The estimator sample proportion is mathematically unbiased
What is the estimator sample proportion?Generally, the equation for is mathematically given as
Population sample \mu=1.3
The sample to sample proprotion table will have
first column= 3,5 3,5 3,10,5,3 5,5 5,10 10,3 10,5 10,10
Second coumn= 0,0,0.5,0,0,0.5,05,0.5, total 3
The probability distribution of the distinct variance values table will have
p row=0,0.5,1, Total
probability row= 4/9, 4/9, 1/9, 1
In conclusion, The mean sample
x=3/9
x=1.3
Where
population sample \mu=1.3
\mu= x
Therefore the estimator sample proportion is unbiased for population mean
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Solve x 6x+2=2x-1 give your answer as a fraction in its simplest form
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathbf{6x + 2 = 2x - 1}[/tex]
[tex]\huge\textbf{SUBTRACT 2x to BOTH SIDES:}[/tex]
[tex]\mathbf{6x + 2 - 2x = 2x - 1 - 2x}[/tex]
[tex]\huge\textbf{Simplify it!}[/tex]
[tex]\mathbf{4x + 2 = -1}[/tex]
[tex]\huge\textbf{SUBTRACT 2 to BOTH SIDES:}[/tex]
[tex]\mathbf{4x + 2 - 2 = -1 - 2}[/tex]
[tex]\huge\textbf{Simplify it!}[/tex]
[tex]\mathbf{4x = -3}[/tex]
[tex]\huge\textbf{DIVIDE 4 to BOTH SIDES:}[/tex]
[tex]\mathbf{\dfrac{4x}{4} = \dfrac{-3}{4}}[/tex]
[tex]\huge\textbf{Simplify it!}[/tex]
[tex]\mathbf{x = \dfrac{-3}{4}}[/tex]
[tex]\mathbf{x = -\dfrac{3}{4}}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = -\dfrac{3}{4}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assigiment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]The number of column inches of classified advertisements appearing on Mondays in a certain daily newspaper is normally distributed with population mean of 320 and population standard deviation of 20 inches.
For a randomly chosen Monday, what is the probability there will be less than 340 column inches of classified advertisement?
For a randomly chosen Monday, the probability there will be less than 340 column inches of classified advertisement is 0.8413.
What is Normal Distribution?The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.
The number of column inches of classified advertisements appearing on Mondays in a certain daily newspaper is normally distributed with a population mean of 320 and a population standard deviation of 20 inches.
[tex]P(X < 340) = P(z < \dfrac{(340-320)}{20})[/tex]
= P(z < 1)
= 0.8413
Hence, For a randomly chosen Monday, the probability there will be less than 340 column inches of classified advertisement is 0.8413.
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1. A(–6 , 2) , B(4 ,7) are endpoints of a line segment.
(2) a) Calculate the length of AB.
(2) b) Calculate the slope of AB.
(2) c) Calculate the coordinates of the midpoint of AB.
(2) 2. Determine the radius of the circle .
State the answer as an exact number, and as a decimal rounded to 1 decimal place.
(2) 3 Write the equation of a circle with centre (0, 0) that passes through the point (5, –3)
The length of the line AB as described by points A and B in the task content is; √125.
What is the length of the line?a) The length of AB as described is;
AB = √((7-2)² + (4-(-6))²)
AB = √(25 + 100) = √125.
b) The slope of AB is;
Slope, m = (7-2)/(4-(-6)) = 5/10
Slope = 1/2.
c). The coordinates of the midpoint of AB are;
x = (4+(-6))/2 = -1
y = (7+2)/2 = 4.5
The midpoint is; (-1, 4.5).
2) The radius of the circle as described with centre (0, 0) that passes through the point (5, –3) is;
Radius = √((5-0)² + (-3-0)²)
Radius = √(25+9) = √34 = 5.8
3) Hence, the equation of a circle with centre (0, 0) that passes through the point (5, –3) is;
(x-5)² + (x-3)² = 5.8².
