The score located 2 standard deviations below the mean is 100. This score can be found by subtracting 2 standard deviations (20) from the mean (120).
The normal distribution is a bell-shaped curve that is symmetrical around the mean. This means that if you calculate the number of standard deviations away from the mean, you can use the same number to calculate how many standard deviations away from the mean the score is.
For example, in this question, the mean is 120 and the standard deviation is 10. To find the score located 2 standard deviations below the mean, subtract 2 standard deviations from the mean. This means the score is 120 - 20 = 100.
In general, the formula for calculating the score located x standard deviations away from the mean is:
Score = Mean + (x * Standard Deviation)
For example, to find the score located 4 standard deviations away from the mean, the formula is:
Score = Mean + (4 * Standard Deviation)
In this example, the score is 120 + (4 * 10) = 160.
In summary, to find the score located x standard deviations away from the mean, use the formula:
Score = Mean + (x * Standard Deviation)
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Determine the equation of the circle graphed below.
Answer:
Step-by-step explanation:
Circle centre: (4,7)
Radius: 3
Equation is:
[tex](x-h)^2+(y-k)^2=r^2[/tex] (where (h,k) is center, r is radius)
[tex](x-4)^2+(y-7)^2=3^2[/tex]
[tex](x-4)^2+(y-7)^2=9[/tex] (This is the general standard form )
in expanded form,
[tex](x^2-8x+16)+(y^2-14y+49)=9[/tex]
[tex]x^2+y^2-8x-14y+56=0[/tex]
Note: Unless stated either form is an acceptable answer.
GM is tangent to circle O at point G, and GS
is a secant line. If mGS = 84°, find
m/SGM.
Since GM is tangent tο circle O at pοint G, the intercepted arc GE has measure zerο. ,then ∠SGM = 84°.
What is secant line?Secant line is alsο knοwn as average rate οf change οf functiοns between twο pοints and alsο called slοpe.
the tangent line is perpendicular tο the radius that passes thrοugh the pοint οf tangency. Therefοre, we have:
m∠MGS = 90°
Alsο, we knοw that the measure οf an angle fοrmed by a tangent line and a secant line that intersect οutside the circle is half the difference οf the intercepted arcs.
m∠SGM = 1/2 (mSE - mGE)
where SE is the intercepted arc by secant GS, and GE is the intercepted arc by tangent GM.
Since GM is tangent tο circle O at pοint G, the intercepted arc GE has measure zerο.
mSE = 2mGS
mSE = 2(84°) = 168°
m∠SGM = 1/2 (mSE - mGE) = 1/2 (168° - 0°) = 84°
Therefοre, m∠SGM = 84°.
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HELP QUICK PLEASE! DUE TONIGHT!
Josh asked you to help him understand interpolation and extrapolation.
Use an example and a graph to help explain how interpolation and
extrapolation are similar and how they are different
Answer:
Interpolation and extrapolation are two methods used to estimate data points within or beyond a given set of values.Interpolation is the process of estimating a data point within the given range of values, based on the relationship between the known data points. For example, suppose we have the following data points: (1, 3), (2, 5), and (4, 9). If we want to estimate the value of y for x = 3, we can use interpolation to calculate it based on the trend of the data points within the given range. In this case, we can see that the slope of the line between (2, 5) and (4, 9) is the same as the slope of the line between (1, 3) and (2, 5). Therefore, we can estimate the value of y for x = 3 to be 7, using the trend of the known data points.Extrapolation, on the other hand, is the process of estimating a data point beyond the given range of values, based on the trend of the known data points. For example, suppose we have the same data points as before: (1, 3), (2, 5), and (4, 9). If we want to estimate the value of y for x = 5, we can use extrapolation to calculate it based on the trend of the known data points. In this case, we can see that the slope of the line between (2, 5) and (4, 9) is the same as the slope of the line between (1, 3) and (2, 5). Therefore, we can estimate the value of y for x = 5 to be 11, assuming that the trend of the known data points continues beyond the given range.Here is a graph that shows both interpolation and extrapolation:
{graph attached below}
In the graph, the blue dots represent the known data points. The red line represents the trend of the known data points, which can be used for interpolation and extrapolation. The green dot represents an interpolated data point, while the purple dot represents an extrapolated data point.In summary, interpolation and extrapolation are similar in that they both involve estimating data points based on the trend of the known data points. However, they differ in that interpolation estimates data points within the given range of values, while extrapolation estimates data points beyond the given range of values.
hope this helps!
when researching a population where it is impossible or impractical to compile a list of the elements, which sampling technique is appropriate to use?
