a) 55 people expect to be between 165 and 175 cm.
b) 76 people to be taller than 166 cm.
What is Standard normal distribution?
The standard normal distribution is a special type of normal distribution where the mean is 0, and the standard deviation is 1.
a) To answer this question, we can use the standard normal distribution table to find the proportion of heights that fall within certain ranges of the mean.
The standard normal distribution table gives us the proportion of values within a certain number of standard deviations of the mean.
Since the standard deviation of the heights is 5, we can find the proportion of heights between 165 and 175 cm by looking at the range of values that are one standard deviation below and one standard deviation above the mean.
The mean of the heights is 170, so one standard deviation below the mean is 170 - 5 = 165. One standard deviation above the mean is 170 + 5 = 175. Therefore, the range of heights that are one standard deviation below and one standard deviation above the mean is 165 to 175.
If we look at the standard normal distribution table, we find that approximately 68% of the values fall within one standard deviation of the mean. Since 80 is approximately 68% of 118, we would expect approximately 55 people to have heights between 165 and 175 cm.
Hence, 55 people expect to be between 165 and 175 cm.
b) For the second part of the question, we can find the proportion of heights that are taller than 166 cm by looking at the range of values that are more than one standard deviation above the mean.
The mean of the heights is 170, so more than one standard deviation above the mean is anything greater than 175. If we look at the standard normal distribution table, we find that approximately 95% of the values fall within two standard deviations of the mean.
Since 80 is approximately 95% of 84, we would expect approximately 76 people to be taller than 166 cm.
Hence, 76 people to be taller than 166 cm.
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A 12 -foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 10 feet from the base of the building. How high up the wall does the ladder reach?
The height of the wall where the ladder reaches will be 6.33 feet.
What is a Pythagoras theorem?It communicates that the area of the square whose side is the hypotenuse is identical to how much the locale of the squares on the other various sides.
The Pythagoras theorem formula is given as
H² = P² + B²
A 12-foot ladder is set against a vertical mass of construction, with the lower portion of the ladder staying on level ground 10 feet from the underpinning of the design.
The height of the wall where the ladder reaches will be calculated as,
12² = P² + 10²
144 = P² + 100
P² = 44
P =6.33 feet
The level of the wall where the stepping stool arrives freely will be 6.33 feet.
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Carter is ordering a taxi from an online taxi service. The taxi charges $2.50 just for
the pickup and then an additional $2 per mile driven. How much would a taxi ride
cost if Carter is riding for 7 miles? How much would a taxi ride cost that is m miles
long?
Answer:
$16.50
Step-by-step explanation:
y=mx+b
y is total cost, m is the miles, x is the cost per mile driven, and b is the pickup charge.
y=(7 miles x $2) + $2.50
y= $16.50
Answer:
Step-by-step explanation:
y=(7 miles x $2) + $2.50
y= $16.50
which inequality matches the graph 1,0,-1,-2,-3
3x+1>4
3x+1≥4
3x+1<4
3x+1≤4
In the inequality 3x + 1 ≤ 4 at x = {1, 0, -1, -2, -3} all the values are satisfied therefore, the graph matches with this inequality.
What is Linear Inequality?
A linear inequality is a mathematical inequality that incorporates a linear function. A linear inequality contains one of the inequality symbols. It displays data that is not equal in graph form.
Solution:
To find the answer we need to put the values of x in options
3x + 1 ≤ 4
Putting x = {1, 0, -1, -2, -3}
At x = 1
3*1 + 1 ≤ 4
At x = 0
3*0 + 1 ≤ 4
At x = -1
3*-1 + 1 ≤ 4
At x = -2
3 * -2 + 1 ≤ 4
At x = -3
3*-3 + 1 ≤ 4
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How do you compute the mean and standard deviation of the random variable with the given discrete probability distribution?
For a given discrete probability distribution, The random variable also contains discrete values, The mean and standard deviation are computed in terms of Expected values E(X).