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PLEASE ANSWER ,in terms of the trigonometric ratios for BCD,what is the lenght of BD? insert text on the triangle in geogebrea to show the lenght of BD. take a screenshot of the triangle with the text,save it,and insert the image in the space below
By applying the law of sine, the length of side BD is equal to 9.05 cm and the image of right-angled triangle BCD is shown in the image attached below.
How to calculate the length of BD?In order to determine the length of side BD, we would apply the law of sine because both side BD and side BC represent the opposite side and hypotenuse of right-angled triangle BCD respectively.
Mathematically, the law of sine is given by this mathematical expression:
sin(θ) = Opp/Hyp
Where:
Opp is the opposite side of a right-angled triangle.Hyp is the hypotenuse of a right-angled triangle.θ is the angle.Substituting the parameters into the formula, we have;
sin(θ) = BD/BC
sin(74) = BD/9.41
Cross-multiplying, we have:
BD = 9.41 × sin(74)
BD = 9.41 × 0.9613
BD = 9.05 cm.
By applying the law of sine, the length of side BD is equal to 9.05 cm and the image of right-angled triangle BCD is shown in the image attached below.
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Helppppppp pleaseeeee
Answer:
is it asking how many times u would get then number 5 when u roll or asking how you would expect for the first 5 rolls?
Two student clubs were selling t-shirts and school notebooks to raise money for an upcoming school event. In the first few minutes, club A sold 3 t-shirts and 2 notebooks, and made $19. Club B sold 1 t-shirt and 1 notebook, for a total of $8. Use the given matrix equation to solve for the cost of t-shirts and notebooks that were sold. Explain the steps that you took to solve this problem.
A matrix with 2 rows and 2 columns, where row 1 is 3 and 2 and row 2 is 1 and 1, is multiplied by matrix with 2 rows and 1 column, where row 1 is x and row 2 is y, equals a matrix with 2 rows and 1 column, where row 1 is 19 and row 2 is 8.
Using a system of equations, it is found that the cost of a t-shirt is of $3 and the cost of a notebook is of $5.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
The variables are given as follows:
Variable x: Cost of a t-shirt.Variable y: Cost of a notebook.Considering the costs of the purchases of Clubs A and B, the matrices give the equations as follows:
3x + 2y = 19.x + y = 8 -> y = (8 - x).Hence, replacing the second equation into the first:
3x + 2(8 - x) = 19
x = 3.
y = 8 - x = 8 - 3 = 5.
The cost of a t-shirt is of $3 and the cost of a notebook is of $5.
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About 145 out of 500 students prefer walking instead of
riding the bus to school. About what percent of the
students prefer walking?
30%
50%
70%
145%
Answer:
30%
Step-by-step explanation:
[tex]\frac{145}{500} = 0.29[/tex] ≅ 0.30 or 30%
How many different strings can be made by shuffling the letters in DISCRETEMATHS?
Answer:
I found 14 but their might be more!
hope that helps! :)
Step-by-step explanation:
In AUVW, m/U = (9x - 8)°, m/V = (2x + 2)°, and m/W = (3x + 4)º.
Find m/V.
Answer:
m∠V = 28°
Step-by-step explanation:
In ΔUVW:
m∠U = (9x - 8)°m∠V = (2x + 2)°m∠W = (3x + 4)°To find the measure of angle V, first find the value of x.
Interior angles of a triangle sum to 180°.
⇒ m∠U + m∠V + m∠W = 180°
⇒ (9x - 8) + (2x + 2) + (3x + 4) = 180
⇒ 9x + 2x + 3x - 8 + 2 + 4 = 180
⇒ 14x - 2 = 180
⇒ 14x = 182
⇒ x = 13
Substitute the found value of x into the expression for angle V:
⇒ m∠V = 2(13) + 2
⇒ m∠V = 26 + 2
⇒ m∠V = 28°
Therefore, the measure of angle V is 28°.
