8y³+10y²-63y÷2y+7
give me ans quickly
Answers
Step-by-step explanation:
you can simply solve this question by simple division
Related Questions
p(1)=0.08, p(2)=0.02, p(3)=1.03
Answers
The correct statement regarding whether each set of values form a discrete probability distribution is given as follows:
p(1)=0.08, p(2)=0.02, p(3)=1.03 -> No.P(1) = 0.42, p(2) = 0.31, p(3) = 0.37 -> No.P(1) = 9/14, P(2) = 4/14, P(3) = 1/14 -> Yes.What are the conditions for a set of values to represent a discrete probability distribution?There are three conditions for a set of values to represent a discrete probability distribution, and they are given as follows:
Sum of all values is of 1.Non-negative values.No values greater than 1.Hence the sets are justified as follows:
p(1)=0.08, p(2)=0.02, p(3)=1.03 -> No, as p(3) = 1.03 > 1.P(1) = 0.42, p(2) = 0.31, p(3) = 0.37 -> No, as the sum of the probabilities is of 1.1 > 1.P(1) = 9/14, P(2) = 4/14, P(3) = 1/14 -> Yes.More can be learned about discrete probability distributions at https://brainly.com/question/27899440
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This is not a math question, but can someone please tell me how to put my questions in the high school section instead of the college one?
Answers
Answer:
it should give you the option right before you post the answer, what subjectand grade level
Step-by-step explanation:
is -2-3=-2+-3 justify your answer
Answers
Answer:
- 2 - 3 is the same thing as -2 + -3. This is because taking away 3 is the same thing as adding - 3. -2 -3 is just a more simplified version of -2 + -3.
Hope this helps!
Explanation
The sum of two negative numbers always results in a negative number. This can be explained with the Number Line Rule. To add negative numbers we move to the left on the number line.
You can also use the “+” sign as an “and” so -2 and -3 = -5
which reason justifies
Answers
(C) Alternate interior angles are congruent.
Step-by-step explanation:
Given: Lines A and B are parallel lines and C and D are transversals.
To prove: ZX + LY + 2Z = 180°
Proof:
Statement
Reason
1. Lines A and B are parallel lines;
Given
C and D are transversals
2.Alternate
interior angles
3.Alternate
interior angles
4.2X+24+26=180°
Straight line
property
5. Substitution
property
Hence proved.
Therefore, option C is correct.
When Silvia feeds her cat, she places food in
3 different locations. She wondered if her cat was equally likely to eat first from each of the locations, so she tallied which location her cat chose first in a sample of
30 feedings. Here are the results along with a chi-square goodness-of-fit test:
-------------------------kitchen-----bedroom-----Living room
Hypothesized:-----0.333--------0.333---------0.333
Observed-----------13--------------13--------------4
Expected------------10--------------10-------------10
Components-------0.9------------0.9------------3.6
chi-squared statistic = 5.4, df = 2
p-value =0.067
Assume that all conditions for inference were met.
At the 0.05 significance level, what should Silvia conclude about her cat's feeding preferences?
A: There is sufficient evidence to conclude that her cat prefers to eat first from some locations more than others.
B: There's not enough evidence to conclude that her cat prefers to eat first from some locations more than others.
C: There is sufficient evidence to conclude that her cat is equally likely to eat first from each of the locations.
D: No conclusions can be made from this test, because one of the observed counts is too low for the calculations to be accurate.
for my khan bros (ignore this part):
When Silvia feeds her cat, she places food in
3
33 different locations. She wondered if her cat was equally likely to eat first from each of the locations, so she tallied which location her cat chose first in a sample of
30
3030 feedings. Here are the results along with a chi-square goodness-of-fit test:
Location Kitchen Bedroom Living room
Hypothesized
0.333
0.3330, point, 333
0.333
0.3330, point, 333
0.333
0.3330, point, 333
Observed
13
1313
13
1313
4
44
Expected
10
1010
10
1010
10
1010
Components
0.9
0.90, point, 9
0.9
0.90, point, 9
3.6
3.63, point, 6
�
2
=
5.4
,
DF
=
2
χ
2
=5.4, DF=2\chi, squared, equals, 5, point, 4, comma, start text, space, D, F, end text, equals, 2
P-value
=
0.067
P-value=0.067start text, P, negative, v, a, l, u, e, end text, equals, 0, point, 067
Assume that all conditions for inference were met.
