The shape of the population can be disregarded when working with sampling distribution of sample mean.
The correct option is Option D)
What is central limit theorem?
The central limit theorem in probability theory proves that, even if independent random variables are not normally distributed in themselves, in many cases, when they are added together, their correctly normalized sum tends toward a normal distribution.
As in the central limit theorem mean and standard deviation is given but there is not mention of shape of the distribution.
Hence shape of the distribution is not taken into considerations.
Therefore, The shape of the population can be disregarded when working with sampling distribution of sample mean.
The correct option is Option D)
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Question 4
The graph of f(x) is shown below.
What is the value of f(-3)?
(1) 6
2) 2
(3)-2
(4) -4
The value of the function instance, f (-3) as required to be determined according to the graph of f (x) as in the attached image is; -4.
What is the value of the function instance; f (-3)?It follows from the task content that the value of the function instance; f (-3) is to be determined according to the attached graph.
By observation; when a vertical line; x = -3 is drawn; it follows that the line passes through and intersects the lines; y = -1 and y = -4.
However, there's an open circle at; y = -1 which indicates that; -1 is not in the range of f (x).
Ultimately, the value of the function instance; f (-3) as required to be determined is; Choice 4; -4.
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What is 35 percent of 80? = 28 - Percentage Calculator
The percentage of 35 percent of 80 is 28
Percentage:
In mathematics, a percentage (from Latin: per centum, "by a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number (pure number); it has no unit of measurement.
For example, 45% (read as "forty-five per cent") is equal to the fraction
45/100, the ratio 45:55 (or 45:100 when comparing to the total rather than the other portion), or 0.45. Percentages are often used to express a proportionate part of a total.
The percentage of 35 percent of 80 is
= [tex]\frac{35}{100}[/tex]× 80
=28
The percentage of 35 percent of 80 is 28
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Match each number on the left with the correct description of the number on the right.
Answer options on the right may be used more than once.
-10
This is an integer.
This is a rational number, but not an integer.
This is an irrational number.
√5
-5.6
31/
π
The numbers are matched to description as follows
-10 This is an integer
31/π This is an irrational number
√5 This is an irrational number
-5.6 This is a rational number, but not an integer
What is an integer?An integer are whole numbers both positive and negative
hence -10 is an integer
What are rational numbers?A rational number is one that has the form p/q, where p and q are both integers and q is not zero
Rational function means that the equation will be a fraction
-5.6 can be written as a fraction and the decimals can be terminated
Irrational numbers are made up of repeating decimals
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in a particular game, a fair die is tossed. if the number of spots showing is either 4 or 5 you win $1, if the number of spots showing is 6 you win $4, and if the number of spots showing is 1, 2, or 3 you win nothing. let x be the amount that you win. use scenario 6-2. which of the following is the standard deviation of x?
The standard deviation of X is $2.00.
Probability is the likelihood that a specific occurrence will occur. Probabilities can be written as proportions with a 0 to 1 or 0% to 100% range.
Let X be the amount one wins. If the die is 4 or 5, the amount one wins is $1. If the die is 6, the amount one wins is $4. If the die is 1, 2, or 3, the amount is $0. Then, the probability of winning from 1 to 6 is 1/6.
The value of the expected mean (μ) is,
[tex]\begin{aligned}\mu&=\sum X P(X)\\&=1\times \frac{1}{6}+1\times \frac{1}{6}+4\times \frac{1}{6}+0\times\frac{1}{6}+0\times\frac{1}{6}+0\times\frac{1}{6}\\&=\frac{6}{6}\\&=1\end{aligned}[/tex]
Therefore, the standard deviation (σ)is [tex]\begin{aligned}\sigma&=\frac{\sum(X-\mu^2)}{n}\\&=\frac{(1-1)^2+(1-1)^2+(4-1)^2+(0-1)^2+(0-1)^2+(0-1)^2}{6}\\&=\frac{12}{6}\\&=2\end{aligned}[/tex]
The answer is $2. The correct option is option E.
