a) The proportion of the students scored at least 26 points on this test is 0.02275.
b) The 71 percentile of the distribution of test scores is 24.073
What is meant by standard deviation?A low standard deviation suggests that values are often close to the mean of the collection, whereas a large standard deviation suggests that values are dispersed over a wider range.
Standard deviation, often known as SD, is most frequently represented in mathematical texts and equations by the lower case Greek letter (sigma), for the population standard deviation, or the Latin letter s, for the sample standard deviation.
Let the scores be X and X is normally distributed with a mean of 22 and standard deviation of 2.
μ=22
σ=2
X≈N(22,2)
a) P(X≥26)=P(((X-μ)/σ)≥(26-μ)/σ)
=1-P(Z≥2)
=1-P(Z<2)
=1-0.97725
=0.02275
b) Let a is the 71th percentile of X,
P(X≤a)=0.71
P((X-μ)/σ)≤(a-μ)/σ)=0.71
P(Z≤z)=0.71
From the standard normal table by calculating with z value, we get
a=24.073
Therefore,
a) The proportion of the students scored at least 26 points on this test is 0.02275.
b) The 71 percentile of the distribution of test scores is 24.073.
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A rectangular pool 24 meters by 16 meters is surrounded by a walkway of width x meters. At what value of x will the area of the walkway equal the area of the pool?
The value of x that the walkway will be equal to the area of the rectangular pool is 5 meters
How to find the value of x that equals the dimension of the poolArea of a rectangle is given by
length * width
Area of the pool
= 24 * 16
= 384
area of the walk way
= (24 + 2x) * (16 + 2x) - area of the pool
= 384 + 58x + 4x² - 384
= 4x² + 58x
when the area will be equal
4x² + 58x = 384
4x² + 58x - 384 = 0
solving the quadratic equation gives
x= 4.9386 OR -19.4386
ignore the negative value
x = 5 meters
at x = 5 meters the walkway will have same area with the pool
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Expressing trig ratios as fractions in simplest terms ?
What effect does a scale factor less than 1 have on the dimensions of the image being scaled?
A scale factor less than 1 will decrease the dimensions of the image being scaled
The process of dilation entails scaling or changing a thing. It is a transformation that uses the specified scale factor to make the objects smaller or larger.
The resizing happens from a point called the center of dilation. It is the center of dilation from which the objects/figures are expanded or contracted.
Scale factor is a number by which the size of any geometrical figure can be changed with respect to its original size.
An image's dimension expand , when scale factor is greater than one
An image's dimension will decrease when the scale factor is less than one
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what is price of $80 hoodie on 24% discount
Answer: 60.80
Step-by-step explanation:
you saved 19.20
A regular polygon is shown, with one of its angle measures labeled a.
If m∠a = (5z + 65)°, find the value of z.
z = 15
z = 20
z = 23
z = 41
The value of z in the regular nonagon is 15.
How to find the angles of a congruent polygon?A regular polygon is a polygon with congruent sides and equal angles.
If all the polygon sides and interior angles are equal, then they are known as regular polygons.
Therefore, the regular polygon above is a nonagon because it has 9 sides. Therefore, the sum of interior angles of a nonagon is 1260 degrees.
Hence, all the angles of the regular nonagon are congruent.
9 m∠a = 1260 degrees
m∠a = 5z + 65
9(5z + 65) = 1260
45z + 585 = 1260
45z = 1260 - 585
45z = 675
divide both sides by 45
z = 675 / 45
Therefore,
z = 15
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What is the solution y 2 3x 3 x =- 2?
The solution of the equation y = (2/3)x + 3 is 5/3
The given equation is
y = (2/3)x + 3
The slope of the line is the change in y coordinates with respect to the change in x coordinates.
This is the linear equation in the the slope intercept form
y = mx + b
Where m is the slope of the line
b is the y intercept
y is the y coordinates
x is the x coordinates
The value of x = -2
Substitute the value of x in the equation
y = (2/3) × -2 + 3
Do the arithmetic operations
= -4/3 + 3
Add the numbers
= 5/3
Therefore, the solution is 5/3
I have solved the question in general, as the given question is incomplete
The complete question is:
What is the solution of the equation y = (2/3)x + 3x, when x = -2?
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5 years ago Patricia put 1200 in a saving account with a 1.5% interest rate. how much does she have now in her savings account now
PLEASE HELP!!!!!
The amount of money in her account after five years will be $1,292.74.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
A long time back Patricia put 1200 in a saving record with a 1.5% financing cost. Then the amount of money in her account after five years will be given as,
A = $1,200 × (1 + 0.015)⁵
Simplify the expression, then we have
A = $1,200 × (1.015)⁵
A = $1,200 × 1.07728
A = $1,292.74
The amount of money in her account after five years will be $1,292.74.