What do you mean by random variable?The mathematical formalization of a number or object that is subject to chance events is known as a random variable. It is a function or mapping between a space of potential outcomes, commonly real numbers, to a space of measurement.
What is mean and standard deviation?The arithmetic mean, also known as the arithmetic average or simply the mean or average, is the sum of a set of numbers divided by the total number of numbers in the set. The collection frequently consists of a series of findings from a survey, experiment, or observational study.
The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
For discrete probability distribution with P(x) as the probability of the event 'x'.
Mean = E(X) = x*P(x).
Variance = [tex]E(X^{2})-(E(X))^2[/tex]
standard deviation = [tex]\sqrt {Variance}[/tex]
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What is an example of continuity vs discontinuity?
Continuity refers to the property of a function or a curve in which a small change in the input results in a small change in the output, while discontinuity is a break or interruption in a function or curve.
An example of continuity is the function f(x) = x^2, which is a continuous function because, for any value of x, there is a corresponding y-value that is obtained by squaring x. This means that if x changes slightly, the value of y will change in a corresponding way.
An example of discontinuity is the function g(x) = 1/x, which is a discontinuous function because it has a break or singularity at x=0, where the function is undefined. This means that there is a gap in the curve at x=0, and the function is not defined for any value of x that is equal to zero
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The function f(x) = x2 serves as an illustration of continuity because there is always a corresponding y-value that can be calculated by squareing x. This implies that if x marginally changes, the value of y will also change.
The function g(x) = 1/x, which has a break or singularity at x=0, where the function is undefined, is an example of a discontinuous function. This indicates that the curve has a gap at x=0 and that the function is not defined for any x value equal to zero.
Farmer Pisquet put grain into bins Y, A and P. The ratio of weight of
flour in bin Y to weight of flour in bin A was 9:3. The ratio of weight of
flour in bin A to weight of flour in bin P was 4:3. If there were 36
pounds of grain in bin A, how many pounds of grain were there
altogether?
The weight of Y = 108 pound and weight of P is 27 pound
What does the math ratio mean?
Definitions: An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)
Given that :
A = 36 pound
A:P =4:3
so when A is 36 = 4*9
then P is 3*9 = 27
Hence the weight of P is 27 pound
Now we have Y:A = 9:3
when A = 36 = 3*12
Then Y is 9*12 = 108
Hence weight of Y is 108 pound
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Why is the use of 0 and necessary in a measuring instrument?
In order for measuring devices to produce correct findings, they must have zero error. Zero error also makes it possible to determine if an instrument is functioning properly or not.
what is measuring instrument?Instruments used by researchers and practitioners to assist in the assessment or evaluation of subjects, clients, or patients are known as measurement tools. From physical functioning to psychosocial welfare, the tools are used to assess or gather data on a number of aspects.
Electrical instruments are one of three categories for measuring devices. Instrument for electronics. a mechanical instrument.
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Which expression is equivalent to b-2/ab-3? assume a=0, b=0.
O a/b5
O 1/ab5
O a3b/1
O b/a
The expression b/a is equivalent to the given expression b⁻²/ab⁻³ when a≠ 0 and b ≠ 0. So, option D is correct.
What are the equivalent expressions?The two or more expressions are said to be equivalent expressions if their value is the same even if they look different.
This is the same concept as equivalent fractions.
Calculation:The given expression is b⁻²/ab⁻³.
This expression is a fraction.
Simplifying the given expression:
b⁻²/ab⁻³
we know a⁻ⁿ = 1/aⁿ
So, we can write b⁻² = 1/b² and b⁻³ = 1/b³
Then, b⁻²/ab⁻³ = (1/b²)/a(1/b³)
⇒ b⁻²/ab⁻³ = 1/b² × 1/a × b³ = b × 1/a
∴ b⁻²/ab⁻³ = b/a
Thus, the equivalent expression for the given expression is b⁻²/ab⁻³ = b/a.