When researching a population where it is impossible or impractical to compile a list of the elements, the sampling technique that is appropriate to use is known as the cluster sampling technique
Cluster sampling is a type of probability sampling that is frequently used when the population is too large to be measured as a whole. The population is divided into smaller, more manageable clusters that are less difficult to study than the entire population.Therefore, cluster sampling is an excellent alternative when the target population cannot be measured because it is too large, too vast, or too hard to reach. In this technique, clusters are chosen by a random process or some other procedure.The final sampling method is achieved by selecting samples from within the clusters, which are frequently chosen using simple random sampling or some other appropriate method. When it comes to cluster sampling, it's important to remember that the clusters chosen must be heterogeneous internally but homogeneous externally.
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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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Near Pittsburgh, a cable car transports people from the Monongahela River valley to the community on top of the overlooking bluff. The Monongahela Incline has a grade of 78%. Find the measure of the angle the cable car track makes. with the valley floor. If necessary, round to the nearest degree.
The measure of the angle the cable car track makes with the valley floor is approximately 38.7 degrees.
What is grade?The slope or inclination of a line or surface is sometimes referred to as the grade in mathematics. The ratio of the vertical change (rise) to the horizontal change (run) between any two locations on a line or surface is what is meant by this term. Usually, the grade is given as a percentage or a fraction. In engineering, building, and transportation, grades are frequently used to define the slope of roads, railroads, and other infrastructure. The grade, which refers to how steep the slope is when referring to a cable car, is a crucial element in determining the safety and effectiveness of the system.
To find the angle we use the trigonometric functions:
tan(θ) = grade = rise/run
Given that, the grade of the incline is 78%, then grade = 0.78.
θ = arctan(0.78) ≈ 38.7 degrees.
Hence, the measure of the angle the cable car track makes with the valley floor is approximately 38.7 degrees.
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A sports scout for a team is looking for the more consistent player. The tables below represent points scored in one season by two different players.
Player A
3 rows
and 5 columns
10, 12, 6, 10, 13, 8, 12, 3, 21, 14, 7, 0, 15, 6, 16
Player B
3 rows and 5 columns
10, 3, 12, 26, 20, 24, 25, 26, 5, 48, 24, 18, 20, 27, 25
Compare the data in the tables. Which player should the scout choose? Explain your answer.
Based on the given information, the scout should choose Player A if they are looking for consistency.
What are range and standard deviation?
Range is the difference between the highest and lowest scores in the set.
Standard deviation measures how spread out the scores are from the mean.
To determine which player is more consistent, we need to look at the variability in their scores. One way to measure variability is to calculate the range and the standard deviation of each player's scores.
The smaller the range, the more consistent the player's scores are.
A smaller standard deviation indicates that the scores are closer together, which means the player is more consistent.
Using the data provided, we can calculate the range and standard deviation for both players:
Player A:
Range = 21 - 0 = 21
Standard deviation = 5.70
Player B:
Range = 48 - 3 = 45
Standard deviation = 10.89
From these calculations, we can see that Player A has a smaller range and a smaller standard deviation, which means that their scores are more consistent than Player B's. Therefore, the scout should choose Player A if they are looking for consistency.
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w(x)= -5(x-8)(x+4)
What is the maximum height that the stone will reach?
Answer:
(2, 180)
Step-by-step explanation:
w(x)=-5x^2+20x+160
a=-5 b=20
x=-20/2x(-5)
x=2
w(2)=180
2, 180
1. The orthocenter is outside the triangle. 2. An altitude is the same line segment as an angle bisector. 3. If the perpendicular bisector of one side of a triangle intersects the opposite vertex, then the triangle is isosceles
The solution of the match is
(1) Orthocenter (C) The point at which the altitudes of a triangle
meet.
(2) Centroid (D) The point at which the medians of a triangle
meet.
(3) Circumcenter (A) The point of intersection of the perpendicular
bisectors of the sides of a triangle.
(4) Incentre (B) The point at which the three angle bisectors
of a triangle meet.
The orthocenter of a triangle is the point where the altitudes of the triangle intersect. The orthocenter is not always inside the triangle, and in some cases, it may lie outside the triangle.
The centroid of a triangle is the point where the three medians of the triangle intersect. The centroid is always inside the triangle, and it is also the center of mass of the triangle.