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What needs to be known to determine the critical values for an independent-samples t test?
the sample size of the power analysis
degrees of freedom for the smallest group
total degrees of freedom
degrees of freedom for the largest group
Total degrees of freedom needs to be known to determine the critical values for an independent-samples t-test. So, option 3 is correct.
What is meant by critical value?To evaluate whether the null hypothesis should be rejected or not, a critical value is a value that is contrasted with a test statistic in hypothesis testing. The null hypothesis cannot be rejected if the test statistic's value is not more extreme than the crucial value.
In the sampling distribution of a test statistic, a crucial value delimits areas. Both hypothesis tests and confidence intervals take these values into consideration. When conducting hypothesis testing, crucial values are used to assess whether the findings are statistically significant.
A t-test with independent samples.
To compute the critical values, one must therefore be aware of the degrees of freedom and significance level.
Therefore, total degrees of freedom needs to be known to determine the critical values for an independent-samples t-test.
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Which cost will increase or decrease with increase in production?
The variable costs will increase or decrease with an increase in production.
A variable cost could be a corporate expense that changes in the extent to how much a company produces or offers. Variable costs increment or decrease depending on a company's generation or sales volume. When production or deals increment, variable costs increment; when generation or deals decrease, variable costs decrease. Variable costs stand in differentiate from settled costs, which don't alter the extent of production or sales volume. Variable costs are a central portion in deciding a product's contribution margin, the metric utilized to decide a company's break-even or target profit level.
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Diego measured the length of a pen to be 22 cm. The actual length of the pen is 23 cm. Which of these is closest to the percent error for Diego's
measurement?
4.3%
4.5%
95.7%
104.5%
Answer: 4.3%
Step-by-step explanation:
His accuracy was 22/23 which, as a percentage, is somewhere around 95-96%
To find his percentage error, you would do 1 - 22/23 (or the decimal- whichever you prefer)
1 - 22/23 ≈ 4.3% (as a decimal, it would be approximately 0.043)
If you're allowed to use a calculator, I recommend Desmos Scientific Calculator
I hope this helps!
Write an equation of the line that passes through (4,3) and is parallel and perpendicular to -4x+10
This s the answer
Answer y=(-1/4)x+10
What type of dilation is formed when the scale factor K is greater than 1?
An expansion where image size increased is formed when scale factor k is greater than 1
The process of dilation entails scaling or changing a thing. It is a transformation that uses the specified scale factor to make the objects smaller or larger.
The initial figure is referred to as the pre-image, and the new figure that results from dilatation is known as the image.
The resizing happens from a point called the center of dilation. It is the center of dilation from which the objects/figures are expanded or contracted. Scale factor is a number by which the size of any geometrical figure can be changed with respect to its original size.
when the scale factor K is greater than 1 , The image will enlarged
Hence, An expansion will be occur.
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Given:BC is congruent to DC, AB is congruent to ED, AG is congruent to EF. With the given information above, what is needed to prove that triangle ABF is congruent to triangle EDG
Answer:
To prove that triangle ABF is congruent to triangle EDG, we need to show that the three sides of triangle ABF are congruent to the corresponding three sides of triangle EDG.
Since we are given that BC is congruent to DC, AB is congruent to ED, and AG is congruent to EF, we can conclude that the three sides of triangle ABF are congruent to the corresponding three sides of triangle EDG. Therefore, triangle ABF is congruent to triangle EDG.
a designer of custom windows wishes to build a norman window with a total outside perimeter of 60 feet. how should the window be designed to maximize the area of the window? a norman window contains a rectangle bordered above by a semicircle
The Dimensions are 16.402 in wide by 8.401 in tail
Can the perimeters of two dissimilar shapes match each other?
Be aware that shapes with similar areas might have dissimilar perimeters, and vice versa. The perimeter of shapes that have the same area are not always the same. Similar to how not all forms with the same perimeter have the same area.Perimeter of custom windows = Perimeter of (rectangle+ semicircle)
Perimeter of rectangle = 2xy
Perimeter of semicircle = 1/2 πx²
A = 2xy + 1/2 πx²
2x + 2y + πx = 60
y = (60 - 2x -πx) / 2
A = 2x([60 - 2x - πx] /2) + 1/2(πx²)
0 = 60 - 4x - πx
x = 60 / (π+4)
x = 8.401
Hence, Dimensions are 16.402 in wide by 8.401 in tail.
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The population of a small town, P, as a function of time, t, in years past 1940 is given below.
