The proportion of the population exists less than 30 then
(x< 30) = 0.986.
How to estimate the proportion of the population that exists less than 30?To estimate the z-score using the formula, z = (x - µ)/σ
Where, x be the randomly chosen values = 30
µ be the mean = 31
σ be the standard deviation = 10
Proportion of the population that exists less than 18 = P(x < 30)
Plug in the values into z = (x - µ)/σ, to get z-score.
Substitute the values in the above equation, we get
z = (30 - 31)/10
z = -1/10 = -0.1
Therefore, the value of z = - 0.1.
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The following scatterplot shows the percentage of the vote a candidate received in the 2016 senatorial elections
according to the voter's income level based on an exit poll of voters conducted by a news agency. The income
levels 1-8 correspond to the following income classes:
1 = Under $15,000; 2 = $15-30,000; 3 = $30-50,000; 4 = $50-75,000; 5 = $75-100,000;
6 = $100-150,000; 7 = $150-200,000; 8 = $200,000 or more.
Use the election scatterplot to the find the critical values corresponding to a 0.01 significance level used to test
the null hypothesis of ρs = 0.
A) -0.881 and 0.881
B) -0.881
C) -0.738 and 0.738
D) 0.881
The critical values corresponding to a 0.01 significance level used to test the null hypothesis of ρs = 0 is (a) -0.881 and 0.881
How to determine the critical values corresponding to a 0.01 significance level?The scatter plot of the election is added as an attachment
From the scatter plot, we have the following highlights
Number of paired observations, n = 8Significance level = 0.01Start by calculating the degrees of freedom (df) using
df =n - 2
Substitute the known values in the above equation
df = 8 - 2
Evaluate the difference
df = 6
Using the critical value table;
At a degree of freedom of 6 and significance level of 0.01, the critical value is
z = 0.834
From the list of given options, 0.834 is between -0.881 and 0.881
Hence, the critical values corresponding to a 0.01 significance level used to test the null hypothesis of ρs = 0 is (a) -0.881 and 0.881
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A local anime fan club surveyed 81 of its members regarding their viewing habits last weekend, and the following information was obtained: 40 members watched an episode of Naruto, 54 watched an episode of Death Note, 40 watched an episode of Inuyasha, 32 watched both Naruto and Inuyasha, 12 watched Naruto and Inuyasha but not Death Note, 25 watched both Death Note and Inuyasha, and 23 watched only Death Note. a. How many of the club members watched exactly one of the shows? b. How many of the club members watched all three shows? c. How many of the club members watched none of the three shows?
The solutions for the Questions are
a) Given that, the minimum requirement is 58 out of 75.
a=0.7733
b) For 16 out of a total of 75
b=0.2133
c) For 11 out of a total of 75
c =0.1466
How many of the club members watched all three shows? c. How many of the club members watched none of the three shows?Generally, we need to determine the total number of students who exhibit each behavior by seeing the habits and assets contained inside a Venn diagram.
Therefore, let's assume that:
- In Set A, I watched one of the Naruto episodes.
Set B: Observed a new segment of the anime series Death Note.
Hence, 23 of them have seen an episode of Death as well as an episode of Naruto, which means that
(A intercept B) equals 23.
In addition to this, it is a given that 42 has seen one episode of Death Note.
This indicates that B is equal to 42.
This pertains to us:
[tex]B = (B-A)+(A \cap B)[/tex]
In this case, members of B through A are individuals who have only viewed Death Note. So
42=(B−A)+23
(B-A) = 11
Finally, It is a known fact that 39 of the members have seen at least one episode of Naruto.
Therefore, the value of A is 39.
A=(A−B)+(A intercept B)
39=(A−B)+23
(A−B)= 16
(A union B)= 42+ 39- 23
(A union B)=58
In conclusion, the total number of pupils is:
58 with at least one and 17 with none, for a total of 75
a) Given that, the minimum requirement is 58 out of 75.
a=58*100/75
a=0.7733
b) For 16 out of a total of 75
b= 16/75*100
b=0.2133
c) For 11 out of a total of 75
c= 11/75*100
c =0.1466
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25(0.3x-4)-5(1.5x-6)+100·13/4
Answer:
255 (assuming x is the variable x)
340 (assuming x is the multiplication sign)
See explanation below.