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How do you know if a line is positive negative or undefined?
A line is positive negative or undefined as per its slope is positive negative or undefined.
The slope is the ratio of change of the dependent variable with respect to the change in the independent variable.
It is calculated for both straight lines as well as curves.
for example, let us say , we have a straight line y = mx +c , then the coefficient of the dependent variable 'm' is the slope of the line. It is also calculated by (y2-y1)/ (x2-x1) where y2, x2 are the final positions and y1,x1 are the initial positions.
So, we can say that if the slope is positive, i.e. the line extends up to right , its a positive line ; if the slope is negative, i.e. the line extends down to right , its a negative line and if the slope is undefined i.e. the change in the independent variable is zero like for a vertical line, then its an undefined line.
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In 2005, Cory put $5,000 in an account that grows in value by 3.7% per year. what is the value of the account in 2020?
The value of the account in 2020 is given as $8622.86.
What is compound interest?The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.
The amount of one interval of time becomes the principal to the next one.
Suppose in 2005 t = 0.
Then, in the year 2020 t = 15.
Now, the given question can be solved by finding the Amount using the expression as below,
P(1 + r/100)ⁿ
Where p, r and n are the principal, rate and time for the compounding.
Substitute all the corresponding values to obtain,
A = 5000(1 + 3.7/100)¹⁵
= 5000 × 1.037¹⁵ = 8622.86
Hence, in 2020 the money invested in the account becomes as $8622.86.
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What is 2 3 times 2 as a fraction?
2 × 3 × 2 can be written as 2 × 6, so the answer is 6/1, which is an equivalent fraction to 6.
We can solve this problem by converting the expression into a fraction. First, we need to multiply 2 and 3 together, which gives us 6. Then, we need to multiply this result by 2, so we get 12. Finally, we need to express this result as a fraction. To do this, we put the numerator (12) over the denominator (1). So, the answer is 12/1, which simplifies to 4/32 × 3 × 2 can be written as 2 × 6, so the answer is 6/1, which is an equivalent fraction to 6
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how do you simplify 75 65/1000
What is the solution of 2x² 3x 2 0?
The solution of the function 2x² + 3x + 2 = 0 is the zeros obtained after factorizing them which is found to be as -2 and -1 / 2.
The given equation is , 2x² + 3x + 2 = 0
On factorizing this we will get ,
2x² +4x - x +2 = 0
=> 2x(x +2) - ( x + 2) = 0
=> (2x-1) (x + 2) = 0
Therefore , the zeroes are -2 and -1 / 2.
Factorization is a process in which we write a given equation in terms of their prime factors. The result of factorization is known as zeros off a polynomial and are the solution for the given equation.
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Which table represents exponential growth? a 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 6, 8. A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 8, 16.
The table that represents exponential growth is the second table.. The second column is labeled y with entries 2, 4, 6, 8. A 2-column table has 4 rows.
What is exponential growth?
Exponential growth simply means a process that increases quantity over time. It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself.
Exponential growth is the pattern of data which shows sharper increases over time. In finance, compounding creates exponential returns and the savings accounts with a compounding interest rate can show exponential growth.
In this case, the second table described represents an exponential function. It has a common ratio of 4, meaning that each y-value is multiplied by 4 to get to the next value. Here, every time the Xs increase by 1, the Ys increase by a multiple of 4.
One of the best examples of exponential growth is observed in bacteria. Here, it takes bacteria roughly an hour to reproduce through prokaryotic fission. This illustrates exponential growth.
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Step-by-step explanation:
if the variance between treatments increases and the variance within treatments decreases, what will happen to the f-ratios and the likelihood of rejecting the null hypothesis in an anova test?
When the null hypothesis is rejected, the F-ratio and probability of rejection both rise.