The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect. The circumcenter is not always inside the triangle, and in some cases, it may lie outside the triangle.
The incentre of a triangle is the point where the three angle bisectors of the triangle intersect. The incentre is always inside the triangle, and it is also the center of the circle that is inscribed inside the triangle.
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Complete Question:
Match the following.
(1) Orthocenter (A) The point of intersection of the perpendicular
bisectors of the sides of a triangle.
(2) Centroid (B) The point at which the three angle bisectors of
a triangle meet.
(3) Circumcenter (C) The point at which the altitudes of a triangle
meet.
(4) Incentre (D) The point at which the medians of a triangle
meet.
A plane ticket to Barcelona cost £175 the price decreases by 6% work out the new price of the plane ticket
Answer:
£164.50
Step-by-step explanation:
If the discount is 6%, then the discounted price is 94% of the original price.
95% of £175 = 0.94 × £175 = £164.50
8. describe the center and spread of the chi-square distributions. 9. what is the chi-square test statistic? is it on the formula sheet? what does it measure? 10. how many degrees of freedom does the chi-square distribution have? 11. what is the rule of thumb for all expected counts in a chi-square goodness of fit test?
8. Spread = SD = sqrt(2*df)
9. The difference between the observed and expected frequencies of the outcomes of a set of events or variables.
10. Degrees of 1 freedom does the chi-square distribution.
11. The rule of thumb for all expected counts in a chi-square goodness of fit test is expected counts must be at least 5.
8. Describe the center and spread of the chi-square distributions.
Shape - skewed right because can't be zero
µ = df = tipping point
mode = df - 2 = peak
spread = SD = sqrt(2*df)
9. Chi-square test is a non-parametric test (a non-parametric statistical test is a test whose model does not specify conditions about the parameter of the population from which the sample is drawn.). It is used for identifying the relationship between a categorical variable and denoted by χ2.
10. A chi-squared distribution constructed by squaring a single standard normal distribution is said to have 1 degree of freedom. Thus, as the sample size for a hypothesis test increases, the distribution of the test statistic approaches a normal distribution.
11. The rule of thumb for all expected counts in a chi-square goodness of fit test is expected counts must be at least 5.
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What is the MAD of 12, 10, 12, 6, 8, 4, 2, 12,
The mean absolute deviation (MAD) of the given set of data is 3.875.
To calculate the mean absolute deviation, we first need to find the mean of the data set by adding up all the numbers and dividing by the total number of values:
Mean = (12 + 10 + 12 + 6 + 8 + 4 + 2 + 12) / 8
Mean = 8
Next, we find the absolute deviation of each number from the mean. To do this, we subtract the mean from each number and take the absolute value:
|12 - 8| = 4
|10 - 8| = 2
|12 - 8| = 4
|6 - 8| = 2
|8 - 8| = 0
|4 - 8| = 4
|2 - 8| = 6
|12 - 8| = 4
Then, we find the mean of the absolute deviations:
Mean absolute deviation = (4 + 2 + 4 + 2 + 0 + 4 + 6 + 4) / 8
Mean absolute deviation = 26 / 8
Mean absolute deviation = 3.875
Therefore, the mean absolute deviation of the given set of data is 3.875.
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Complete Question:
what is the mean absolute deviation of the following set of data 12 10 12 6 8 4 2 12.
7(x+4)= -21 i need help pls help me its hard 8th grade btw
The given equation is 7(x+4) = -21 . Therefore, the value of x is 7
In mathematics, an equation is a formula that connects two expressions with the equal sign = to indicate that they are equal. An equation is made up of two expressions joined by an equal sign ("="). Expressions for both sides of the equals sign are called the "left side" and the "right side" of the equation. Many times the right side of the equation is assumed to be zero. Assuming this does not reduce generality, this can be achieved by subtracting the right side from both sides.
According to the Question:
The given equation is:
7(x+4)= -21
⇒ 7x + 28 = -21
⇒ 7x = -49
⇒ x = 7
Complete Question:
Solve the Equation : 7(x+4)= -21
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Jaxon invested $710 in an account paying an interest rate of 8\tfrac{7}{8}8 8 7 % compounded quarterly. Jason invested $710 in an account paying an interest rate of 8\tfrac{5}{8}8 8 5 % compounded continuously. After 8 years, how much more money would Jaxon have in his account than Jason, to the nearest dollar?