The complete question is -
In a particular game, a fair die is tossed. If the number of spots showing is either 4 or 5 you win $1, if the number of spots showing is 6 you win $4, and if the number of spots showing is 1, 2, or 3 you win nothing. Let X be the amount that you win. Use Scenario 6-2. Which of the following is the standard deviation of X? A. $1.00 B. $1.35 C. $1.41 D. $1.78 E. $2.00
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Please Help!!
It's urgent somebody
2) Write a word problem using the information from the given equation and inequality. Be sure to include all seven parts and an appropriate question requesting a solution for the unknown (variable).
The seven parts of a one-variable equation are as follows:
1 – correct variable term for the left side expression
2 – correct constant term for the left side expression
3 – correct operation between the terms of the left side expression
4 – correct equal sign or inequality symbol
5 – correct variable term for the right side expression
6 – correct constant term for the right side expression
7 – correct operation between the terms of the right side expression
Inequality: 58x+170>42x+320
The solution for the variable is that the variable should be greater than 9.375
How to write a word problem using an inequality?An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g 2x > 4
Given: the inequality 58x+170 > 42x+320. The unknown variable is x
In word problem, we can write:
When a variable x is multiplied by 58 and then 170 is added. The result is greater than variable x multiplied by 42 with 320 added
Solution for the unknown
58x+170 > 42x+320
58x-42x > 320-170
16x > 150
x > 150/16
x > 9.375
Thus, the solution for the unknown is that the unknown should be greater than 9.375
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certain kind of sheet metal has, on average, 4 defects per 13 square feet. Assuming a Poisson distribution, find the probability that a 14 square foot metal sheet has at least 5 defects.
Using Poisson distribution to calculate the probability distribution of the event, the probability is 0.2084
What is Probability DistributionProbability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 indicates an impossibility and 1 indicates a certainty.
A probability distribution is a mathematical function that describes the likelihood of a random variable taking on a particular value or set of values. It is used to describe the behavior of random variables, either discrete (e.g. coin flips) or continuous (e.g. temperatures), and is often used in the field of statistics to predict the behavior of a system or process.
Using Poisson distribution;
P(X ≥ 5) = 1 - P(X ≤ 4)
P= 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4))
P= 1 - (e^(-4.615) + (4.615*e^(-4.615))/1! + (4.615^2*e^(-4.615))/2! + (4.615^3*e^(-4.615))/3! + (4.615^4*e^(-4.615))/4!)
P = 0.2084
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suppose annual salaries for sales associates from a particular store have a mean of $32,500 and a standard deviation of $2,500
. a. Calculate and interpret the z-score for a sales associate who makes $36,000.
b. Use Chebyshev's theorem to calculate the percentage of sales associates with salaries between $26,250 and $38,750
. c. Suppose that the distribution of annual salaries for sales associates at this store is bell-shaped. Use the empirical rule to calculate the percentage of sales associates with salaries between $27,500 and $37,500.
d. Use the empirical rule to determine the percentage of sales associates with salaries less than $27,500. e. Still suppose that the distribution of annual salaries for sales associates at this store is bell-shaped. A sales associate makes $42,000. Should this salary be considered an outlier? Explain.
a) The z-score for a sales associate who makes $36,000 is 1.4
b) The percentage of sales associates with salaries between $26,250 and $38,750 is 84%
c) The percentage of sales associates with salaries between $27,500 and $37,500 is 95.4%
d) The percentage of sales associates with salaries less than $27,500 is 2.3%
e) Yes, the salary of $42000 should be considered as outlier.
Given,
Mean, [tex]\mu[/tex]=32500
Standard deviation, [tex]\sigma[/tex]=2500
a)
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{36000-32500}{2500}=1.40[/tex]
The sales associate who makes 36000 is 1.4 standard deviation above the mean salary.
b)
As per chebyshev's theorem, [tex](1-\frac{1}{k^2})[/tex] of the observations fall within k standard deviation of the mean, i.e. within [tex]\mu\pm k\sigma[/tex]
[tex]z_1=\frac{x_1-\mu}{\sigma}\\\\z_1=\frac{26250-32500}{2500}=-2.50\\\\z_2=\frac{x_2-\mu}{\sigma}\\\\z_2=\frac{38750-32500}{2500}=2.50[/tex]
Hence, we need to find proportion of observations within [tex]\mu\pm2.5\sigma[/tex]
k=2.5
[tex](1-\frac{1}{k^2})=1-\frac{1}{2.5^2}=0.84=84\%[/tex]
Hence, 84% of sales associates have salaries between 26250 and 38750.