The F-ratio is calculated using the formula F = variance between treatments/variety within treatments. An increase in the numerator will raise the F-ratio, while a reduction in the denominator will raise it even further. The probability of rejecting the null hypothesis rises with increasing F.When the null hypothesis is rejected, the F-ratio and probability of rejection both rise.
The null hypothesis for an ANOVA test is that the means of the different groups are equal. If the F-ratio is high enough (i.e., if it is significantly different from 1), then it is likely that the means of the different groups are indeed different. Therefore, if the variance between treatments increases and the variance within treatments decreases, then the F-ratio will be higher, and the likelihood of rejecting the null hypothesis will be greater.
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does the residual plot support the appropriateness of a linear model? responses yes, because there is a clear pattern displayed in the residual plot. yes, because there is a clear pattern displayed in the residual plot. yes, because about half the residuals are positive and the other half are negative. yes, because about half the residuals are positive and the other half are negative.
Answer:
Step-by-step explanation:
Yes, the residual plot supports the appropriateness of a linear model because it displays a clear pattern and has roughly equal amounts of positive and negative residuals.
Is the residual plot relatively symmetrical around the centerline?
Yes, if the residual plot is relatively symmetrical around the centerline, it suggests that the linear model is appropriate because it is capturing the variance in the data evenly. If the residual plot is skewed or has outliers, it may indicate that the linear model is not accurately representing the data and a different model may be needed.
A residual plot is a graph that plots the residuals (the differences between the observed values and the predicted values) on the y-axis and the independent variable on the x-axis. The residual plot is used to assess the appropriateness of a linear model. If the residual plot displays a clear pattern and has roughly equal amounts of positive and negative residuals, it suggests that the linear model is appropriate. On the other hand, if the residual plot is scattered randomly or displays a clear pattern, it suggests that the linear model is not appropriate. In this case, the residual plot supports the appropriateness of a linear model because it displays a clear pattern and has roughly equal amounts of positive and negative residuals. This suggests that the linear model is able to accurately predict the dependent variable based on the independent variable.
Therefore, the residual plot supports the appropriateness of a linear model.
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Yes, because it displays a clear pattern and has roughly equal amounts of positive and negative residuals.
What is a residual plot and how does it support the appropriateness of a linear model?
A residual plot is a graphical representation of the residuals (prediction errors) of a regression model. It can be used to assess the appropriateness of a linear model by examining the pattern of the residuals and the presence of any unusual points or trends.
If the residual plot shows a clear pattern, such as a trend or curvature, it suggests that the linear model may not be appropriate for the data. On the other hand, if the residual plot appears random and shows roughly equal amounts of positive and negative residuals, it supports the appropriateness of a linear model.
The residual plot is used to judge whether a linear model is suitable. The linear model may be useful if the residual plot exhibits a distinct pattern and contains nearly equal numbers of positive and negative residuals. On the other hand, it indicates that the linear model is inappropriate if the residual plot is dispersed randomly or exhibits a distinct pattern. The residual plot shows a distinct pattern and about equal numbers of positive and negative residuals, which in this instance confirms the suitability of a linear model. This suggests that the dependent variable may be accurately predicted by the linear model utilising the independent variable.
Therefore, the residual plot confirms that a linear model is adequate.
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A real estate agent, working entirely on commission, makes a weekly average of $850 with da
standard deviation of $260 selling property in the city, and an average of $1340 with a standard
deviation of $390 selling property in the suburbs. Assuming independence, what are the mean and
standard deviation of her total weekly sales?
If the real estate agent's average weekly sales are $850 in the city and $1340 in the suburbs, then her total average weekly sales are $850 + $1340 = $2190.
The standard deviation of her weekly sales in the city is $260, and the standard deviation of her weekly sales in the suburbs is $390. If the sales in the city and the suburbs are independent, then the standard deviation of her total weekly sales is the square root of the sum of the squares of the standard deviations of her weekly sales in the city and the suburbs, which is the square root of $260^2 + $390^2 = $67600 + $152100 = $219100. This is equal to $468.