At the
�
=
0.05
α=0.05alpha, equals, 0, point, 05 significance level, what should Silvia conclude about her cat's feeding preferences?
Choose 1 answer:
Choose 1 answer:
Answers
B .The results of the chi-square goodness-of-fit test, with a chi-squared statistic of 5.4 and a p-value of 0.067, Silvia cannot reject the null hypothesis that her cat is equally likely to eat first from each of the three locations at the 0.05 significance level.
Therefore, the correct answer is B: There's not enough evidence to conclude that her cat prefers to eat first from some locations more than others. It is important to note that while the p-value is relatively close to the significance level of 0.05, it does not meet the threshold for statistical significance, and the sample size may not be large enough to draw definitive conclusions about the cat's feeding preferences.
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Answer: There's not enough evidence to conclude that her cat prefers to eat first from some locations more than others.
Step-by-step explanation: Since the P-value is greater than the significance level, we can't reject the null hypothesis. In this context, the null hypothesis is that cat is equally likely to choose each of the locations. (Got it right on Khan academy)
Solve. d + (-d) =
• 0
• 2d
• -2d
• d
Answers
Answer:
0
Step-by-step explanation:
When adding a negative, just get rid of the negative and subtract.
D-d=0
work shown will receive only 1 credit. nd explain your reasoning. For all questions in this part, a correct 9. In the following diagram it is given that OS is congruent to WT. Fill in the reasons below in the proof that QW is congruent to ST. (1) QS = WT (2) OW+WS (3) WS=WS (4) OW ST Statements WS+ST a whole's Sum of its part (1) Given W Reasons R (2) addition (3) Refleytive property (4) CPCTZ 2
Answers
The reasons that complete the table in the prove that the segment [tex]\overline{QW}[/tex] is congruent to [tex]\overline{ST}[/tex]can be presented as follows;
Statements [tex]{}[/tex] Reasons
(1) [tex]\overline{QS}[/tex] ≅ [tex]\overline{WT}[/tex] (1) Given
(2) [tex]\overline{QW}[/tex] + [tex]\overline{WS}[/tex] ≅ [tex]\overline{WS}[/tex] + [tex]\overline{ST}[/tex] [tex]{}[/tex] (2) Segment addition postulate
(2) [tex]\overline{WS}[/tex] ≅ [tex]\overline{WS}[/tex] [tex]{}[/tex] (3) Reflexive property of congruence
(4) [tex]\overline{QW}[/tex] ≅ [tex]\overline{ST}[/tex] [tex]{}[/tex] (4) Subtraction property of congruence
What are congruent segments?Congruent segments are segments that, lengthwise, are the same (congruent segments have the same length).
Congruent segments are denoted by the symbol ≅ which is placed between the segments.
The details of the reasons in the above prove are presented as follows;
Segment addition postulate
The segment addition postulate states that the point B is located on the segment AC if we get AC = AB + BC
Reflexive property of congruence
The reflexive property of congruence states that a geometric figure or shape is congruent to itself.
Subtraction property of congruence
The subtraction property of congruence states that the remaining segments, following the subtraction of the same lengths of segments from two segments that are congruent segments, are also congruent.
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Choose True or False for each statement.
a. The numbers 0.3 and 0.3. . . are equal to the same fraction.
b. The number 0.111000111000 . . . is a repeating decimal.
c. The fraction 1/9 is equal to a repeating decimal.
d. The fraction 2/11 is equal to 0.1818 . . . .
Answers
Answer:
a. True. Both 0.3 and 0.3... represent the decimal expansion of one-third, which is equivalent to the fraction 1/3.
b. True. The number 0.111000111000... is a repeating decimal, with a repeating block of three digits (111) that starts repeating from the fourth decimal place.
c. True. The fraction 1/9 is equal to the repeating decimal 0.1111..., where the digit 1 repeats infinitely.
d. True. To convert the fraction 2/11 to a decimal, we can perform long division. We get a repeating decimal expansion of 0.181818... where the digits 18 repeat infinitely. Therefore, the statement is true.
Step-by-step explanation:
5. Find the time in which the loan of N3,900 at the rate of 5% yields N585=
6 What time will the simple interest N70,000 at the rate of 7% be used
for a loan of N20,000.00=
7.If N300.00 amount to N390 at the rate of 3%. Find the time.=
8.The simple interest on N5600.00 in 1 year is N80.00, find the rate percent per annum=
9.What year will N5100 yield an interest of N170.00 at the rate of 2 1/2 per annum=
10.What rate per annum will N4,600 yield an interest of N230.00 for 2 years=
11. What time will N8100 yield an interest of N729 at the rate of 9% per annum=
12.Report from the bank says the interest on N2300 is N23.00 for 2 years find the rate of interest per annum.=
Answers
Therefore, the rate per annum at which N4,600 will yield an interest of N230 for 2 years is 2.5%.
