To Prove :
[tex] \sf \dfrac{\cos9\degree + \sin9\degree }{\cos9\degree- \sin9\degree} = \tan54\degree \\ \\ [/tex]
[tex] \sf LHS = \dfrac{\cos9\degree + \sin9\degree }{\cos9\degree- \sin9\degree} \\ \\ [/tex]
[tex] \sf RHS = \tan54\degree \\ \\ [/tex]
Solving for LHS :
Divide numerator and denominator by cos9°
[tex]\longrightarrow \: \: \sf\dfrac { \dfrac{ \cos9\degree}{ \cos9\degree} + { \dfrac{\sin9}{ \cos9} }}{ \dfrac{ \cos9\degree }{ \cos9\degree} - { \dfrac{ \sin9\degree}{ \cos9\degree}}} \\ \\ [/tex]
[tex] \longrightarrow \: \: \sf\dfrac{1 + { \dfrac {\sin9\degree}{ \cos9\degree}} }{1 - { \dfrac{ \sin9\degree}{ \cos9\degree} }} \\ \\ [/tex]
[tex]\longrightarrow \: \: \sf \dfrac{1 + \tan9\degree}{1 - \tan9\degree} \\ \\ [/tex]
[tex]\longrightarrow \: \: \sf{ \dfrac{ \tan45 \degree + \tan9\degree}{1 - \tan45 \degree \tan9 \degree}} \: \: \: \: \: \: \: \sf \red{\bigg( \tan(A + B) = \dfrac{ \tan A + \tan B}{1 - \tan A \tan B} \bigg)} \\ \\ [/tex]
[tex]\longrightarrow \: \: \sf \tan(45\degree + 9\degree) \\ \\ [/tex]
[tex]\longrightarrow \: \: \sf \tan54 \degree[/tex]
LHS = RHS
Hence, proved!!DUE TODAY HELP!!!!!!
5. Write the (x, y) coordinates for P in terms of cosine and sin.
6. Using the image above, if cos(Θ) = 0.6, what are the coordinates of P? Explain your reasoning.
the coordinates of P on the given diagram is (0.6, -0.8).
The Pythagoras Theorem: What is it?the Pythagoras theorem is defined as, the square of the hypotenuse of a right-angled triangle equals the sum of the squares of the other two sides.
The formula for the Pythagoras theorem is written as c² = a² + b², where c is the hypotenuse of the right triangle and a and b are its other two legs. As a result, the Pythagoras equation may be used to any triangle that has one angle that is exactly 90 degrees to create a Pythagoras triangle.
Using the Pythagoras trigonometric identity to determine sine based on cos(Θ) = 0.6
Sin²Θ+Cos²Θ=1
SIn²Θ=1-Cos²(0.6)
Sin²Θ=1-.36
SinΘ=-0.8
Since , CosΘ=0.6 and SinΘ=-0.8 the location of point P is (0.6, -0.8)
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The answer of the given question based on the Compound interest the answer is option a) Rounding to 2 decimal places gives D ≈ 824.50, so the closest option provided is a) 825. Therefore, the number that goes in box D is approximately 824.50, rounded to 2 decimal places.
What is Principal?In compound interest, term "principal" refers to the initial amount of money that is invested or borrowed. The principal is starting point for calculating interest that will be earned or paid over time.
When you invest money at compound interest rate, interest earned is added to principal amount, and resulting sum becomes new principal for next interest calculation.
Based on the information provided in the image, we can calculate the value in box D by multiplying the values in boxes B and C and then dividing by 100:
D = (B × C) ÷ 100
D = (850 × 97) ÷ 100
D = 824.5
Rounding to 2 decimal places gives D ≈ 824.50, so the closest option provided is a) 825. Therefore, the number that goes in box D is approximately 824.50, rounded to 2 decimal places.
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Total equity after adding the simple interest in the amount will be $825.
What is simple interest?
Simple interest is a type of interest that is calculated only on the principal amount of a loan or investment, without taking into account any interest that may have accumulated in previous periods.
In simple interest, the amount of interest earned or owed is calculated as a percentage of the principal amount, multiplied by the time period for which the interest is being calculated.
simple interest is found using
I = P * r * t
Where I is the amount of interest earned or owed, P is the principal amount, r is the annual interest rate as a decimal, and t is the time period in years.