Therefore, the mean and standard deviation of the real estate agent's total weekly sales are $2190 and $468, respectively.
Múltiple representación
The given data is used to obtain the equation as y = x - 2 and the table and graph has been drawn clearly.
How to write the equation of a straight line in slope-intercept form?A straight line can be written in the slope-intercept form as, y = mx + c.
In order to obtain the slope, the ratio of the difference of the coordinates are taken and c is the y-intercept which can be found by substituting x = 0 in the equation.
The data is given as below,
slope = 1 and y-intercept = -2.
The equation, graph and table for the given data can be formed as follows,
(a) The slope-intercept equation is y = mx + c, where m is the slope and c is the y-intercept.
Substitute the corresponding values to obtain,
y = 1 × x + (-2)
= x - 2
(b) The graph for the given equation is plotted below as,
(c) The table for the given equation can be formed with different values of x and y as below,
y = x - 2
Substitute x = 0 to get y = -2, x = 1, y = -1 and x = 2, y= 0.
Now, the table can be formed as below,
Hence, the equation is given as y = x - 2 and the graph and table for the equation is drawn properly.
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State whether the product of √3 and √9 is rational or irrational. Explain your answer. I’ll mark brainliest
Answer: √3 is irrational whereas √9 is rational
Step-by-step explanation:
3x3=9. 3^2=9. but, ?x?=3 and ?^2=3. there is no number for that
The product of [tex]\sqrt{3}[/tex] and [tex]\sqrt{9}[/tex] is irrational
•
An irrational number is a type of real number which cannot be represented as a simple fraction and [tex]\sqrt{3}[/tex] falls under this category. As fractions are just ratios, being multiplied by another number will not affect the ratio, thus making the product irrational.
What is another way to describe an equilateral triangle?
Answer:
The answer is: Acute.
Step-by-step explanation:
All sides of a equilateral triangle are 60 degrees, meaning it is acute.
Just need help with 21-23 missed lessons and it’s not making any sense
Find the sum of the first 7 terms of the following series, to the nearest integer.
Answer:
32, 40, 50, ...
The sum of the first 7 terms of the following series is 52
What is a geometric sequence?'A geometric sequence is a sequence where every term has a constant ratio to its preceding term. A geometric sequence with the first term a and the common ratio r and has a finite number of terms.'
According to the given problem,
Sequence = 32,40,50
Let the common ratio be r,
Let the first term of the sequence be a,
⇒ a × r = second term
⇒ 32 × r = 40
⇒ r = 40/32
⇒ r = 5/4
We know,
Sum of n number of terms in a geometric sequence can be represented by,
sn=a(1-[tex]r^{7}[/tex])/1-r
⇒ [tex]s_{7}[/tex] =32(1 - (5/4)[tex]^{7}[/tex]/1 - 5/4
⇒ [tex]s_{7}[/tex] = 32 (1 - (5/4)[tex]^{7}[/tex]/3/5
⇒ [tex]s_{7}[/tex] = 5*32(1 - (5/4)[tex]^{7}[/tex])/3
⇒ [tex]s_{7}[/tex] = 160(0.972)/3
⇒ [tex]s_{7}[/tex] = 156/3
=52
Hence, we can conclude, the sum of the first 7 terms of the geometric sequence is 52
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5. The value of
√33
is between what two numbers?
Obetween 3 and 4
between 5 and 6
Obetween 32 and 34
between 16 and 17
Answer: between 5 and 6
Step-by-step explanation: The square root of 5 is 25 and the square root of 6 is 36 . Hence, the square root of 33 lies between 5 and 6.
What are the roots of the quadratic equation 2x² 7x +6 0 *?
The roots of the quadratic equation are 3/2 and 2.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
2x² - 7x + 6
We can find the roots by middle-term factorization.