What is percent?Percent is a term used to describe a fraction or ratio that represents a portion of 100. It is often represented by the symbol % and is commonly used to express a portion or a rate of change. For example, if an item is discounted by 20%, it means the price has been reduced by 20% of the original price or 20/100 of the original price. Similarly, if someone earns a grade of 85% on a test, it means they answered correctly 85 out of 100 questions.
Here,
7. To find the time (in years) in which a loan of N3,900 at the rate of 5% yields N585.60 in simple interest, we can use the formula:
I = P * r * t
where I is the interest, P is the principal, r is the interest rate, and t is the time in years.
Substituting the given values, we get:
585.60 = 3,900 * 0.05 * t
Solving for t, we get:
t = 3 years
Therefore, it will take 3 years for the loan of N3,900 at the rate of 5% to yield N585.60 in simple interest.
8. To find the time (in years) for a loan of N20,000 at the rate of 7% to accumulate N70,000 in simple interest, we can use the formula:
I = P * r * t
where I is the interest, P is the principal, r is the interest rate, and t is the time in years.
Substituting the given values, we get:
70,000 = 20,000 * 0.07 * t
Solving for t, we get:
t = 50 years
Therefore, it will take 50 years for the loan of N20,000 at the rate of 7% to accumulate N70,000 in simple interest.
9. To find the time (in years) for N300 to accumulate to N390 at the rate of 3%, we can use the formula:
I = P * r *t
where I is the interest, P is the principal, r is the interest rate, and t is the time in years.
Substituting the given values, we get:
90 = 300 * 0.03 * t
Solving for t, we get:
t = 10 years
Therefore, it will take 10 years for N300 to accumulate to N390 at the rate of 3%.
10. To find the year in which N5,100 will yield an interest of N170 at the rate of 2.5% per annum, we can use the formula:
I = P * r * t
where I is the interest, P is the principal, r is the interest rate, and t is the time in years.
Substituting the given values, we get:
170 = 5,100 * 0.025 * t
Solving for t, we get:
t = 2 years
Therefore, it will take 2 years for N5,100 to yield an interest of N170 at the rate of 2.5% per annum. If the interest is compounded, we would need to use the compound interest formula instead.
11. To find the rate per annum at which N4,600 will yield an interest of N230 for 2 years, we can use the formula:
I = P * r * t
where I is the interest, P is the principal, r is the interest rate, and t is the time in years.
Substituting the given values, we get:
230 = 4,600 * r * 2
Solving for r, we get:
r = 0.025 or 2.5%
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Laars earns an annual salary of $90,000. Determine his gross earnings per pay period under each of the following payment frequencies: a. Monthly b. Semi-monthly c. Biweekly d. Weekly
Answers
Answer:
To determine Laars' gross earnings per pay period under different payment frequencies, we need to divide his annual salary of $90,000 by the number of pay periods in a year for each frequency.
a. Monthly: Laars will receive 12 paychecks per year, one per month.
Gross earnings per pay period = $90,000 / 12 = $7,500 per month
b. Semi-monthly: Laars will receive 24 paychecks per year, two per month.
Gross earnings per pay period = $90,000 / 24 = $3,750 per semi-monthly period (twice per month)
c. Biweekly: Laars will receive 26 paychecks per year, one every two weeks.
Gross earnings per pay period = $90,000 / 26 = $3,461.54 per biweekly period (every two weeks)
d. Weekly: Laars will receive 52 paychecks per year, one per week.
Gross earnings per pay period = $90,000 / 52 = $1,730.77 per weekly period (every week)
Therefore, Laars' gross earnings per pay period are $7,500 per month, $3,750 per semi-monthly period, $3,461.54 per biweekly period, and $1,730.77 per weekly period.
on new year’s day the average temperature of the city is 5.7 degrees celsius. but for new year’s day 2012 the temperature was 9.8 degrees below the average
Answers
Answer:
-4.1
Step-by-step explanation:
5.7-9.8= -4.1
solve:
f(x)=3x^2-2x+4
x=2
Answers
Answer:
to find f(2), we need to substitute x=2 into the equation:
f(2) = 3(2)^2 - 2(2) + 4
Simplifying:
f(2) = 3(4) - 4 + 4
f(2) = 12
Therefore, f(2) = 12.
Step-by-step explanation:
Answer:
Step-by-step explanation:
[tex]f(2) = (3)(2^2) - 2(2) +4[/tex]
[tex]= 12 - 4+ 4[/tex]
[tex]= 12[/tex]
c is greater than or equal to 3
Answers
Answer:
Step-by-step explanation:
equal
For the first two years of her mortgage stress was making fixed monthly payments of 1000 per month her two year fix rate. Has just ended and now she must pay an interest rate of 6%. The amount understanding on her mortgage is 170,000 after two years and the mortgage will last for 28 years more. Calculate the increased in monthly payments that she must be now.
Answers
Answer:
The new monthly payment will be $944.16
Lin says that 4÷3/4 equals 5 1/4 because there are five groups of 3/4 and 1/4 left. Do you agree with Lin?
Answers
The result is 5 1/3, not 5 1/4 as Lin suggested.
No, I don't agree with Lin's statement. Lin's explanation is incorrect.
When evaluating the expression 4 ÷ (3/4), we need to remember the order of operations, which states that we should perform the division before the multiplication.
To divide by a fraction, we can multiply by its reciprocal. The reciprocal of 3/4 is 4/3. Therefore:
4 ÷ (3/4) = 4 * (4/3)
Now we can simplify the expression:
4 * (4/3) = (4 * 4) / 3 = 16 / 3
The result, 16/3, is an improper fraction. To convert it to a mixed number (a whole number and a fraction), we divide the numerator (16) by the denominator (3):
16 ÷ 3 = 5 with a remainder of 1
The quotient is 5, and the remainder is 1. Therefore, the result is 5 1/3, not 5 1/4 as Lin suggested.
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7. From the observation deck of a skyscraper, Matthew
measures a 45° angle of depression to a ship in the harbor
below. If the observation deck is 1053 feet high, what is
the horizontal distance from the base of the skyscraper out
to the ship? Round your answer to the nearest tenth of a
foot if necessary.
Answers
The horizontal distance from the base of the skyscraper out to the ship would be 1053 feet.
What are the trigonometric ratios?Trigonometric ratios for a right-angled triangle are from the perspective of a particular non-right angle.
In a right-angled triangle, two such angles are there which are not right angled(not of 90 degrees).
The slanted side is called the hypotenuse.
Let d the horizontal distance from the base of the skyscraper out to the ship. Since the angle of depression is 45°, hence:
[tex]\text{Angle} = 90 - 45 = 45^o[/tex]
Using trigonometric ratio:
[tex]tan(45) = \dfrac{d}{1053}[/tex]
[tex]d = 1053\ \text{feet}[/tex]
The horizontal distance from the base of the skyscraper out to the ship would be 1053 feet.
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A recipe calls for 2 cups of peanuts for 3 cups of flour. Using the same recipe, how many cups of flour will you need for 5 cups of peanuts?
Answers
2 + 2 + 1 = 5 cups of peanuts
3 + 3 + 1.5
= 7.5
Yo are going to need 7.5 cups of flour for the 5 cups of peanuts
please help me I need help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
reflection around the y-axis
Step-by-step explanation:
you really don't see that the picture just flipped from left to right and vice versa (around a central vertical mirror line through the black center dot) ?
to make it simple I just declare this line to be the y-axis.
Which equation shows the relationship between the angles in the triangle?
Answers
Step-by-step explanation:
One of the basic facts of triangles, no matter the triangle, is that all the interior angles add up to 180 degrees. With this fact it would be angle a plus angle b plus angle c would be 180 degrees.
Please help me Graph this in a line graph(economics)
The Pound to Australian Dollar (GBP/AUD) exchange rate has been going up besides the drop in UK business optimism. The CBI business optimism index dropped from 0 to -22 in the first quarter, which shows the negative impact of the recent lockdown. However, this had been changed by the idea of greater US fiscal stimulus measures and the global economic outlook improving. On the other hand, the Australian Dollar (AUD) struggled to find support despite the December unemployment rate decreasing from 6.8% to 6.6%. This shows that the labor market remains elevated by previous trends, weighing on AUD exchange rates. The retail sales trends for December is expected to show a -2.5% monthly contraction, signaling a continued impact of Covid-19. The UK PMIs could also have an impact on the GBP/AUD exchange rate, with signs of the UK economy likely to limit any potential gains.