Step-by-step explanation:
I assume that x is the variable x.
25(0.3x-4)-5(1.5x-6)+100·13/4 =
= 7.5x - 100 - 7.5x + 30 + 25 × 13
= -70 + 325
= 255
If my assumption above is incorrect, and x really means the multiplication sign, then we have this:
25(0.3×-4)-5(1.5×-6)+100·13/4 =
= 25(-1.2) - 5(-9) + 100(3.25)
= -30 + 45 + 325
= 340
Evaluate 3|12−x|−4 when x=15
Answer:
5
Step-by-step explanation:
3 x |12 - x| - 4
3 x |12 - 15| - 4
3 x 3 - 4
9 - 4
5
The volume of this regular pentagonal pyramid is 82.5 cubic meters. What is the height of the pyramid?
the height of the pentagonal pyramid is 5. 70 meters
Volume of a regular pentagonal pyramidThe formula for determining the volume of a regular pentagonal pyramid is given as;
V=5/12tan(54°)ha^2
Where
a is the base edgeh is the heightWe have the volume to be;
volume = 82. 5 cubic centers
height = h
a = 5m
Substitute the values
[tex]82. 5 = \frac{5}{12}[/tex] × [tex]tan 54[/tex] × [tex]h[/tex] ×[tex]5^2[/tex]
[tex]82. 5 = 0. 42[/tex] × [tex]1. 3764[/tex] × [tex]25[/tex] × [tex]h[/tex]
Make 'h' subject of formula
[tex]h = \frac{82. 5}{14. 45}[/tex]
h = 5. 70 meters
The height of the pentagonal pyramid is 5. 70 meters
Thus, the height of the pentagonal pyramid is 5. 70 meters
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A cylinder has radius of 4 inches and height 10inches.There’s a small cylinder inside the previous cylinder of radius of 2 inches with the same height and same centre.What is total surface area?
The surface area of the cylinder is 48π inches².
How to find the Surface area of a cylinder?Surface area of a cylinder = 2πr(r + h)
where
r = radiush = heightTherefore,
Surface area of the smaller cylinder = 2 × π × 2(2 + 10)
Surface area of the smaller cylinder = 4π(12)
Surface area of the smaller cylinder = 48π
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help pleaseeeee
tysm
Answer: Either Rohmbus or Parallelogram...
Step-by-step explanation: Your picture is a bit small, sry
H2 Worksheet #8
Complete the table for the following rule
y = 2x + 2.
X
1
3
9
10
y
A1
Answer:
It's easy to solve the problem.
let's start...
given equation:- y = 2x+2
X y
1 (2× 1 )+ 2 = 4 .
3 (3×2)+2 = 8 .
9 (9×2) + 2 = 20 .
10. (10× 2)+2 = 22 .( table completed)
just put the value of X in the expression.
How many workers will be needed to complete a task in 6 days, given that 8 workers can complete the same task in 9 days?
Considering the simple inverse rule of three, 12 workers will be needed to complete a task in 6 days, given that 8 workers can complete the same task in 9 days.
Inversely proportional relationshipTwo variables are related when a change in one of them causes a change in the other.
Two variables have an inversely proportional relationship when an increase in one variable causes the other to decrease or, analogously, a decrease in one causes the other to increase.
In other words, two magnitudes are inversely proportional when as one increases, the other decreases in the same proportion, and as the first decreases, the second increases in the same proportion.
Simple inverse rule of threeThe simple inverse rule of three is used when the problem deals with two inversely proportional magnitudes where the amount of one of a magnitude corresponding to a given amount of the other magnitude must be calculated.
To carry out an inverse rule of three, it must be taken into account that if for a value A of one magnitude, there is a value B of the other magnitude, while for a value of C of the first magnitude, the second magnitude is will correspond a value of X:
A → B
C → X
So: [tex]X=\frac{AxB}{C}[/tex]
Amount of workers neededThe number of people who perform a task is inversely proportional to the time it takes: a greater number of workers corresponds to less time to perform the task. Then:
9 days → 8 workers
6 days → amount of workers
So:[tex]amount of workers=\frac{9 daysx8 workers}{6 days}[/tex]
amount of workers= 12 workers
Finally, 12 workers will be needed to complete a task in 6 days, given that 8 workers can complete the same task in 9 days.