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Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise unless otherwise indicated. ?C(lnx+y)dx−x2dy where C is the rectangle with vertices (1, 1), (3, 1), (1, 4), and (3, 4)
By Green's theorem,
[tex]\displaystyle \int_C P(x,y)\,dx + Q(x,y)\,dy = \iint_D \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} \, dA[/tex]
where [tex]D[/tex] is the interior of [tex]C[/tex]. It's easy to see that
[tex]D = \left\{(x,y) ~:~ 1 \le x \le 3 \text{ and } 1 \le y \le 4\right\}[/tex]
Now,
[tex]\dfrac{\partial Q}{\partial x} = \dfrac{\partial}{\partial x}(-x^2) = -2x[/tex]
[tex]\dfrac{\partial P}{\partial y} = \dfrac{\partial}{\partial y}(\ln(x) + y) = 1[/tex]
so that the line integral reduces to
[tex]\displaystyle \int_C (\ln(x)+y)\,dx - x^2\,dy = -\int_1^3 \int_1^4 (2x+1) \, dy\,dx = \boxed{-30}[/tex]
5. The function h(t) = 1 + 4t - 1.86t? models the height of a rock thrown upward on the planet Mars, where h(t) is height in meters and t is time in seconds. Use a graph to determine:
a. the maximum height the rock reaches
b. how long the rock will be above the surface
The maximum height the rock reaches 3.15 feet and the rock will be above the surface for 2.6 seconds
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
From the graph of the function h(t) = 1 + 4t - 1.86t²:
The maximum height the rock reaches 3.15 feet.
Time spent on air = 2.38 - (-0) = 2.38 seconds
The maximum height the rock reaches 3.15 feet and the rock will be above the surface for 2.6 seconds
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A rectangle has length of 10 mm. • and breadth 7mm calculate its perimeter YW
Answer:
34 mm
Step-by-step explanation:
P = 2 x (L + B) for a rectangle
P = 2 x (10 + 7) = 2 x 17 = 34
8 of 8
A vase with a circular base exerts a force of 15 N on a table with a pressure of 750 N/m2.
Find the radius of the base of the vase in cm to 2 dp.
The radius of the circular vase is 6.37 * 10^-3 m.
What is pressure?The term pressure is defined as the ratio of force to area. Hence we can write;
P = F/A
F = 15 N
P = 750 N/m2
A = F/P
A = 15 N/750 N/m2
A = 0.02 m^2
Now;
A = πr^2
r = √A/ π
r = √ 0.02/3.142
r = 6.37 * 10^-3 m
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DUE IN 3MINUTes
There is a strong positive linear correlation between rainfall and the number
of peaches a tree produces. Does this mean that more rainfall causes peach
trees to produce more fruit?
A. No. Any number of factors could also be affecting the number of
peaches produced.
B. No. Since rainfall and number of peaches are linearly correlated,
this means that more rainfall causes peach trees to produce less
fruit.
C. Yes. Since rainfall and number of peaches are positively
correlated, this means that more rainfall causes peach trees to
produce more fruit.
D. Yes. Since rainfall and number of peaches are linearly correlated,
this means that more rainfall causes peach trees to produce more
fruit.
Answer:
A. No.
Step-by-step explanation:
The job of science is to explain relationships in the real world. Scientists do this by making observations, forming theories regarding relationships, and conducting experiments to test those theories.
An observation of correlation may result in a theory that one of the correlated phenomena causes another. The correlation, by itself, does not demonstrate causation. Any number of other factors could be involved.
During the first year of life, a whale gains about 30 tons of weight what is the average weight gain per month?
A rectangular prism with a base that is
5 inches by 4 inches and a height of 15 inches.
The surface area and the volume of the rectangular prism are 310 in² and 300 in³, respectively.