Now,
Assuming that the return rate of 10% is a simple annual interest rate, the total equity after one year can be calculated using the formula for simple interest:
Total equity = Principal + Interest
where the interest is calculated as:
Interest = Principal x Rate x Time
In this case, the principal is $750, the rate is 10%, and the time is one year.
Then,
Interest = $750 x 0.10 x 1 = $75
Therefore, the total equity after one year would be:
Total equity = $750 + $75 = $825
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. cards are dealt from a standard shuffled deck of cards until the first ace is drawn. what is the chance that the next card is a king?
Cards are dealt from a standard shuffled deck of cards until the first ace is drawn. So the chance that the next card is a king is 0.05 percent.
When drawing a card from a standard deck of 52 cards, the chance of drawing an ace is 4/52 or 1/13. After an ace has been drawn, there are 51 cards left in the deck, and 4 of them are kings.
So, the probability of drawing an ace and then a king is
(1/13) × (4/51) = 4/663.
There are 4 different aces that could be drawn, each with the same probability of
(1/13) × (4/51) = 4/663,
So we multiply by 4 to account for all the possible aces that could be drawn.
Therefore, the total probability of drawing an ace and then a king is
(4/663) × 4 = 16/663.
Once an ace has been drawn, there are 51 cards remaining in the deck, and only one of them is a king. Therefore, the probability of drawing a king after an ace has been drawn is 1/51.
The probability that the next card is a king after the first ace is drawn is thus:
(16/663) × (1/51) = 16/33663
= 1/2104.
This simplifies to 0.0475 percent or approximately 0.05 percent.
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the fifth term of the sequence is 5 and the sixth term is 2.5. What is the 2nd term?
Answer:
Let's denote the first term of the sequence as a, and the common difference between consecutive terms as d.
Then, we know that the fifth term is 5, so:
a + 4d = 5
Similarly, we know that the sixth term is 2.5, so:
a + 5d = 2.5
We can solve this system of equations by subtracting the first equation from the second:
(a + 5d) - (a + 4d) = 2.5 - 5
d = -2.5
Now, we can substitute this value of d into either equation to find the value of a:
a + 4d = 5
a + 4(-2.5) = 5
a - 10 = 5
a = 15
Therefore, the first term of the sequence is 15, and the common difference is -2.5. We can use this to find the value of the second term:
a + d = 15 + (-2.5) = 12.5
Therefore, the second term of the sequence is 12.5.
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Christine's regular bedroom has a perimeter of 44 feet. The length of her bedroom is 2 more than the width. What are the dimensions of her room?
Answer:
12 feet by 10 feet
Step-by-step explanation:
Let length = x + 2 and breadth = x
[tex]2(x+2+x)=44[/tex]
[tex]2(2x+2)=44[/tex]
[tex]2x+2= 44\div2[/tex]
[tex]2x=22-2[/tex]
[tex]2x=20[/tex]
[tex]x=20\div2= 10 \ \text{feet}[/tex]
Thus, breadth = 10 feet
length = 10 + 2 = 12 feet
The radius of a circle is 3 meters. What is the circle's area?
Use 3.14 for л.
Submit
square meters
Answer:
28.26 meters squared
Step-by-step explanation:
Answer:
28.26 m²
Step-by-step explanation:
The equation for the area of a circle is πr²
We're given the radius at 3 meters.
Using 3.14 for π ; 3.14×3²=28.26 meters²
Find the missing dimension of the triangle
Area= 14 ft squared
Height=6 ft
the missing dimension of the triangle is the base, which has a length of 21 feet. To find the missing dimension of the triangle, we will use the formula for the area of a triangle, which is:
Area = 1/2 x base x height
We know that the area of the triangle is 14 ft squared and the height is 6 ft. We can substitute these values into the formula and solve for the base:
14 = 1/2 x base x 6
Multiplying both sides by 2/6 (or simplifying to 1/3) gives:
14 x 3/2 = base
21 = base
Therefore, the missing dimension of the triangle is the base, which has a length of 21 feet.
This means that the triangle has a height of 6 feet and a base of 21 feet, and its area is 14 square feet. The height of a triangle is the perpendicular distance from the base to the opposite vertex, and in this case, it is given as 6 feet. The base of a triangle is the side opposite the height, and we have found that it has a length of 21 feet.
In summary, we can find the missing dimension of a triangle by using the formula for the area of a triangle and the given dimensions. In this case, we found that the missing dimension is the base, which has a length of 21 feet, and we know that the height is 6 feet.