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Let g(x)= 18 - 3x
Find g-¹ (0). Final answer is just a number.
Answer:
g(0)⁻¹ = 6
Step-by-step explanation:
First, you must find the inverse of the function. Remember, another way of representing g(x) is with "y". To find the inverse, you must swap the positions of the "x" and "y" variables in the equation. Then, you must rearrange the equation and isolate "y".
g(x) = 18 - 3x <----- Original function
y = 18 - 3x <----- Plug "y" in for g(x)
x = 18 - 3y <----- Swap the positions of "x" and "y"
x + 3y = 18 <----- Add 3y to both sides
3y = 18 - x <----- Subtract "x" from both sides
y = (18 - x) / 3 <----- Divide both sides by 3
y = 6 - (1/3)x <----- Divide both terms by 3
Now that we have the inverse function, we need to plug x = 0 into the equation and solve for the output. In the inverse function, "y" is represented by the symbol g(x)⁻¹.
g(x)⁻¹ = 6 - (1/3)x <----- Inverse function
g(0)⁻¹ = 6 - (1/3)(0) <----- Plug 0 in for "x"
g(0)⁻¹ = 6 - 0 <----- Multiply 1/3 and 0
g(0)⁻¹ = 6 <----- Subtract
There were 48 peaches in a carton. The average mass of all the peaches was 0.17 kg. What was their total mass?
Answer:
8.16 Kg
Step-by-step explanation:
average is calculated as
average = [tex]\frac{sum}{count}[/tex]
here average = 0.17 and count = 48 , then
0.17 = [tex]\frac{sum}{48}[/tex] ( multiply both sides by 48 )
8.16 = sum
that is total mass = 8.16 Kg
QUESTION IS DOW BELOW 5 POINTS EACH PLEASE HELP PLEASE HELP PLEASE HELP
WILL GIVE BRAINLIEST FOR ACCURATE ANWSER
The central angle in the circle is ∠DAC,major arc is BED, minor arc is ADC and BC=(5π*BD)/18.
Given that BD is diameter of the circle and angle BAC is 100°.
We are required to find the central angle, major arc, minor arc, m BEC, BC.
Angle is basically finding out the intensity of inclination of something on the surface.
In the circle central angles are many like BAC and CAD. We can write CAD as DAC also.
Major arc of a circle is that arc whose length is larger than all other arcs in the circle.
In our circle the major arc is arc BED.
Minor arc of a circle is that arc whose length is smaller.
In our circle the minor arc is arc ADC.
We know that arc's length is 2πr(Θ/360)
In this way BC=2π*(BD/2)*100/360
=(5π*BD)/18
We cannot find angle BEC.
Hence the central angle in the circle is ∠DAC,major arc is BED, minor arc is ADC and BC=(5π*BA)/18.
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If the formula r=1/n-1 .....following data, what would be the value of x?
The solution or the value of x = 14 (Option C). See the explanation below.
Where x (bar) is the mean.
What is the calculation for the above?x = (12 + 13 + 14 + 15 + 16)/5
= 14
Hence option C is correct.
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Donna is putting 9 books in a row on the bookshelf she will put one of the books gullivers travel in the first spot she will put in another of the bucks a tale of two cities in the last spot in how many ways can she put the books on the shelf
There are 5,040 different ways in which she can order the books.
In how many ways can she put the books on the shelf?We know that Donna has 9 books, but 2 of these books already have fixed positions (the first one and the last one).
So we only need to order the remaining 7 books in 7 positions.
On the first position, we have 7 options (7 books to put there).On the second position, we have 6 options (because one book is already in the first position).On the third position, we have 5 options.And so on for the remaining positions.
The total number of different combinations in which she can order the books is given by the product between the numbers of options above, so we will get:
C = 7*6*5*4*3*2*1 = 5,040
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I need help with this question
The cost of goods sold using LIFO is $99.