P = 2,323 + 200t
For which of the following years was the population of the town 7,723?
A.
1967
B.
1927
C.
1937
The population grew to the number 7,723 in 27 years past 1940, i.e., 1967.
What is the linear function?
In mathematics, the term linear function refers to two distinct but related notions: In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.
We have,
The population of a small town, P, as a function of time, t, in years past 1940 is:
P = 2,323 + 200t
Let t be the year in which the population reached a count of 7,723. Solve for t:
P = 2,323 + 200t
7,723 = 2,323 + 200t
7,723 - 2,323 = 200t
5,400 = 200t
t = 5400/200
t = 27 years
Hence, The population grew to the number 7,723 in 27 years past 1940, i.e., 1967.
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What is Y value in relation?
In relation, the y values represents the range of the relation
The relation is defined as the relationship between set of ordered pairs. So generally we can say that the relation is defined as the relationship between x values and y values
We know the domain is the set of all inputs of the relation, that means the domain consist of the x values of the relations
Similarly, the range is the set of all outputs of the relation, that means the ranges consist of the y values of the relations
For example
The relation {(1, 2), (3, 4), (5, 6)}
Here x value = {1, 3, 5}
The y value = {2, 4, 6}
Therefore, the y values represents the range
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Consider the data set 92, 100, 98, 89, 95, 100, 97. How will adding 65 to the data set affect the mean and the median?
A. The median will increase less than the mean.
B. The median will increase more than the mean.
C. The median will decrease less than the mean.
D. The median will decrease more than the mean.
The arithmetic mean is frequently used when discussing a bunch of numbers as being "average." One of three possible averages—the others being the median and the mode—is the one we're discussing here.
What is the Relationship Between Mean, Median and Mode?It would appear that the mean, median, and mode have no relationship at first glance. Measuring the center of a data collection, however, does have an empirical link.There is typically a difference between the median and the mode, and it is typically three times larger than the gap between the mean and the median, according to mathematicians.Formula below illustrates how the empirical relationship works:Mean minus Mode = 3 (Mean – Median)
For Given
Median, Mode, and Median Results: 95.85714 (Mean (Average)).
A middle value of 97
100 is the Mode (Most Popular)
Variety & Totals
Maximum to Minimum Results: 11
Total Numbers in the Set: 7
in descending order: 89, 92, 95, 97, 98, 100, 100
Ordered in decreasing order: 100,100,98,97,95,92,89
Even Numbers: 92, 98, 100, 100.
Odd Numbers: 89,95,97.
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Use the least squares regression equation to predict the number of soft drinks sold a day that had a high temperature of 90 degrees. Round your answer to the nearest whole number.
The estimate of the the number of soft drinks sold a day that had a high temperature of 90 degrees is of:
856.
How to obtain the equation for the line of fit?The equation for the line of fit is obtained inserting the points of the data-set into a linear regression calculator.
From the table given in the problem, the points are listed as follows:
(55, 340), (58, 335), (64, 410), (68, 460), (70, 450), (75, 610), (80, 735), (84,780).
Inserting these points into the linear regression calculator, the equation is defined as follows:
y = 16.42x - 621.83.
For a high temperature of 90 degrees, the estimate is calculated when x = 90, hence:
y = 16.42(90) - 621.83 = 856 soft drinks.
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what is the equation of the least squares regression line that describes the relationship between operating cost per hour and number of passenger seats in the plane? define any variables used in this equation.
The equation of the Least squares regression line is:
y(hat) = a + bx ,
⇒y(hat) = 1136+14.673x,
y(hat) = cost per hour and x= number of seats
If the data show a slimmer relationship between the two variables, the line that best fits this linear relationship is called the least-squares regression line, which minimizes the vertical distance between the data points and the regression line. The term "least squares" is used because it is the smallest sum of squared errors, also known as "variance".
In regression analysis, the dependent variable is plotted on the vertical Y-axis and the independent variable is plotted on the horizontal X-axis. These labels form the equation of the best-fit line determined by the least-squares method.
Operating costs are related to the day-to-day maintenance and management of your business. Operating expenses include direct cost of goods sold (COGS) and other operating expenses, often referred to as selling, general and administrative expenses (SG&A). These costs include rent, labor costs, other overhead costs, raw material costs, and maintenance costs. Operating expenses do not include non-operating expenses related to financing such as interest, investments and foreign currency translation. Operating expenses are deducted from revenue to determine operating profit and reflected in the company's income statement.