c)
As per empirical rule for a bell shaped distribution:
68.3% of the observations fall within 1 standard deviation of the mean i.e. within [tex]\mu\pm 1\sigma[/tex]95.4% of the observations fall within 2 standard deviation of the mean i.e. within [tex]\mu\pm 2\sigma[/tex]99.7% of the observations fall within 3 standard deviation of the mean i.e. within [tex]\mu\pm 3\sigma[/tex][tex]z_1=\frac{x_1-\mu}{\sigma}\\\\z_1=\frac{27500-32500}{2500}=-2\\\\z_2=\frac{x_2-\mu}{\sigma}\\\\z_2=\frac{37500-32500}{2500}=2[/tex]
Hence, we need to find the proportion of observations within \mu \pm 2\sigma
As per empirical rule, 95.4% of the observations fall within 2 standard deviation of the mean .i.e within [tex]\mu \pm 2\simga[/tex] .Therefore, percentage of sales associates with salaries between 27500 and 37500=95.4%
d)
[tex]z_1=\frac{x_1-\mu}{\sigma}\\\\z_1=\frac{27500-32500}{2500}=-2[/tex]
Percentage of sales associates with salaries less than 27500 will be equal to the area under the normal curve to the left z=-2
As per empirical rule 95.4% of the observations fall within 2 standard deviation of the mean
Therefore, the percentage of sales associates with salaries less than 27500 : [tex]\frac{100-95.4}{2}=2.3\%[/tex]
e)
[tex]z_1=\frac{x_1-\mu}{\sigma}\\\\z_1=\frac{42000-32500}{2500}=3.8[/tex]
A z-value greater than 3 is considered as an outlier.
Hence, the salary of 42000 should be considered as outlier.
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In Original Source 2, "Development and initial validation of the Hangover Symptoms Scale: Prevalence and correlates of hangover symptoms in college students," one of the questions was how many times respondents had experienced at least one hangover symptom in the past year. Table 3 of the paper (page 1,445) shows that out of all 1,216 respondents, 40% answered that it was two or fewer times. Suppose the researchers are interested in the proportion of the population who would answer that it was two or fewer times. Can they conclude that this population proportion is significantly less than half (50% or 0.5)? Go through the four steps of hypothesis testing for this situation for women only. Use appropriate software or a calculator to find the standard deviation and the test statistic. (Round your standard deviation to three decimal places and your test statistic to two decimal places.) Test Statistic?
Only twice or less, according to 40% of respondents. Suppose the researchers are curious about the percentage of the population that would respond that it was two or less times, in which case the test statistic would be -0.208 and the standard deviation would be 0.048.
H0: The population proportion of women who have experienced two or fewer hangover symptoms in the past year is equal to or greater than 0.5.
Ha: The population proportion of women who have experienced two or fewer hangover symptoms in the past year is less than 0.5.
Set the alpha level
α = 0.05
Calculate the test statistic
n = 618 (women only)
p = 0.4 (from Table 3)
Standard Deviation = sqrt[p*(1-p)/n]
Standard Deviation = sqrt[0.4*(1-0.4)/618]
Standard Deviation = 0.048
Test Statistic = (0.4 - 0.5) / 0.048
Test Statistic = -0.208
Step 4: Make a decision
Since the test statistic (-0.208) is less than the alpha level (0.05), we reject the null hypothesis and conclude that the population proportion of women who have experienced two or fewer hangover symptoms in the past year is less than
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Based on the 2010 US census, the population of Milwaukee, Wisconsin, was about 96% of the population of Baltimore, Maryland. In 2010, if Milwaukee's population was about 595,000, which of the following is the best
approximation of Baltimore's population?
A 620,000
B 570,000
C 300,000
D 95,000
Answer: A
Step-by-step explanation:
Because Milwaukee's population is smaller than that of Baltimore, the only correct answer would be one that has the population of Baltimore higher than that of Milwaukee, which is only A
Given the speeds of each runner below, determine who runs the fastest.