Cost of goods sold using LIFOUsing this formula
Cost of goods sold=(March 3 Purchased units × March 3 Purchase price)+ [(March 3 Purchased units -March 9 sold units)×March 1 Beginning inventory cost]
Let plug in the formula
Cost of goods sold=(15 units×$3.90)+[(22 units-15 units)×$5.80]
Cost of goods sold=$58.5+(7 units×$5.80)
Cost of goods sold=$58.5+$40.6
Cost of goods sold=$99.1
Cost of goods sold=$99 (Approximately)
Therefore the cost of goods sold using LIFO is $99.
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Mitch throws a baseball straight up in the air from a cliff that is 95 ft high. The initial velocity is 95 /ftsec. The height (in feet) of the object after t sec is given by =ht+−19t2+95t95. Find the time at which the height of the object is 114 ft. Round your answers to two decimal places.
The time at which the height of the object is 114 ft rounded to two decimal places is; 5.85 seconds
How to find the height of a projectile?We are given;
Height of cliff = 95 ft
Initial velocity of throw = 95 ft/s
The height (in feet) of the object after t sec is given by;
h(t) = −19t² + 95t + 95.
Now, we want to find the time at which the height of the object is 114 ft. Thus, we will set h(t) = 114 ft to get;
114 = −19t² + 95t + 95.
Subtract 114 from both sides to get;
−19t² + 95t + 95 = 0
Using quadratic formula, we have;
t = [-95 ± √(95² - 4(-19 * 95))]/(2 * -19)
t = [-95 ± √(16245)]/-38
t = (-95 ± 127.4559)/(-38)
t = (-95 - 127.4559)/-38 or (-95 + 127.4559)/-38
t = 5.85 s or -0.85
Time cannot be negative and so t = 5.85 seconds
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How many milliliters are contained in 3 liters of fluid?
Answer:
3000Step-by-step explanation:
1 liter = 1000 milliliters
so
3 liters = 3000 milliliters
------------------------
1 : 1000 = 3 : x
x = 3 * 1000 : 1
x = 3000
Answer: 3000 mL
Step-by-step explanation:
1 L = 1000 mL
3x1000 = 3000
If
f(x) = 2x2 − 7,
0 ≤ x ≤ 3,
evaluate the Riemann sum with
n = 6,
taking the sample points to be midpoints.
What does the Riemann sum represent? Illustrate with a diagram.
The Riemann sum with n = 6, taking the sample points to be midpoints is - 12.0625
What is Riemann sum?
Formula for midpoints is given as;
M = ∑0^n-1f((xk + xk + 1)/2) × Δx;
From the information given, we have the following parameters
x0 = 0 n = 6 xn = 3Let' s find the parameters
Δx = (3 - 0)/6 = 0.5
xk = x0 + kΔx = 0.5k
xk+1 = x0 + (k +1)Δx
Substitute the values
= 0 + 0.5(k +1) = 0.5k - 0.5;(xk + xk+1)/2
We then have;
= (0.5k + 0.5k + 05.)/2
= 0.5k + 0.25.
Now f(x) = 2x^2 - 7
Let's find f((xk + xk+1)/2)
Substitute the value of (xk + xk+1)/2)
= f(0.5k+ 0.25)
= 2(0.5k + 0.25)2 - 7
Put values into formula for midpoint
M = ∑05[(0.5k + 0.25)2 - 7] × 0.5.
To evaluate this sum, use command SUM(SEQ) from List menu.
M = - 12.0625
A Riemann sum represents an approximation of a region's area from addition of the areas of multiple simplified slices of the region.
Thus, the Riemann sum with n = 6, taking the sample points to be midpoints is - 12.0625
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What is the length of the hypotenuse of a 45°-45°-90° triangle with legs that are 8 cm long?
Answer:
Step-by-step explanation:
Use your 45-45-90 special triangle with side lengths 1, 1, sqrt(2).
The given triangle has legs length 8 (given) which is 8 times the size of our special 1-1-sqrt(2) triangle.
Therefore the length of the hypotenuse is 8 times the length of the hypotenuse in our special triangle
= 8 sqrt(2)
Harry took a loan from the bank.