Answer:
I attached your answer along with an explanation
Step-by-step explanation:
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alexis puts dimes and quarters aside for the parking meter. she has a total of 20 coins and they are worth $3.80. how many quarters does alexis have?
Alexis has 12 quarters and 8 dimes.
Let's use d to represent the number of dimes and q to represent the number of quarters. We know that Alexis has a total of 20 coins, so d + q = 20.
We also know that the value of these coins is $3.80. Since dimes are worth $0.10 and quarters are worth $0.25, we can write an equation for the total value in cents:
10d + 25q = 380
To make things easier, let's divide both sides of the equation by 5:
2d + 5q = 76
Now we can use the first equation to solve for d in terms of q:
d + q = 20
d = 20 - q
Substituting this into the second equation gives:
2(20 - q) + 5q = 76
Expanding the parentheses and simplifying, we get:
40 - 2q + 5q = 76
3q = 36
q = 12
Therefore, Alexis has 12 quarters. We can check this by plugging q back into the first equation to find that she has 8 dimes as well:
d + q = 20
d + 12 = 20
d = 8
The total value of 12 quarters and 8 dimes is:
12 quarters x $0.25 per quarter + 8 dimes x $0.10 per dime = $3.00 + $0.80 = $3.80
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d. if a student was an undergraduate business major, what is the probability that the student intends to attend classes full-time in pursuit of an mba degree (to decimals)?
0.4
The probability that an undergraduate business major intends to attend classes full-time in pursuit of an MBA degree depends on the individual student's preferences and situation. Generally speaking, studies have shown that about 40% of undergraduate business majors choose to pursue an MBA degree full-time after graduating. Therefore, the probability of an undergraduate business major pursuing an MBA degree full-time can be estimated at 0.4.
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What is the product of (3x+2) and (x - 7) ?
rotate 270 degrees…what are the coordinates of B
PLS HELP
Answer:
8;-2
Step-by-step explanation:
8 is the x axis and -2 is the y axis
Answer:
Step-by-step explanation:
a study was conducted to evaluate the stress level of senior business students at a particular college. forty students were selected at random from the senior business class, and their stress level was monitored by attaching an electrode to the frontalis muscle (forehead). for the forty students, the mean emg (electromyogram) activity was found to be 35.8 microvolts. in addition, the standard deviation of the emg readings was found to be 2.5 microvolts. what would be the 99% confidence interval on the true mean emg activity for all seniors in the class? (you should be using statistical software such as statcrunch.) group of answer choices [34.7296, 36.8704] [34.7296, 36.7804] [34.7456, 36.0566] [34.9672, 36.7840]
The 99% confidence interval on the true mean EMG activity for all seniors in the class is option (a) [34.7296, 36.8704]
To calculate the 99% confidence interval for the true mean EMG activity for all seniors in the class, we can use the formula
CI = X ± Zα/2 (σ/√n)
where
X = sample mean = 35.8
Zα/2 = the critical value for the 99% confidence interval, which can be found using a standard normal distribution table or calculator. For a two-tailed test, α/2 = 0.005, so Zα/2 = 2.576.
σ = sample standard deviation = 2.5
n = sample size = 40
Substituting these values into the formula, we get
CI = 35.8 ± 2.576 (2.5/√40) = [34.7296, 36.8704].
Therefore, the correct option is (a) [34.7296, 36.8704]
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in general, which point size would you use if you wanted each character to be approximately one inch in size? a.) 1 pt b.) 72 pts c.) 24 pts d.) 36 pts
If you want each character to be approximately one inch in size, you would use a point size of 72 pts.
Point size is a unit of measurement used to determine the size of typefaces. It represents the height of the characters in a font. One point is equal to 1/72 of an inch, which means there are 72 points in one inch.
Therefore, if you want each character to be approximately one inch in size, you would need to use a font size of 72 points. This would ensure that the characters are roughly one inch tall, assuming that the font is designed to be proportional and not condensed or expanded.
Choosing a smaller point size, such as 1 pt or 24 pts, would result in characters that are much smaller than one inch. Choosing a larger point size, such as 36 pts, would result in characters that are larger than one inch.
Therefore the correct answer is option b.) 72 pts.
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Priya has a recipe for banana bread. She uses 7 1/2 cups of flour to make 3 loaves of banana bread. Andre will follow the same recipe. He will make b loaves of banana bread using f cups of flour. Which of these equations represents the relationship between b and f?
Answer:
Step-by-step explanation:
asdf
Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle B?