\text{Adam runs 13 feet per second.}
Adam runs 13 feet per second.
\text{Stephanie runs 199 feet in 17 seconds.}
Stephanie runs 199 feet in 17 seconds.
\text{Noah runs 1 mile in 592 seconds.}
Noah runs 1 mile in 592 seconds.
\text{Katie runs 878 feet in 1 minute.}
Katie runs 878 feet in 1 minute.
Katie runs fastest among all .
What is the units of conversion ?
Unit of Conversion is a multi-step process involving multiplication or division by a numerical factor.
Given:
Speed of Adam = 13 feet per second
Speed of Stephanie = 199 feet in 17 seconds
Speed of Noah = 1 mile in 592 seconds
Speed of Katie = 878 feet in 1 minute
Now on converting all the units to one single unit,we get
1 mile = 5280 feet
1 minute = 60 seconds
Speed of Adam = 13 feet per second
Speed of Stephanie = 199 feet in 17 seconds
= [tex]\frac{199}{17}[/tex] feet per second
= 11.705 feet per second
Speed of Noah = 1 mile in 592 seconds
= 5280 feet in 592 seconds
= [tex]\frac{5280}{592}[/tex] feet per second
= 8.919 feet per second
Speed of Katie = 878 feet in 1 minute
= 878 feet in 60 seconds
= [tex]\frac{878}{60}[/tex] feet per second
= 14.6333 feet per second
Hence ,Katie runs fastest among all sice its speed is the highest .
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Of the 1500 trains leaving a train station one day, 1290 left within 5 minutes
Of the scheduled time. What percentage of the trains left within 5 minutes
of the scheduled time?
Answer:
55
Step-by-step explanation:
Which is always true about a trapezoid?
Answer: They always have one pair of parallel lines.
Step-by-step explanation:
find the area of a circle with a radius of 13 inches use 3.14 for pi do not round your answer
The area is:
530.66 in^2Explanation:
To find the circle's area, use the formula [tex]\sf{A=\pi r^2}[/tex].
where:
A = area;
π = 3.14 (pi);
r = radius
Diagram:
[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 13\ in}\end{picture}[/tex]
Plug in the data:
[tex]\sf{A=3.14\times13^2}[/tex][tex]\sf{A=3.14\times169}[/tex][tex]\sf{A=530.66\:in^2}[/tex]
An ice cream stand uses the expression 2 + 0.5x2+0.5x2, plus, 0, point, 5, x to determine the cost (in dollars) of an ice cream cone that has xxx scoops of ice cream.
How much does an ice cream cone with 555 scoops cost?
\$$dollar sign
Answer:
qwqe
Step-by-step explanation:wqeqwe
The propagation of fatigue cracks in various aircraft parts has been the subject of extensive study in recent years. The accompanying data consists of propagation lives (flight hours/104) to reach a given crack size in fastener holes intended for use in military aircraft. 0.737 0.843 0.871 0.911 0.920 0.932 0.961 1.010 1.039 1.050 1.102 1.120 1.138 1.161 1.241 1.352 (a) Compute and compare the values of the sample mean x and median . (Round your answers to four decimal places.) x = flight hours/104 = flight hours/104 (b) By how much could the largest sample observation be decreased without affecting the value of the median? (Enter your answer to three decimal places.) flight hours/104
On solving the provided question we got to know that, the median value won't change if the greatest sample Observation is decreased to 1.3735.
What is median?One of three ways to gauge central tendency is the median. The center position of a record is specified when describing it. A measure of central tendency is what this is. The mean, median, and mode are the three most frequently used indicators of central tendency.
The sum of all the values is divided by the total number of values, giving the mean value.
[tex]0.736 + 0.863 + 0.865 + 0.913 + 0.915 + 0.937 + 0.983 + 1.001 + 1.011 + 1.064 + 1.109 + 1.132 + 1.140 + 1.153 + 1.253 + 1.397 = 16.472\\16.472 /16 = 1.0295\\1.0295 is the mean value[/tex]
The number near the middle of the point is the median value. At the halfway point, there are two values.