DDD represents Harry's remaining debt (in dollars) after ttt months.
D=-200t+9000D=−200t+9000D, equals, minus, 200, t, plus, 9000
What was the size of Harry's loan?
The amount of Harry's loan is $9000.
A loan is when money is lent to another person with the understanding that it would be repaid, along with interest.
According to the question,
A bank loan is taken up by Harry.
After t months, D indicates Harry's outstanding debt (in dollars).
D=-200t+9000
In order to find the initial size of Harry's loan, the time(t)=0, that is, the time when no debts had been paid.
The negative sign in the expression of D denotes the payment of debt.
Substituting t=0, we get,
D=-200*0+9000
D=9000
Thus, the amount of loan taken by Harry is $ 9000.
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Circle B has a radius of 24 units, Circle E has a radius of 9 units, and segment CD = 4. Find segment A.F. Round your answer to the nearest tenth.
The length of segment A.F in the circles given is: 62 units.
What is the Radius of a Circle?A radius of a circle is half the diameter of a circle, which is a point from the center to any point on the circumference of the circle. This implies that any segment that is drawn from the center of a circle to any point on the circumference of a circle is a radius. Also, all radii of a circle are always congruent to each other.
Radius of circle B = AB = BD = 24 units [all radii of a circle are congruent to each other].
Radius of circle E = CE = EF = 9 units [all radii of a circle are congruent to each other].
CD = 4
DE = x
CD + DE = CE
Plug in the values into the equation
4 + x = 9
x = 9 - 4
x = 5
DE = 5
The length of segment DE is 5 units
A.F = AB + BD + DE + EF
Plug in the values into the equation
A.F = 24 + 24 + 5 + 9
A.F = 62 units.
Therefore, the length of segment A.F in the given circle is determined as: 62 units.
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please help pls thanks
Reason:
The angles x and 71 are opposite the congruent sides. We call these the base angles. The base angles are congruent for any isosceles triangle. Therefore, x = 71.
It might help to rotate the triangle so that the angles x and 71 are flat along the ground (rather than tilted).
Find the length of the arc of a circle of diameter 14 meters subtended by a central angle of π/6 radians. Round your answer to two decimal places
The length of the arc of the circle is 3.67 meters
What is an arc?The arc of a circle is a part of the circumference that makes up the circle
How to determine the length of the arc?From the question, we have the following parameters
Diameter, d = 14 meters
Central angle = π/6 radians
Start by calculating the radius of the circle using
Radius, r = Diameter/2
This is so because radius is half the diameter
So, we have
r = 14 meters/2
Evaluate the quotient of 14 meters and 2
r = 7 meters
The length of the arc of the circle is then calculated using
L = Radius * Central angle
Substitute known values in the above equation
L = 7 meters * π/6
Evaluate the product of 7 and π/6
L = 3.67 meters
Hence, the length of the arc of the circle is 3.67 meters
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Justin recently drove to visit his parents who live 270
miles away. On his way there his average speed was 11 miles per hour faster than on his way home (he ran into some bad weather). If Justin spent a total of 9 hours driving, find the two rates.
Answer:
66 mph to visit55 mph to homeStep-by-step explanation:
An equation can be set up and solved based on the relation between the two speeds and the relation between time, speed, and distance.
Setuptime = distance/speed
Let x represent the (slower) speed on the way home. Then the total time for the round trip was ...
time going + time coming home = total time
270/(x +11) +270/x = 9
Solution30x +30(x +11) = x(x +11) . . . . . . multiply by x(x+11)/9
x^2 -49x -330 = 0 . . . . . . . . rewrite in standard form
(x -55)(x +6) = 0 . . . . . . . . factor
x = 55 or x = -6 . . . . . . . solutions to this equation; x < 0 is extraneous
Justin's rate on the way there was 66 mph; on the way home, it was 55 mph.
Question 26: [4 points]
1% of a population have a certain disease and the remaining 99% are free from this disease. A test is used to detect this disease. This test is positive in 95% of the people with the disease and is also (falsely) positive in 2% of the people free from the disease.
If a person, selected at random from this population, has tested positive, what is the probability that she/he has the disease?