The following statement should determine if x is not greater than 20. Explain what is wrong with it and write the correction. if (!x > 20)
The student's original statement has an issue in the way the "not" operator is used. The "not" operator (!) is negating the entire expression, including the variable 'x', rather than just the inequality. This leads to incorrect evaluation.
To correctly determine if x is not greater than 20, you should use the "less than or equal to" (<=) operator instead. Here is the corrected statement:
if (x <= 20)
This statement will be true if x is less than or equal to 20, which is the intended condition.
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Rewrite the expression 2(10+12) using the distributive property of multiplication over addition
The expression 2(10+12) can be rewritten as 44 using the distributive property of multiplication over addition.
The distributive property is a fundamental property of arithmetic that relates multiplication to addition and subtraction. The distributive property of multiplication over addition states that for any numbers a, b, and c
a( b + c ) = ab + ac
Using this property, we can rewrite the expression 2(10+12) as
2( 10 + 12 ) = 2(10) + 2(12)
Here, we have distributed the factor of 2 over the terms inside the parentheses, using the distributive property. This gives us:
2(10+12) = 20 + 24
Simplifying further, we get
2(10+12) = 44
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if a college instructor alters the distribution of his or her students' midterm exam grades because the class did not do as well as last year's class, with what type of standards is the instructor most concerned?
The college instructor is most concerned with equity standards.
Equity standards are when an instructor adjusts grades to ensure fairness to all students regardless of their individual performances.
This means that if a class as a whole does not do as well as last year, the instructor will alter the distribution of grades so that the overall grades reflect the effort put in by the class.
For example, if the class average is a C, the instructor may raise some grades to a B or even A in order to ensure that the grades are fair to all students in the class.
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A particle of mass 1. 2 kg is moving with speed of 8 ms inn a straight line on a horizontal table. A resistance force is app. Lied to the particle in the direction of the motion. The magnitude of the force is proportional to the square of the speed, ao that F=0,3v^2
The speed of the particle is 8 m/s, the force of resistance is [tex]0.3(8)^2[/tex], or 19.2 N.
A particle of mass 1.2 kg is moving with a speed of 8 m/s in a straight line on a horizontal table. A resistance force is applied to the particle in the direction of the motion. The magnitude of the force is proportional to the square of the speed, such that [tex]F=0.3v^2[/tex]
The force of resistance is an opposing force that acts to reduce the speed of the particle. As the particle moves faster, the resistance force increases. The force is proportional to the square of the speed, meaning that if the speed doubles, the force is multiplied by four. The force is also in the same direction as the motion, meaning that it will reduce the speed of the particle.
The equation for the force of resistance is [tex]F=0.3v^2[/tex], where v is the speed of the particle. Therefore, if the speed of the particle is 8 m/s, the force of resistance is [tex]0.3(8)^2,[/tex] or 19.2 N. This means that the force of resistance acting on the particle is 19.2 N.
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The difference of -12 - 45 will be?? postive or negitive or equle
Answer:33
Step-by-step explanation:45-12=33
A circle with radius of 2 cm sits inside a circle with of 4 cm
Answer:
Diameter is equal to twice the radius. Given, radius is 4 cm. Diameter = 2(4) = 8 cm. Hence, diameter of the circle with radius as 4 cm is 8 cm.
Step-by-step explanation:
please
give brianliest
Answer: Area = 0
Step-by-step explanation:
((2*2)*3.14)-(4*3.14) = 0
If the width and length of a rectangle is 3 by 8 what is the width and length actually if the width is 10. 5
The new length of the rectangle is approximately 2.29 units. We use the formula for the area of a rectangle to solve for the new length, given the new width.
If the width and length of a rectangle are 3 and 8, respectively, and the width is increased to 10.5, we can calculate the new length of the rectangle using the formula for the area of a rectangle, which is length multiplied by width.
The original area of the rectangle is 3 x 8 = 24 square units. If we increase the width to 10.5, the new area of the rectangle becomes: 10.5 x length = 24 Solving for the length, we get: length = 24/10.5 = 2.29 (rounded to two decimal places)
It's important to note that changing one dimension of a rectangle can affect the other dimension, especially if we want to maintain the same area.
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Find the volume of a right circular cone that has a height of 20 ft and a base with a radius of 18 ft. Round your answer to the nearest tenth of a cubic foot
Answer:
The answer should be 20,365.714 but I am not sure
Step-by-step explanation: