answer:
16 chairs
Step-by-step explanation:
800 - 300 = 500
500/30 = 16.6 since it's money you can only afford 16
Which set of ordered pairs could be generated by an exponential function?
The set of ordered pairs that could be generated by an exponential function is; C: (-1,1/2), (0, 1), (1, 2), (2, 4)
How to find the ordered pairs?An exponential function is represented by the general form;
y = abˣ
The above equation means that the value (0, 0) cannot be an ordered pair in an exponential function.
The highlight above means that, the options A, B and D cannot generate an exponential equation because they contain the point (0,0).
Thus, the set of ordered pairs that could be generated by an exponential function is option C: (-1,1/2), (0, 1), (1, 2), (2, 4)
The missing options are;
A. (-1,-1/2), (0, 0),(1,1/2), (2, 1)
B. (–1, –1), (0, 0), (1, 1), (2, 8)
C. (-1,1/2), (0, 1), (1, 2), (2, 4)
D. (–1, 1), (0, 0), (1, 1), (2, 4)
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the function f(t) = 5 cos(pi/4*t) + 11 represents the tide in dark sea. it has a maximum of 16 feet when time (t) is 0 and a minimum of 6 feet. the sea repeats this cycle every 8 hours. after six hours, how high is the tide?
The height of the tide after eight hours is 16 feet.
How to illustrate the function?From the information given, the function is given as 5cos (π/4)t + 11.
In this case, the time is given as eight hours. This will be:
f(8) = 5 × cos (π/4) × 8 + 11
f(8) = 5 × cos(2π) + 11
= (5 × 0.999) + 11
= 16 feet
The height is 16 feet.
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What is the perimeter of a yard with length = 4 x + 6 2 x + 1 feet and width = x − 3 2 x + 1 feet? 4 x − 3 4 x + 12 feet 4 x − 3 2 x + 6 feet 8 x − 6 4 x + 12 feet 8 x − 6 2 x + 6 feet
The perimeter of the given yard is P = 10x + 6
Perimeter of a rectangleThe formula for calculating the perimeter of a rectangle is expressed as:
P = 2(l + w)
where
l is the length
w is the width
Given the following parameters
length = 4x+6
width = x-3
Substitute
P = 2(4x+6+x-3)
P = 2(5x + 3)
P = 10x + 6
Hence the perimeter of the given yard is P = 10x + 6
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What is the range of the function graphed below? A bidirectional arrow rises steeply through (negative 2, negative 8), (negative 1 point 5, negative 4), (negative 1, 0), (0, 2) and extends linearly through (2, 2), (3, 2), (4, 2), (5, 2), (6, 2) and (8, 2) on the x y coordinate plane. A. B. C. D.
Answer:
A. -∞ < y < 2
Step-by-step explanation:
The range is the vertical extent of the graph.
Lower limitThe arrow pointing down tells you the graph extends toward -∞.
Upper limitThe arrow pointing right suggests that y=2 is a horizontal asymptote. A graph will approach, but never cross, an asymptote. Thus, we can conclude y < 2.
RangeThe range is the set of values that lie between the limits:
-∞ < y < 2
there are 60 minutes in one hour and 60 seconds in one minute. Using this information, explain how you could convert 20 miles per hour to feet per second
The conversion is given as 1, 760 feet per second
How to convert the valueWe need to convert 20miles per hour to feet per second
First, we should convert miles to feet
1 mile = 5280 feet
Then,
20 miles = x
Cross multiply
20 × 5280 = x
x = 105, 600
Per hour = I hour = 60 seconds
To find the conversion, we divided the conversion to feet by that of the time
= 105, 600/60
= 1, 760 feet per second
Thus, the conversion is given as 1, 760 feet per second
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can two equilateral triangles always be congrunet ? give resons
SOLUTION :
YES as well as NO , two equilateral ∆s can be congruent if any of their side matched to one another,
& CANNOT be congruent if any of their side didn't matched in terms of length (magnitude).
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solve 4/7- (-4/7)
A. 8/7
B.-8/7
C.-4/7
D.4/7
Answer:
A. 8/7
Step-by-step explanation:
Step 14/7 - (-4/7) --> 4/7 + 4/7
The two minutes turn into a plus, removing the bracket.
Step 24/7 + 4/7 = 8/7
Add the two fractions together.
Answer:
A. 8/7
Step-by-step explanation:
How large a sample should be selected to provide a 95% confidence interval with a margin of error of 6? Assume that the population standard deviation is 40 . Round your answer to next whole number.
Using the z-distribution, it is found that a sample of 171 should be selected.
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
The margin of error is:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.For this problem, the parameters are:
[tex]z = 1.96, \sigma = 40, M = 6[/tex]
Hence we solve for n to find the needed sample size.
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]6 = 1.96\frac{40}{\sqrt{n}}[/tex]
[tex]6\sqrt{n} = 40 \times 1.96[/tex]
[tex]\sqrt{n} = \frac{40 \times 1.96}{6}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{40 \times 1.96}{6}\right)^2[/tex]
n = 170.7.
Rounding up, a sample of 171 should be selected.
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someone please help me with this
Answer:
x = 60 degrees
Step-by-step explanation:
1. We know that a triangle has a total angle of 180. If we look at the image closely, triangle GEH can be found, and since we know two angles, which are 40 and 80, we can find the other angle. 180 - (40+80) = 60. Angle GEH is 60 degrees.
2. If angle GEH is 60 degrees, angle EFD will also be 60 degrees, since they have the same angle side. To prove this, we can use alternate interior angles. This means that if a line crosses two parallel lines, the inner angles made have the same size.
3. Since angle EFD is x, we can find that x is equal to 60 degrees.