Operating cost=Cost of goods sold + Operating expenses
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A woman at a point A on the hore of a circular lake with radiu 2 mi want to arrive at the point C diametrically oppoite A on the other ide of the lake in the hortet poible time (ee the figure). She can walk at the rate of 4 mi/h and row a boat at 2 mi/h. For what value of the angle hown in the figure will he minimize her travel time?
She should make a 90° turn from the starting location. Taking this viewpoint will cut down on her trip time.
What does a math angle mean?An angle is a figure in plane geometry that is created by 2 rays and lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
Briefing :Radius of lake= 2mi
walk rate= 4mi/h
boat speed= 2mi/h
cosθ=adj/hyp=d1/4
d1=4cosθ
The arc length from A to C
S=rθ
arc length is expressed as 2θ
S=2(2θ)
S=4θ=d2
d2=4θ
time= distance/speed
t1=d1/2= 4cosθ/2=2coθ
t2=d2/4=4θ/4=4
total time =t1+t2
T=2cosθ+θ
T(θ)=2cosθ+θ
T'(θ)= -2sinθ+1
0=-2sinθ+1
2sinθ=1
sinθ=1/2
T(π/6)=2.25hours
for 90 we have
T(π/2)=1.57hours
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NEED HELP ASAP HAVE 4 MINUTESSS
There are two numbers. Twice the small number increased by the larger number is six less than triple the smaller number. The large number is equivalent to twice the smaller number. Find the larger number.
PLEASE THANK YOUUU
Answer:
i believe the answer is 60 I have know clue if im right or not but here is a guess just incase nobody else answers
Step-by-step explanation:
Answer:
larger number is -4
Step-by-step explanation:
Lets say the two numbers are x and y. x is the bigger number and y is the smaller one.
2y+x = y - 6 [equation 1]
x = 2y [equation 2]
these are the 2 equations we get from the text then we can simplify eq 1
y+x=-6
rearrange eq 2
-2y+x=0
subtract equations
3y = -6
y = -2
substitute -2 into earlier equations
x = 2*-2 = -4
Garrick and Zan are measuring the heights of seedling plants for science class.
Use the drop-down menus to complete the statements about the measured heights and the actual heights of the plants.
The complete statements are
Garrick's plant is shorter than Zan's plant, each millimetre of error results in a 11.11% percent error.Garrick's measurement was 2 millimetres off and Zan's was 12 millimetres off. Garrick's measurement was 20% off and Zan's was 12% off.How to complete the statements?The complete question is added at the end of this solution
From the question, we have the following parameters that can be used in our computation:
Garrick's plant:
Actual height = 10 mmMeasured height = 8 mmZan's plant:
Actual height= 100 mmMeasured height = 88 mmGarrick's plant is shorter than Zan's plant and the difference in heights is
Actual difference = 100 mm - 10 mm = 90 mm
Measured difference = 88 mm - 8 mm = 80 mm
The percentage errors are calculated using
Percentage errors = Difference/Actual measurement * 100%
So, we have
Garrick's actual error = (10 - 8)/10 *100% = 20%
Zan's actual error = (100 - 88)/10 * 100% = 12%
Hence, Garrick's measurement was 20% off and Zan's was 12% off.
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luis thinks the slope is 1/2 explain his mistake and give the correct slope
The correct slope of the line is 5/2 and the mistake made by Luis is that he didn't correctly interpret the scale of both x and y axes.
How to find the slope of the line?To find the slope, we will divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points
By looking at the given graph, we could easily suspect that the slope is 1/2, but then we have to look at it closely to get the correct thing.
The y-axis shows that 1 unit represents 5 while for the x-axis, 1 unit represents 1.
To get the slope, we need two points on the line (w, x) and (y, z), and the slope is given by the quotient:
m = (z - x)/(y - w)
Looking at the graph we can see that the points (0, 5) and (2, 10) are on the line, and as such the slope is;
m = (10 - 5)/(2 - 0) = 5/2
The slope of the linear equation is 5/2.
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what is the largest possible area for a right triangle in which the sum on the lengths of the two shorters sides is 1q00 in
The largest possible area for the right triangle is 1250 in² in which the sum on the lengths of the two shorter sides is 100 in.
we know that in a right triangle the two shorter sides are the base and the perpendicular. Here we have to find the largest possible area of the triangle in which the sum of the shorter sides is 100 in.
Let the base and perpendicular be x and y respectively.
Therefore,
x+y = 100
y = 100 -x
Also, Area A
= 1/2 xy
= 1 x(100-x)/z
= 100x-x²/2
so the coordinate of vertex = -b/2a
= - 50/2(1-1/2)
= 50
Also,
y = 100-50 [Putting the value of x in equation 1]
= 50
Therefore Maximum, area:
= 1/2 (50)(50)
= 1250 in²
Hence we get the required maximum area.
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an arched window is in the shape of a rectangle surmounted by a semicircle. if the perimeter is 5 m, what should the radius of the semicirculoar part be if the window is to admit as much light as possible?
The radius of the semicircle surmounted on the rectangle with perimeter 5m is equal to 5 / ( 4 + π )meters
As given in the question,
Let '2x' be the side where semicircle surmounted on rectangle.
And y be the width of the rectangle.
Total perimeter = 5m
⇒ Perimeter of three sides rectangle + circumference of semicircle with radius 'x' = 5
⇒ 2y + 2x + πx = 5
⇒ 2y + x ( 2 + π ) = 5
⇒ y = (1/2)[5 - x ( 2 + π )]
Let 'A' be the total area
Total area of the shape = area of rectangle + area of semicircle
⇒A = 2xy + (1/2)πx²
⇒A = 2x( (1/2)[5 - x ( 2 + π )]) + (1/2)πx²
⇒A = 5x - x²(2 + π) + (1/2)πx²
⇒A = 5x - 2x² - (1/2)πx²
For maximum light
dA/dx = 0
dA/dx = 5 -4x -πx
⇒5 - 4x - πx = 0
⇒x = 5 / ( 4 + π )meters
Therefore, the radius of the semicircular part to have maximum light is equal to 5 / ( 4 + π )meters.
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Han's cell phone plan costs $200 to start. Then there is a $50 charge each month. What is the total cost for x months? write an equation:
Answer:
200+50x
Step-by-step explanation:
If Han's cell phone plan costs $200, Han will have to pay $200 at the start, and since Han has to pay $50 dollars each month, and x = months, we can create 50x for $50 each month. Put both of these together, and we get 200+50x.
What is the formula of Aeroplane?
The formula for the aerodynamic force acting on an aeroplane is F = (1/2) * p * v^2 * A * C, where F is the force, p is the density of the air, v is the velocity of the aeroplane, A is the surface area of the aeroplane, and C is the coefficient of drag.
1. F = (1/2) : This is the coefficient of air resistance, which is a constant value of 1/2.
2. p : This is the density of the air, which is a measure of the mass of air per unit volume.
3. v : This is the velocity of the aeroplane, which is the speed at which it is travelling through the air.
4. A : This is the surface area of the aeroplane, which is the total area of the wings, fuselage and other exposed parts of the aircraft.
5. C : This is the coefficient of drag, which is a measure of how much air resistance the aeroplane experiences.
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Find the z-score for the given shaded region under the standard normal distribution. Round your answer to two decimal places
The Z - score for the given shaded region under the standard normal distribution = - 0.61
What is Standard Normal Distribution ?A normal distribution with a mean of zero and a standard deviation of one is known as the standard normal distribution. The standard deviation shows how far a given measurement deviates from the mean, and the standard normal distribution is centered at zero.
According to the given information
P(Z > z) = 0.73
= 1 - P(Z < z) = 0.73
= P(Z < z ) = 1 - 0.73
= P(Z < z ) = 0.27
= P(Z <-0.61 ) = 0.27
z = -0.61 (using standard normal (Z) table )
The Z - score for the given shaded region under the standard normal distribution = - 0.61
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What are the 5 transformations of a linear function?
The 5 transformations of a linear function are translation , reflection , dilation , vertical transformation and horizontal transformation.
In the question ,
we have to write the different types of transformation .
A transformation is defined as an alteration in the parent function’s graph .
there are basically 3 main types of transformations .
(i) the first type is Translations ,
the translation causes the graph to shift left, right, up, or down so many units.
(ii) the second type is Reflection ,
the Reflections cause the graph to rotate/flip over the x-axis or y-axis.
(iii) the third type is Dilation ,
In dilation the shape of a graph is changed by a certain factor. that is the graphs will look narrower or wider .
the other two transformations are
(iv) vertical transformation : it affects the y axis .
(v) horizontal transformation : it affects the x axis .
Therefore , the 5 types of transformation are explained above.
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What is the dilation called if scale factor is less than 1?
The dilation is known as contraction when the scale factor is less than 1
The process of dilation entails scaling or changing a thing. It is a transformation that uses the specified scale factor to make the objects smaller or larger.
The initial figure is referred to as the pre-image, and the new figure that results from dilatation is known as the image.
The resizing happens from a point called the center of dilation. It is the center of dilation from which the objects/figures are expanded or contracted.
Scale factor is a number by which the size of any geometrical figure can be changed with respect to its original size.
when the scale factor K is greater than 1 , The image size decreased. It gets contracts
Hence, The dilation is called Contraction
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