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find the probability of choosing a letter other than the letter s from a bag that contains the eighteen letters of the name srinivasa ramanujan. express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
The probability of choosing letter other than 's' from srinivasa ramanujan is 0.888889 ( nearest millionth)
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur.
Probability = sample space / total outcome
For example if a fair die is rolled, the total outcome is 6, because a die has 6 faces. The probability of getting 1 = 1/6
Similarly, The number of times s appeared in the name is 2. This means sample space is 2. The total outcome is 18.
The probability of picking letter 's' out of the name is 2/18 = 1/9 = 0.111111
Therefore the probability of picking letter other than 's' is 1-0.111111 = 0.888889( nearest millionth)
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The probability of choosing a letter other than s in the name srinivasa ramanujan is 0.89
Calculating the probability of choosing a letter other than sThe name "srinivasa ramanujan" contains 2 instances of the letter "s" and a total of 18 letters.
So, the bag contains 16 letters that are not "s".
Therefore, the probability of choosing a letter other than "s" from the bag is:
16/18 = 8/9
So the probability of choosing a letter other than "s" is 8/9, which is already in its lowest terms.
Alternatively, as a decimal rounded, it is 0.89.
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question jenna flipped a coin 36 times, and it landed on tails 17 times. shay flipped a coin 22 times, and it landed on heads 12 times. based on these experiments, which event is more likely to occur: shay's coin landing on heads or jenna's coin landing on tails? responses
It is more likely for Jenna's coin to land on tails than for Shay's coin to land on heads. This can be solved by concept of Probability.
To determine the likelihood of each event, we need to calculate the probabilities of the outcomes. For Jenna's coin, the probability of landing on tails can be calculated as 17 tails out of 36 flips, which is approximately 0.47 or 47%.
For Shay's coin, the probability of landing on heads can be calculated as 12 heads out of 22 flips, which is approximately 0.55 or 55%.
Therefore, the probability of Shay's coin landing on heads is higher than Jenna's coin landing on tails. However, the question asks which event is more likely to occur, which means we need to compare the probabilities of the opposite outcomes.
For Jenna's coin, the probability of landing on heads is 19 out of 36, which is approximately 0.53 or 53%. For Shay's coin, the probability of landing on tails is 10 out of 22, which is approximately 0.45 or 45%.
Since the probability of Jenna's coin landing on heads is closer to 50% than Shay's coin landing on tails, we can conclude that it is more likely for Jenna's coin to land on tails than for Shay's coin to land on heads.
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The volume of the cone shown is 240 cubic meters. The height of the cone is 5 meters. Find the length of the slant height, x.
Answer:
9.4 meters
Step-by-step explanation:
We can use the formula for the volume of a cone:
V = (1/3) * pi * r^2 *h
where V is the volume, r is the radius of the base, and h is the height.
We know the volume and height of the cone, so we can solve for the radius:
240 = (1/3) * pi * r^2 * 5
r^2 = 240 / (pi * 5/3)
r^2 = 45.68
r = sqrt(45.68)
r = 6.76 meters (rounded to two decimal places)
Now we can use the Pythagorean theorem to find the slant height:
x^2 = r^2 + h^2
x^2 = 6.76^2 + 5^2
x^2 = 88.5276
x = sqrt(88.5276)
x = 9.4 meters
i need help with homework
Answer:
(a) To find the mean value, we sum up all the values and divide by the number of values:
Mean = (17 + 22 + 25 + 27 + 32 + 40 + 45 + 51 + 59 + 62) / 10 = 36.0
So, the mean value is 36.0.
To find the median value, we first need to put the data set in order from smallest to largest:
17, 22, 25, 27, 32, 40, 45, 51, 59, 62
The median is the middle value of the data set, which is 36 in this case.
So, the median value is 36.0.
(b) To find the mean absolute deviation (MAD), we first need to find the deviation of each value from the mean:
|17 - 36.0| = 19.0
|22 - 36.0| = 14.0
|25 - 36.0| = 11.0
|27 - 36.0| = 9.0
|32 - 36.0| = 4.0
|40 - 36.0| = 4.0
|45 - 36.0| = 9.0
|51 - 36.0| = 15.0
|59 - 36.0| = 23.0
|62 - 36.0| = 26.0
Next, we find the mean of these deviations:
MAD = (19.0 + 14.0 + 11.0 + 9.0 + 4.0 + 4.0 + 9.0 + 15.0 + 23.0 + 26.0) / 10
MAD = 13.0
So, the mean absolute deviation for this data set is 13.0.