Let D be the event "have the disease" and FD be the event "free from the disease" Let the event TP be the event that the "test is positive".
A diagram with all the above information is shown.
[tex]P(D/TP) = \frac{P(D \: n \: TP)}{P(TP)} [/tex]
[tex]P(TP) = P(TP \: n \: D)+P(TP \: n \: FD) \\ P(TP) = 0.95×0.99 + 0.02×0.01 = 0.9407[/tex]
[tex]P(D/TP) = \frac{0.9405}{0.9407} = \frac{9405}{9407} [/tex]≈0.999787
Question 24: [1 + 1 + 1 + 1= 4 points]
Let X be a discrete random variable with the following
x 0.2 0.4 0.5 0.8 1
P(x) 0.1 0.2 0.2 0.3 0.2 (a) Find () , the range of the random variable X
Considering the given discrete probability distribution, the range of the variable X is given by:
Range(X) = {0.2, 0.4, 0.5, 0.8, 1}.
What is the range of a random variable?The range of a random variable is the set of all values that the variable can assume.
From the table, we have that X can assume the values of 0.2, 0.4, 0.5, 0.8 and 1, hence the range of the variable X is given by:
Range(X) = {0.2, 0.4, 0.5, 0.8, 1}.
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Which graph has a domain of -∞ < x < ∞ and a range of -∞ < y
The graph of the option in the question has a domain of -∞ < x < 3.5.
Please find attached the drawing of a graph that has a domain of -∞ < x < ∞ Which method can be used to find the graph that has a domain of -∞ < x < ∞?The domain of a graph are the possible x-values that can be obtained from the graph.
A graph that has a domain given by the inequality, -∞ < x < ∞ does not have a vertical asymptote.
An asymptote is a straight line to which a graph approaches, as either the x or y-value approaches infinity.
The given graph has a vertical asymptote at y ≈ 3.5
The domain of the given graph is therefore, -∞ < x < 3.5
Similarly, the graph has a horizontal asymptote at x ≈ 3
The range of the given graph is therefore, -∞ < y < 3.
A graph that has a domain of -∞ < x < ∞, extends to infinity to the left and the right of the graph.
A function that has a graph with a domain of -∞ < x < ∞ is one of direct proportionality.
An example is, y = x
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Write the following number in scientific notation.
788,000
Answer:
788,000 =
788 x 10^3
78.8 x 10^4
7.88 x 10^5
.788 x 10^6
and so on
The graph shows a system of inequalities.
Graph of two inequalities. One is a solid line increasing from left to right passing through negative 3 comma 0 and 0 comma 3, and it has shading below the line. The second is a solid upward opening parabola with a vertex at 1 comma negative 4 and x-intercepts at negative 1 comma 0 and 3 comma 0. This parabola is shaded inside the curve.
Which system is represented in the graph?
A. y > x2 –2x – 3
y > x + 3
B. y < x2 – 2x – 3
y < x + 3
C. y ≥ x2 – 2x – 3
y ≤ x + 3
D. y > x2 – 2x – 3
y < x + 3
The graphed system of inequalities is:
y ≥ x^2 - 2x - 3y ≤ x + 3So the correct option is the third one.
Which system is represented by the graph?On the graph we can see that the two lines are solid, so we need to use the symbols ≤ and ≥. (If instead, we had dashed lines, then we would need to use the symbols > and <).
We also can see that the region above the parabola is shaded (the shaded region represents the region of solutions for each inequality), and the region below the line is shaded, then the system of inequalities is of the form:
y ≥ parabola.y ≤ line.Only with that, we conclude that the correct option is the third option:
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Suppose you are in charge of setting up tables and ordering
appetizers and cookies for an awards dinner. The principal
expects 168 seventh-graders and 112 eighth-graders to attend
the dinner. Each grade will have dinner in a separate room.
1. Decide how many tables and how many chairs per table you will need, based on
the following criteria:
• No more than 15 tables in each room, and no more than 15
chairs per table.
• All tables in both rooms must have the same number of chairs.
Only 280 chairs can be ordered.
●
Answer: 10 tables in each room 14 kids at each table