[tex](1.001 + 1.011) / 2 = 1.006\\ 1.006 is the median value.[/tex]
As a result, the median value, which depicts the middle value of the numbers in the result, is less than the mean value, which depicts the real middle value of the numbers if they were equally distributed.
Their difference is that 1.0295 - 1.006 = 0.0235
1.397 observations make up the biggest sample. It may be made smaller by taking the number and removing the difference between the mean and median.
Consequently, there is a 0.0235-point difference between the mean and median.
Therefore;
[tex]1.397 - 0.0235 = 1.3735[/tex]
The median value won't change if the greatest sample Observation is decreased to 1.3735.
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find the slope of the line that passes through 0.6 and 20.14
Answer:
here this should help you
If other factors are held constant, which set of sample characteristics is most likely to lead a researcher to reject a null hypothesis stating that µ = 80? a. M = 85 and s2 = 9 b. M = 90 and s2 = 9 c. M = 85 and s2 = 18 d. M = 90 and s2 = 18
If other factors are held constant, which set of sample characteristics is most likely to lead a researcher to reject a null hypothesis stating that µ = 80 then s2 = 18 and C. M = 85
The standard deviation (s2) is a measure of the variability of the sample data, while the mean (M) is a measure of the central tendency. The higher the mean and the higher the standard deviation, the more likely it is that the null hypothesis will be rejected. Therefore, the set of sample characteristics that is most likely to lead to a rejection of the null hypothesis is M = 85 and s2 = 18.
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a. kira
b. lyric
c. they traveled at the same speed
Answer:
they ran the same speed as each other c
write out the form of the partial fraction decomposition of the function (see example). do not determine the numerical values of the coefficients. (if the partial fraction decomposition does not exist, enter dne.) (a) x4 2 x5 4x3
The partial fraction decomposition of the function is x⁴ + 2 / x⁵ + 4x³ = -1/8x + 1/2x³ + 9/8x(x²+4)
Partial fraction decomposition function:
In algebra, When an algebraic expression is split into a sum of two or more rational expressions, then each part is called a partial fraction.
Given,
Here we have the expression
x⁴ + 2 / x⁵ + 4x³
Here we need to find the partial fraction decomposition function.
In order to solve this, first we have to factorize the denominator, then we get,
=> x⁴ + 2 / x⁵ + 4x³ = (x⁴ + 2) / x³ (x² + 4)
Now, Partial fraction for each factors is written as,
=> A/x + B/x² + C/x³ + (Dx + E)/ (x² + 4)
Now, we have to Multiply through by the common denominator of x³ (x² + 4), then we get,
=> x⁴+2=A (x²(x²+4)) + B(x(x²+4)) + C (x²+4) + (Dx + E)(x³)
When we simplify this one, then we get,
=> x⁴ + 2 =Ax⁴ + 4Ax² + Bx³ + 4Bx + Cx² + 4C + Dx⁴ + Ex³
Group the x-terms and the constant terms
=> x⁴ + 2 =(A +D)x⁴ + (4A + C) x² + (B + E)x³ + 4Bx + 4C
Coefficients of the two polynomials must be equal, so we get equations
A+D=1
B+E=0
4A+C=0
4B=0
4C=2
After solving these equations, we get
A = -1/8, B = 0, C = 1/2, D=9/8, E = 0
Then when we substitute these values in the original fraction,
=> -1/8x + 1/2x³ + 9/8x(x²+4)
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a thief uses a bag of sand to replace a gold statue that sits on a weight-sensitive, alarmed pedestal. the bag of sand and the statue have exactly the same volume, 1.90 ll. (assume that the mass of the bag is negligible.) part a calculate the mass of each object. (densityofgold
4.65 kg the mass of each item (assuming the bag's mass is negligible). (Sand density is 3.00 g/cm3, while the density of gold is 19.3 g/cm3)
Given that,
A gold statue that is perched on a pedestal with a weight-sensitive alarm is replaced by a thief using a bag of sand. The statue and the bag of sand have the exact same volume, 1.55 L.