Answers
The correct answer is interval 2. A function is a rule that relates each element in one set, called the domain, to exactly one element in another set, called the range.
What is function?It is a mathematical expression that takes an input, performs a calculation and produces an output.
In order to determine if dy/dx>0 and d2y/dx2<0 over interval 2, we must take the first and second derivatives of the function y=f(x). The first derivative of the function is dy/dx=2x-3 and the second derivative of the function is d2y/dx2=2.
Now, if we look at the graph, we can see that the function is increasing from 0 to 3 and then decreasing from 3 to 6. This means that over interval 2, which is from 3 to 6, the first derivative, dy/dx, must be negative. This means that dy/dx<0 over interval 2.
Furthermore, the second derivative, d2y/dx2, must be negative over interval 2 since the graph is decreasing over this interval. This means that d2y/dx2<0 over interval 2.
Therefore, the correct answer is interval 2 since it is the only interval for which both dy/dx>0 and d2y/dx2<0 are true.
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Which system of equations has the solution (4, -3)
A. y = -2x + 5 and x + y = 1
B. y = 2x - 5 and x - y = 1
C. y = -5x + 2 and 2x + y = 2
D. y = 5x - 2 and 2y - x = 2
Answers
Answer:
A.Y=-2x+5 and x+y=1 is the system of equation has the solution.i am sorry if iam wrong.
Trapezoid W X Y Z is rotated about point A 180 degrees clockwise to form trapezoid W prime X prime Y prime Z prime. Trapezoid W prime X prime Y prime Z prime is reflected across the line of reflection m to form trapezoid W double-prime X double-prime Y double-prime Z double-prime.
Analyze the diagram. What is the composition of transformations that was applied to map WXYZ to W''X''Y''Z''?
The first transformation was a
.
The second transformation was a
Answers
The first transformation was a rotation about point A.
The second transformation was a reflection across line M.
What is a rotation?In Mathematics, a rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
By critically observing the diagram which illustrates the sequence of transformations, we can logically deduce that the first transformation was a clockwise rotation about point A by 180 degrees.
Furthermore, the second transformation that maps W'X'Y'Z' to W''X''Y''Z'' is a reflection across the line of reflection M.
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I will mark you brainiest!
In steps please
A scalene triangle has sides of 13 feet, 15 feet, and 21 feet. Find the perimeter of the triangle.
Answers
Answer:
the perimeter of the scalene triangle is 49 feet.
Step-by-step explanation:
To find the perimeter of the scalene triangle, you simply add up the lengths of all three sides:
Perimeter = 13 feet + 15 feet + 21 feet
Perimeter = 49 feet
Therefore, the perimeter of the scalene triangle is 49 feet.
Part A
There were 600 water samples taken for an experiment using pH and iron levels. The results are shown in the table.
What are the probabilities for the listed events? Write your answers as decimals rounded to the thousandths place.
Answers
Answer:
The answer to your problem is, 0.275 0.273 0.400 and 0.300
Step-by-step explanation:
My calculation ( May not be correct )
P ( low iron or LI ) [tex]\frac{165}{600}[/tex] = 0.275
P ( low pH | LI ) = [tex]\frac{45}{165}[/tex] = 0.273
P ( low pH ) = [tex]\frac{150}{600}[/tex] = 0.400
P ( LI | Low pH ) = [tex]\frac{45}{150}[/tex] = 0.300
Thus by making these calculations the answer to your problem is, 0.275 0.273 0.400 and 0.300
*Brady has a bankruptcy on his credit report, so he pays higher interest rates on his current loans. He calculates that the extra money he pays in additional interest each year, if invested at the rate of 3% for one year, could earn him simple interest totaling $210. How much does Brady pay in additional interest each month?
Hint: Use the simple interest formula I=P*r*t where P is principal amount, r is rate, and t is time. In this case, for Brady I is the simple interest $210, P is what you are trying to find, r is the rate of 3% (make sure to convert to decimal), and t is time in years, 1 year.
After you find P, divide it by 12 and that is your answer. Round it to the nearest cent.
Answers
Brady pays an additiοnal interest οf $583.33 each mοnth.
What is the interest?Tο calculate simple interest, multiply the principal amοunt by the interest rate and the time. The fοrmula written οut is "Simple Interest = Principal x Interest Rate x Time." This equatiοn is the simplest way οf calculating interest.
Let x be the additiοnal interest Brady pays each mοnth.
Since there are 12 mοnths in a year, the tοtal additiοnal interest he pays in a year is 12x.
Accοrding tο the prοblem, if Brady invests this additiοnal interest at the rate οf 3% fοr οne year, he will earn $210 in simple interest. Using the simple interest fοrmula, we have:
I = Prt
210 = 12x0.031
Simplifying this equatiοn, we get:
210 = 0.36x
Dividing bοth sides by 0.36, we get:
x = $583.33
Therefοre, Brady pays an additiοnal interest οf $583.33 each mοnth.
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Findthe value of x using trigonometry. Round answer to the nearest tenth
Answers
Answer:
x ≈ 20.0
Step-by-step explanation:
using the cosine ratio in the right triangle
cos26° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{18}{x}[/tex] ( multiply both sides by x )
x × cos26° = 18 ( divide both sides by cos26° )
x = [tex]\frac{18}{cos26}[/tex] ≈ 20.0 ( to the nearest tenth )
What is the shape of each cut surface? What are its dimensions?
Answers
Answer:
1. The shape of each cut surface is the same shape as the base it is parallel to: a rectangle. It is an 8" by 10" rectangle
Step-by-step explanation:
PLEASE HELP!!! ASAP, THANK U
Answers
HELP ASAP PLEASE!
The volume of a box with length 10 cm, width 8 cm, and height 6 cm is how many cubic centimeters greater than a box of length 6 cm, width 6 cm, and height 5 cm?
Answers
After finding the volumes of the boxes, we found that the volume of the box with dimensions 10×8×6 cm is 300 cubic centimetres greater than the volume of the box with dimensions 6×6×5 cm.
What is meant by the volume?
Three-dimensional space is quantified by volume. Any three-dimensional solid's volume is just the amount of space it takes up. A cube, cuboid, cone, cylinder, or sphere can be one of these solids. Volumes vary depending on the shape. A solid's volume is expressed in cubic units. Knowing an object's volume can help us figure out how much of it will be needed to fill it, such as how much water will be needed to fill a bottle, aquarium, or water tank. The object's capacity is another name for it.
First box dimensions
Length l = 10 cm
Width w = 8 cm
Height h = 6 cm
The volume of box = l * w * h = 10 * 8 * 6 = 480 cm³
Second box dimensions
Length l = 6 cm
Width w = 6cm
Height h = 5 cm
The volume of box = l * w * h = 6 * 6 * 5 = 180 cm³
The difference between volumes of boxes = 480 - 180 = 300cm³
Therefore after finding the volumes of the boxes, we found that the volume of the box with dimensions 10×8×6 cm is 300 cubic centimetres greater than the volume of the box with dimensions 6×6×5 cm.
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Find X correct to 2 decimal places.
NOTE: The triangle is NOT drawn to scale.
Answers
The length of the side 'х' is 79.20 units to two decimal places.
What is angle?Angle is a two-dimensional figure that is formed by two straight lines intersecting each other. It can also be defined as the amount of rotation between two lines or planes. An angle is measured in degrees, with a full rotation being 360°.
The given triangle is a right-angled triangle as it has an angle of 64° which is a right angle. The angle 35° and 113 are the other two angles of the triangle. To find the length of the side 'х', we need to use the Pythagorean Theorem. The Pythagorean Theorem states that "the square of the hypotenuse is equal to the sum of the squares of the other two sides".
In this case, the hypotenuse is 113, and the other two sides are 'х' and the perpendicular side opposite to the angle of 35°. Therefore, using the Pythagorean Theorem, we can say:
113² = х² + (perpendicular side)²
Using the trigonometric ratio sine, we can calculate the length of the perpendicular side opposite to the angle 35°, which is equal to the sine of 35° multiplied by the hypotenuse.
(perpendicular side) = sin 35° × 113
Therefore, the equation for the triangle now becomes:
113² = х² + (sin 35° × 113)²
Simplifying the equation and solving for 'х' gives us:
х² = 113² - (sin 35° × 113)²
х = √(113² - (sin 35° × 113)²)
Finally, substituting the values, we get:
х = √(113² - (sin 35° ×113)²)
= √(12,841 - (0.5736 × 113)²)
= √(12,841 - 6,539.7808)
= √6,301.2192
= 79.20
Therefore, the length of the side 'х' is 79.20 units to two decimal places.
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