2x² - (4 + 3)x + 6 = 0
2x² - 4x - 3x + 6 = 0
2x(x- 2) - 3(x - 2) = 0
We have,
2x - 3 = 0 and x - 2 = 0
Now,
2x = 3
x = 3/2
x - 2 = 0
x = 2
Thus,
The roots are 3/2 and 2.
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Is a rhombus a 2 D shape?
Answer: yes
Step-by-step explanation: it is a 2 dimensional shape if it was 3d it would end up being a prism
How do you find the horizontal and vertical asymptote of a rational function?
The vertical asymptote of a function can be determined by setting its denominator equal to zero (0) and solving for x.
The horizontal asymptote of a function can be found by determining the degrees of the numerator and denominator.
What is an asymptote?In Mathematics, an asymptote can be defined as a line which the graph of a given function approaches but would never touch. Additionally, the vertical asymptote of a function simply refers to the value of x which makes its denominator equal to zero (0).
In order to graph any rational function, you should determine the values for which it is undefined. This ultimately implies that, a function is considered as undefined when the value of the denominator is equal to zero, which represents vertical asymptote lines.
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Select all that are equal to 5^3 x 5^-7
1/5^-4
1/5^4
5^-4
5^4
1/-625
Answer:
5^-4
1/-625
Step-by-step explanation:
5^3 x 5^-7
They have the same base is 5, which means we just need to add the root, so 3 + (-7) = -4, so the answer is 5^-4
5^ -4
5 times 5 times 5 times 5 = -625
Because it is a negative exponent, means it is a fraction. So, the answer is
1/ -625
When the coordinates 1 1 4 4 7 1 and 4 − 2 are joined which shape is formed 5 points group of answer choices parallelogram rectangle trapezoid Square?
Given the provided coordinates of the points, The shape that is formed is a parallelogram because the slopes of the opposite sides are same.
What do you mean by slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. Divide the difference in elevation between two points by the distance between them to find the percent slope, then multiply the result by 100. The term "rise" refers to the difference in elevation between two sites. The run is the separation between the points. Percent slope is therefore equal to (rise / run) x 100.
What do you mean by coordinates?A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.
slope between (1,1) and (4,4),
m1 = 4-1/4-1 =3/3 =1
slope between (4,-2) and (7,1),
m2= 1+2/7-4 = 3/3 =1
m1=m2
similarly, slope between (1,1) and (4,-2),
m3= -2-1/4-1 = -3/3 =-1
slope between (7,1) and (4,4)
m4= 1-4/7-4 = -3/3 =-1
m3=m4
So, slopes of opposite sides are same that means they are parallel, The shape is parallelogram.
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What is the inverse of 16?
Additive inverse of 16 is -16.
Multiplicative Inverse of 16 is 1/16.
What is Inverse ?To produce a result equal to 0, add the original number and the additive inverse by simply reversing the sign of the integer. On the basis of negation of the original number, the characteristics of additive inverse are listed below. For instance, if x is the starting number, then -x is x's additive inverse.
A multiplicative inverse or reciprocal for a number x is a number that, when multiplied by x, produces the multiplicative identity, or 1. It is represented by 1/x or x/1. A fraction a/b has a multiplicative inverse of b/a. Divide 1 by the real number to obtain the multiplicative inverse of the number.
A function that "undoes" another function is called an inverse. In other words, if f(x) generates y, then y entered into the inverse of f creates x. An invertible function is one that has an inverse, and the inverse is indicated by the symbol [tex]f^{-1}[/tex].
Additive inverse of 16 is -16.
Multiplicative Inverse of 16 is 1/16.
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How many circles are drawn?
we can draw in finite number circle from one point. so there are n number of possibility to draw circle from on given single point.
what is circle?
Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.
Area of circle =
[tex]\pi r^2\\r = 10\\A = 3.14 X 20 X 20\\A = 628unit sq\\[/tex]
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