We have to calculate the mass of each item (assuming the bag's mass is negligible). (Sand density is 3.00 g/cm3, while the density of gold is 19.3 g/cm3)
We know that,
Mass of gold = Volume × Density
= 1.55×1000 cc × 19.3
= 29915 grams
= 29.915 Kg
Mass of sand = 1.55×1000×3
= 4650g
= 4.65 Kg
Volume = 1.55 L
= 1.55 × 1000 cc
= 1550 cc
Mass = Volume × Density
Mass of gold = 1550 × 19.3
= 29915 grams
= 29.915 kg
Mass of sand = 1550 × 3
= 4650 grams
= 4.65 kg
Therefore, 4.65 kg the mass of each item (assuming the bag's mass is negligible). (Sand density is 3.00 g/cm3, while the density of gold is 19.3 g/cm3)
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What is the estimated product of 8.78 and 12.356 as a whole number
Answer: 108
Step-by-step explanation:
8.78x12.356=108.48568 so the estimate would be 108
Please help...........
Answer:
98
Step-by-step explanation:
During the week of a convention, there were 9,800 occupied hotel rooms and 200 unoccupied hotel rooms in Ashley's city. What percentage of the hotel rooms in the city were occupied during the convention?
The percentage of the hotel rooms in the city which were occupied during the convention is 98%.
What is percentage?
A percentage is a piece of a whole expressed as a number between 0 to 100. Nothing is said to be zero percent; everything is said to be 100 percent; half of something is said to be 50 percent; and nothing is zero percent.
You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.
As given in the question,
Number of hotel room occupied = 9,800
Number of hotel room unoccupied = 200
Total number of the rooms in city = 9800 + 200
Total number of the rooms in city = 10,000
To calculate the percentage we proceeds as follow:
(9800/10000)100 = 98%
Therefore, the percentage is 98%.
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The plot below shows the mass of each of 999 puppies in a litter.
A line plot labeled mass of puppies in pounds
shows, moving left to right, labeled tick marks at zero, one-fourth, one-half, three-fourths, and one.There is an unlabeled tick mark between each labeled tick mark. Dots are plotted as follows: 1 dot above one-fourth; 1 dot above one-half; 4 dots above the tick after one-half, and 3 dots above three-fourths.
A line plot labeled mass of puppies in pounds shows, moving left to right, labeled tick marks at zero, one-fourth, one-half, three-fourths, and one.There is an unlabeled tick mark between each labeled tick mark. Dots are plotted as follows: 1 dot above one-fourth; 1 dot above one-half; 4 dots above the tick after one-half, and 3 dots above three-fourths.
How many times as great is the mass of the heaviest puppy than the mass of the lightest puppy?
All measurements are rounded to the nearest \dfrac18
8
1
start fraction, 1, divided by, 8, end fraction pound.
The mass of the heaviest puppy is three times greater than the mass of the lightest puppy.
What is shown by the dot plot?The number of dots for each input of the dot plot shows the number of times that each measure appears in the data-set.
For example, two dots means that the measure appears twice in the data-set.
From the description of the dot plot, the masses are given as follows:
1/4, 1/2, 1/2, 1/2, 1/2, 3/4, 3/4, 3/4.
Then the masses of the lightest and of the heaviest puppy are given as follows:
Lightest: 1/4.Heaviest: 3/4.The ratio of these masses is given as follows:
3/4/(1/4) = 3/4 x 4 = 3.
(division of fractions, the numerator is multiplied by the inverse of the denominator).
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which of the following statements are true of this rational function
On solving the question, we got to know that - Due to this, at x=0 there is no vertical asymptote , there is a removable discontinuity at x= -a
When does a function reach its vertical asymptote?Consider a function f(x) that is continuous for all values of a, changes in value as x approaches a while remaining undefined at x = a. increase. The vertical asymptote of f(x) at x = a is now a vertical line that may be drawn.
According to its study, the function's asymptote and discontinuity are found to be as
Due to this, at x=0 there is no vertical asymptote
and, also there is a removable discontinuity at x= -a
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Twice my hat size is 3 times my shoe size. If my hat size is 18 more than my shoe size, then the sum of my hat size and shoe size together is:
A) 36 B) 54 C) 90 D) 108
What is the least 3-digit odd sum of two prime numbers
A) 101 B) 103 C) 105 D) 107
What is the greatest possible product of the ones digits of 4 numbers
A) 9 B) 105 C) 945 D) 6561
Please give a detailed and simple explanation please!