(c) To find the percentage of the data set that lies closer than the MAD to the mean, we count how many values are within one MAD of the mean. We have:
17, 22, 25, 27, 32, 40, 45, 51, 59, 62
The values within one MAD of the mean (36.0 +/- 13.0) are:
17, 22, 25, 27, 32, 40, 45, 51
So, 8 out of 10 values are within one MAD of the mean.
The percentage of the data set that lies closer than the MAD to the mean is:
8 / 10 * 100% = 80%
(a) To find the mean value, we sum up all the values and divide by the number of values:
Mean = (7 + 7 + 7 + 8 + 8 + 9 + 10 + 32) / 8 = 9.5
So, the mean value is 9.5.
To find the mean absolute deviation (MAD), we first need to find the deviation of each value from the mean:
|7 - 9.5| = 2.5
|7 - 9.5| = 2.5
|7 - 9.5| = 2.5
|8 - 9.5| = 1.5
|8 - 9.5| = 1.5
|9 - 9.5| = 0.5
|10 - 9.5| = 0.5
|32 - 9.5| = 22.
out of 230 racers who started the marathon, 211 completed the race, 12 gave up, and 7 were disqualified. what percentage did not complete the marathon? round your answer to the nearest tenth of a percent.
the percentage of racers who did not complete the marathon is 8.3% when rounded to the nearest tenth of a percent.
To find the percentage of racers who did not complete the marathon, we need to divide the number of racers who did not complete by the total number of racers and then multiply by 100 to get a percentage.
Number of racers who did not complete = 12 + 7 = 19
Total number of racers = 230
Percentage of racers who did not complete = (19/230) x 100% = 8.3%
Therefore, the percentage of racers who did not complete the marathon is 8.3% when rounded to the nearest tenth of a percent.
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Help me pls, i need the process too!
Answer:
D
Step-by-step explanation:
to find the percent discount we should do the follow things:
1) (40-32)/40=0.2=20%
2) (30-24)/30=0.2=20%
3) (50-40)/50=0.2=20%
4) (45-35)/45=0.2222
So the correct answer is D.
Elias calculated the discount in dollars, not in %. 3) 50$-40$=10$, 45$-35$=10$. But he made a mistake
Ella, Danila, and Sophia are competing in an eating contest. Their
probabilities of winning the contest are as follows:
P(Ella wins) = 0.75
P(Danila wins) = 5%
1
P(Sophia wins)
5
Put the following events in order from least to most likely.
Ella wins Sophia wins Danila wins
Answer:
The probabilities are listed as:
P(Ella wins) = 0.75
P(Danila wins) = 5% or 0.05
P(Sophia wins) = 1/5 or 0.2
To determine the order of least to most likely events:
- The probability of Danila winning is the lowest at just 5%. Therefore, Danila winning is the least likely event.
- The probability of Sophia winning (0.2) is greater than Danila's probability of winning (0.05). Hence, Sophia winning is more likely than Danila winning.
- Finally, Ella has the highest probability of winning (0.75) among all three contestants. So, Ella winning is the most likely event.
Therefore, the order of least to most likely events is: Danila wins, Sophia wins, Ella wins.
Answer: Danila, Sophia then Ella
Step-by-step explanation: I took quiz on Khan
does anyone know the answer for 3/7 of 1/5
Answer:
To find the answer, you need to multiply the fractions 3/7 and 1/5 together:
3/7 * 1/5 = (31) / (75) = 3/35
Therefore, the answer to 3/7 of 1/5 is 3/35.
Answer:
The word "of" in math means to multiply.
3/7*1/5= 3/35
Step-by-step explanation:
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Use a calculator to find M Angle B to the nearest 10th.
Answer:
60.3°
Step-by-step explanation:
You want the measure of angle B in right triangle ABC with leg BC = 8 and leg AC = 14.
TangentThe tangent relation is ...
Tan = Opposite/Adjacent
Applying this to the given triangle, we have ...
tan(B) = 14/8
The arctangent function gives you the angle from the tangent.
B = arctan(14/8) ≈ 60.3°
The measure of angle B is about 60.3°.
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If t represents an odd integer , which of the following expressions represents an even integer ?
A) t + 2
B) 2t - 1
C) 3t - 2
D) 3t + 2
E) 5t + 1
Answer: A) t + 2
Step-by-step explanation:
If t represents an odd integer, then it can be written as t = 2k + 1 for some integer k.
A) t + 2 = (2k + 1) + 2 = 2k + 3 = 2(k + 1) + 1, which is an odd integer.
B) 2t - 1 = 2(2k + 1) - 1 = 4k + 1, which is an odd integer.
C) 3t - 2 = 3(2k + 1) - 2 = 6k + 1, which is an odd integer.
D) 3t + 2 = 3(2k + 1) + 2 = 6k + 5 = 2(3k + 2) + 1, which is an odd integer.
E) 5t + 1 = 5(2k + 1) + 1 = 10k + 6 + 1 = 2(5k + 3) + 1, which is an odd integer.
Therefore, the only expression that represents an even integer is option A) t + 2.
Determine the equation of the circle graphed below.
Answer:
The center of the circle is at (0, 3), and the radius of the circle is 2.
So the equation of the circle is
[tex] {x}^{2} + {(y - 3)}^{2} = {2}^{2} [/tex]
[tex] {x}^{2} + {(y - 3)}^{2} = 4[/tex]
Which table represents the function y =1/3 x + 4?
Input x 0 -3 -6
Output y 4 3 2
Input x 6 9 12
Output y 6 9 12
Input x 0 3 6
Output y 4 6 8
Input x 3 6 9
Output y 5 7 9
The table that represents the function y =1/3 x + 4 is the second table. This can be seen by comparing the input and output values of the given tables.
What is function?A function defines the relationship between two variables, wherein one variable depends on the other. In other words, a function is a rule or mapping from one set of values, known as the domain, to another set of values, known as the range.
The table that represents the function y =1/3 x + 4 is the second table. This can be seen by comparing the input and output values of the given tables.
The second table's input values are (6, 9, 12) and the output values are (6, 9, 12). This is equal to the equation y = 1/3 x + 4, where 1/3 x + 4 = x.
The other tables do not represent the function y = 1/3 x + 4. For example, the first table has input values of (0, -3, -6) and output values of (4, 3, 2), which do not match the equation y = 1/3 x + 4.
The third table has input values of (0, 3, 6) and output values of (4, 6, 8), which also do not match the equation y = 1/3 x + 4.
Finally, the fourth table has input values of (3, 6, 9) and output values of (5, 7, 9). This does not match the equation y = 1/3 x + 4 either.
Therefore, the table that represents the function y =1/3 x + 4 is the second table.
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using the applet, how many standard deviations above and below the mean do the quartiles of any normal distribution lie? use the closest available values (the applet can't hit every value exactly).
Normal distribution, the quartiles lie at roughly 0.675 standard deviations below the mean and 0.675 standard deviations above the mean, which corresponds to 25% and 75% of the data, respectively.
To determine the number of standard deviations above and below the mean that the quartiles of any normal distribution lie, use the closest available values (the applet cannot hit every value exactly).
The quartiles of a normal distribution are separated by 1.5 IQR, where IQR is the interquartile range. In a standard normal distribution, the interquartile range spans from approximately -0.675 to 0.675, which corresponds to roughly 0.675 standard deviations above and below the mean.
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Como expresar
[tex]\frac{20*19*18}{4*3*2*1}[/tex]
:>
Based on the information, we can infer that the whole number equivalent to this fraction is 285.
How to isolate the fraction to get a whole number?To clear the fraction and obtain an integer we must perform all the mathematical operations that are in the fraction, in this case it is a division and seven multiplications. Here we show you the result:
20*19*18/4*3*2*16,840 / 4*3*2*16,840 / 24285As evidenced in the procedure, the multiplications were cleared and later the fraction was divided. In this case the result would be the integer 285.
Note: This question is incomplete. Here is the complete information:
How to express this fraction in whole numbers?
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Phillip left his house and bicycled down a trail at a rate of 12 kilometers per hour. He planned to ride his bicycle to the end of the trail, which is 28 kilometers long, and then return to his house. Christine started from Phillip’s house 20 minutes later and caught up to Phillip just as he reached the end of the trail. How fast was Christine traveling?
Answer: 14.0kph
Step-by-step explanation:
The shaded area in the decimal grid below represents the amount of money that Karla has. She plans on dividing the money evenly between her three younger brothers. Her brothers are planning to spend the money on pieces of candy that cost $0.10 each.
What will be the maximum number of pieces of candy that each brother can buy?
(The large square of the grid represents $1.00 and each small square represents $0.01.)
Karla's three brothers can buy a maximum of 4 pieces of candy if they divide the money evenly.
What is division?
Division is a mathematical operation that involves splitting a quantity into equal parts or groups. It is one of the four basic arithmetic operations, along with addition, subtraction, and multiplication. Division is denoted by the symbol "÷" or "/", and it is usually expressed as a fraction or a quotient.
To solve this problem, we need to determine the amount of money represented by the shaded region. Here are the steps:
Count the number of small squares in the grid. For example, if the grid has 10 rows and 10 columns, there are 100 small squares in total.Determine the value of each small square. For example, if the large square of the grid represents $1.00, each small square represents $0.01.Multiply the number of shaded cells by the value of each small square to find the total amount of money represented by the shaded region.Assuming that each small square represents $0.01 and there are 143 shaded cells, the total amount of money represented by the shaded region is:
143 cells x $0.01/cell = $1.43
Now, we need to divide $1.43 evenly among Karla's three brothers to find the maximum number of pieces of candy each brother can buy.
$1.43 ÷ 3 = $0.476666...
Since we cannot buy fractional pieces of candy, we need to round down to the nearest whole number. Therefore, each of Karla's three brothers can buy a maximum of:
$0.47 ÷ $0.10/piece = 4 pieces of candy
So each of Karla's three brothers can buy a maximum of 4 pieces of candy if they divide the money evenly.
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Write a multiplication equation to show an equivalent fraction of 15 using fifteenths.
Answer:2/30
Step-by-step explanation:
1/15*1/15=2/30
The government published the following stem-and-leaf plot showing the number of sloths at each major zoo in the country: pls answer fast if you can :)
For a government published the above stem-and-leaf plot related to number of sloths at each major zoo in the country. The smallest of sloths at any one zoo was three.
A stem-and-leaf plot is a tool for presenting quantitative data in a graphical format, like as histogram for visualizing the shape of a distribution.
It is a special table where each data value is broken into a stem and a leaf. A "stem" is the first digit or digits and a "leaf" usually the last digit. For example, a value of 16, 1 is the stem that present in left of the vertical line and 6 is the leaf that present on right. On a stem and leaf plot, the minimum is the first value and the maximum is the last value.We have a stem-and-leaf plot present above and which showing the number of sloths at each major zoo in the country is published by government. Now, see the above plot carefully, thee smallest number in the stem-and-leaf plot is 03. We can get that by looking at the first stem value and the first leaf value. Hence, required number is 3.
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Complete question:
The government published the above stem-and-leaf plot showing the number of sloths at each major zoo in the country:pls answer fast if you can :
what was the smallest number of sloths at any one zoo?
Given a line with the equation: 4x + 4y = 4.
1) Write the equation of a line that is parallel to this line.
2) Write the equation of a line that is perpendicular to this line.
3) Write the equation of a line that is neither parallel nor perpendicular to this line.
An equation of a line that is parallel to this line is y = -x + 3.
An equation of a line that is perpendicular to this line is y = x + 3.
An equation of a line that is neither parallel nor perpendicular to this line is y = 3x + 3.
How to write the required equations?Based on the information provided about this line, an equation that models it is given by:
4x + 4y = 4.
4y = -4x + 4
y = -x + 1
In Geometry, two (2) lines are parallel under the following conditions:
m₁ = m₂ ⇒ -1 = -1
Slope (m) = -1
Therefore, the required equation is y = -x + 3
In Mathematics, a condition that must be met for two lines to be perpendicular is given by:
m₁ × m₂ = -1
-1 × m₂ = -1
m₂ = 1
Slope, m₂ = 1
Therefore, the required equation is y = x + 3
By using a line with a different slope other than 1 and -1 would produce a line that is neither parallel nor perpendicular to the given line.
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Recall that the length a spring stretches varies directly with the amount of weight attached to it. A certain spring stretches 5cm when a 10 gram weight is attached. A) Write a direct variation equation relating the weight x and the amount of stretch y. B) Estimate the stretch of the spring when it has a 42 gram weight attached
the direct variation equation relating weight x and stretch y is: y = 0.5x , we can estimate that the spring will stretch 21cm when a 42 gram weight is attached.
A) We can use the given information to write a direct variation equation as follows:
y = kx
where y represents the amount of stretch of the spring, x represents the weight attached to the spring, and k is the constant of variation.
Using the given information, we know that when a 10 gram weight is attached, the spring stretches 5cm. Therefore:
5 = k(10)
Solving for k, we get:
k = 0.5
So the direct variation equation relating weight x and stretch y is:
y = 0.5x
B) To estimate the amount of stretch when a 42 gram weight is attached, we can use the direct variation equation we just derived:
y = 0.5x
Substituting x = 42, we get:
y = 0.5(42)
y = 21
Therefore, we can estimate that the spring will stretch 21cm when a 42 gram weight is attached.
It's important to note that this is an estimate, and there may be other factors that could affect the actual amount of stretch, such as the quality and condition of the spring. Additionally, the direct variation equation assumes that the spring behaves in a perfectly linear manner, which may not always be the case in reality. However, for simple applications like this, the direct variation equation can provide a useful estimate of the relationship between weight and stretch.
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What measurement is closest to the area of the largest circle in square centimeters? 6cm 12 cm
Answer:
The area of a circle is given by the formula A = πr², where r is the radius of the circle.
If we have two circles with radii of 6 cm and 12 cm, respectively, their areas are:
A1 = π(6 cm)² ≈ 113.1 cm²
A2 = π(12 cm)² ≈ 452.4 cm²
Therefore, the area of the largest circle is closest to 452.4 square centimeters, which corresponds to the circle with radius 12 cm.
if a random sample of size 555 is selected, what is the probability that the proportion of persons with a retirement account will differ from the population proportion by less than 5% ? round your answer to four decimal places.
The probability that the proportion of persons with a retirement account in a random sample of size 555 differs from the population proportion by less than 5% is approximately 0.8327.
We need to make some assumptions about the population proportion of persons with a retirement account and the standard deviation of the sampling distribution of sample proportions. Let's assume that the population proportion is p = 0.5 (i.e., half of the population has a retirement account) and that the standard deviation of the sampling distribution is given by:
σ = sqrt((p*(1-p))/n)
where n is the sample size.
Substituting the values given in the question, we have:
σ = sqrt((0.5*(1-0.5))/555) = 0.0258
To find the probability that the sample proportion differs from the population proportion by less than 5%, we need to find the probability that the absolute difference between the sample proportion and the population proportion is less than 0.05. This can be written as:
P(|p_hat - p| < 0.05)
where p_hat is the sample proportion.
We can standardize this expression by subtracting the population proportion from both sides and dividing by the standard deviation:
P(|p_hat - p|/σ < 0.05/σ)
P(-0.97 < Z < 0.97)
where Z is a standard normal variable. We can find this probability using a standard normal table or a calculator:
P(-0.97 < Z < 0.97) = 0.8327
Rounding to four decimal places, we have:
P(|p_hat - p| < 0.05) = 0.8327
Therefore, the probability that the proportion of persons with a retirement account in a random sample of size 555 differs from the population proportion by less than 5% is approximately 0.8327.
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5. Challenge Problem
The largest pizza that is sold commercially is available
from Paul Revere's Pizza Company. The pizza has
a 4-foot diameter and costs about $100.00.
a. What is the circumference of the pizza?
b. If the pizza was sliced by cutting eight diameters
with a pizza cutter, how may slices would be created?
I'm a pizza with pizzaz!
c. Sliced according to B (above), what is the measurement
of the outside edge of each of the slices?
d. Sliced according to B (above) what is the cost per slice?
Each slice has an exterior edge that measurement roughly 0.6981 feet in length. Hence, the price per slice is around $11.11.
What does measurement and example mean?
Comparison of a parameter with a predetermined reference value is the process called measurement. For instance, when a measurement is represented as 10 kg, kg is the accepted unit of mass and 10 represents the physical quantity's size. Make correction suggestions.
The formula for calculating the arc length of the a sector, which is as follows, may be used to get the measurement of each slice's outer edge:
arc length is equal to (angle/360) x 2r.
when r is the pizza's radius, which is equal to its diameter. When we replace r with 2 feet & angle with 40 degrees, i get:
arc length is (40/360) x 2 x 2 feet, which is rounded to 0.6981 feet with 4 decimal places.
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