Answer:
Q1. The sum of your hat size and shoe size is 54.
Q2. The correct answer is 101.
Q3. The correct answer is 6561.
Step-by-step explanation:
Q1. Let's call the size of your hat H and the size of your shoe S. You can set up the following equation based on the given information:
H = 2S
H = S + 18
Substituting the first equation into the second equation, we get:
2S = S + 18
S = 18
Then, substituting this value back into the first equation, we get:
H = 2S
H = 2 * 18
H = 36
The sum of your hat size and shoe size is S + H = 18 + 36 = 54.
Q2. The least 3-digit odd sum of two prime numbers is 101, which can be achieved by adding the two prime numbers 2 and 99. Both 2 and 99 are prime numbers, and their sum is 101, which is a 3-digit odd number.
Q3. The greatest possible product of the ones digits of 4 numbers is 6561, which can be achieved by choosing the numbers 9901, 9911, 9921, and 9931. The ones digits of these numbers are 1, 1, 1, and 1, respectively, and their product is 6561.
() Type the missing digits:
6,4 18,6 ? 8
-?,?85,835
2,9 3 2,863
Answer:
6418698
-3485835
2932863
Step-by-step explanation:
What is a special segment?
The special segments of a triangle are median, altitude, perpendicular bisector, angle bisector, and mid-segment.
What is a special segment?A line segment that establishes a special relationship with the existing segments of a geometrical shape is said to be a special segment.
Using this special segment, we can able to find the other characteristics of the geometry (a triangle or a circle, etc.)
Description about special segments:The special segments in a triangle are:
1) Altitude 2) Median 3) Perpendicular bisector and 4) Angle bisector
Altitude: This line segment whose one end starts at one of the vertexes of the triangle and the other end is perpendicular to the opposite side of the triangle.
The point of intersection of three altitudes of a triangle forms an "Orthocenter".
Median: This line segment whose one end starts at one of the vertexes of a triangle and the other end meets at the midpoint of the opposite side.
The point of intersection of three medians of a triangle forms a "Centroid".
Perpendicular bisectors: These line segments whose ends bisect the two sides of the triangle perpendicularly.
The point of intersection of perpendicular bisectors of a triangle form a "Circumcenter".
Angle bisector: This line segment bisects the angle of the triangle and divides the angle into exactly two halves.
The point of intersection of angle bisectors of a triangle form an "Incenter".
We have one more special segment in a triangle i.e., a midsegment. This line connects two midpoints of opposite sides of a triangle and becomes parallel to the third side.
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Which of the following statement is true each parallelogram is a square? a) All the rhombuses are squares b) each square is a parallelogram c) each parallelogram is a square d) each trapezium is a parallelogram
The statement is true for parallelogram is a square is a) All the rhombuses are squares.
What are the 4 properties of a rhombus?In a rhombus, the opposing sides are parallel. In a rhombus, the opposing angles are equal. Diagonals in a rhombus cut each other at right angles. A rhombus' angles are divided by diagonals.
What is the rule of rhombus?Diagonals in a rhombus cut each other at right angles. A rhombus' angles are divided by diagonals. One of the most significant characteristics of rhombus diagonals is this. Two adjacent angles added together equal 180°.
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suppose you roll a special 37-sided die. what is the probability that one of the following numbers is rolled? 35, 25, 33, 9, 19
The probability that one of the following numbers is rolled is 0.135.
We are provided a 37 sided dice. Hence, each of the number between 1 to 37 can be rolled. Now, to find the probability of rolling any of these five numbers, we will simply perform the multiplication.
The formula to be used for calculation of probability to roll any one number on the dice -
Probability = number of favourable outcomes ÷ total number of outcomes
Keep the values in formula
Probability = 1/37
Now, for the mentioned five numbers among which any can be rolled, the probability is -
Probability = 5 × (1/37)
Performing multiplication
Probability = 5/37
Performing division
Probability = 0.135
Hence, the probability is 0.135.
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