How to find the volume of a right rectangular prism?Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units, then its volume is given as:
V = a × b × c unit³
The surface area of the prism = 2[(5×4)+(15×4)+(15×5)]
= 310 inches²
The volume of the prism = 5 × 4 × 15
= 300 in³
Hence, the surface area and the volume of the rectangular prism are 310 in² and 300 in³, respectively.
The complete question is:
A rectangular prism with a base that is 5 inches by 4 inches and a height of 15 inches. Find the volume and the surface area of the rectangular prism?
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The table below shows the number of correct answers that students gave on a recent 5-question quiz. Which of the following statements is true? Number Correct 1 2 3 4 5 3 46 9 8 Frequency
The true statement about the number of correct answers is that the: A. median = mode.
How to calculate the mean?Mathematically, the mean for the number of correct answers can be calculated by using the following formula:
Mean = [F(x)]/n
Total frequency, n = 3 + 4 + 6 + 9 + 8 = 30.
F(x) = [(1 × 3) + (2 × 4) + (3 × 6) + (4 × 9) + (5 × 8)] = 105.
Mean = 105/30
Mean = 3.5.
For the median, we have:
The median for the number of correct answers is the average of the 15th and 16th number:
Median = (4 + 4)/2
Median = 8/2
Median = 4.
For the mode, we have:
The mode for the number of correct answers is the answer with the highest frequency, which is 4 with a frequency of 9.
Therefore, the true statement about the number of correct answers is that the median is equal to mode.
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Complete Question:
The table below shows the number of correct answers that students gave on a recent -question quiz. Which of the following statements is true?
A. median = mode
B. mode > median
C. mode < mean
D. mean > median Reset Selection
1000 mL of D5W is infusing at 20 gtt/min (20 macrogtt/min). Drop factor: 10 gtt/m L.
How long will it take for the IV to infuse? (Express time in hours and minutes
It would take about 8 hours 20 minutes for the 1000 mL of D5W to infuse completely.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that the drop factor is 10 gtt/mL, hence:
Infuse rate = 20 gtt/min ÷ 10 gtt/mL = 2 mL/min
Time taken = 1000 mL / 2 mL per min = 500 min = 8 hours, 20 minutes.
It would take about 8 hours 20 minutes for the 1000 mL of D5W to infuse completely.
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Answer:
Step-by-step explanation:
900mL of RL is infusing at 80 gtt/min (80 macrodrops/min). Drop factor: 15 gtt/mL
calculate the value of the sample variance of 13,−2,−2,−2,13,13,−5
Answer:
13, -2
Step-by-step explanation:
Use
f(x) = 2x − 3
and
g(x) = 4 − x2
to evaluate the expression.
The equation based on the information given will be x⁴ + 8x² - 12.
How to compute the value?It should be noted that from the information given, the expression to compute will be:
= g - g(x)²
This will be:
= 4 - (4 - x²)²
= 4 - (4 - x)(4 - x)
= 4 - (15 - 8x² + x⁴)
= x⁴ + 8x² - 12
The complete question is:
Use f(x) = 2x − 3 and g(x) = 4 − x² to evaluate the expression g - g(x)².
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Bag A contains 7 blue discs, 4 red discs and 1 yellow disc.
Bag B contains 3 blue discs and 6 red discs.
A disc is drawn at random from Bag A and placed in Bag B.
A disc is then drawn at random from Bag B.
Find the probability that the disc drawn from Bag B is red.
Answer:
75% or 65%
Step-by-step explanation: that's what I did at lest
A
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Lennox had been scheduling employees based on the assumption that the
following distribution represented when people made purchases in his store.
Time slot
Predicted
percentage
8 a.m.-12 p.m.
25%
12-4 p.m.
40%
4-8 p.m. 8-12 a.m.
25%
10%
He took a random sample of 300 purchases and recorded their time slot so he
could test whether this was an accurate distribution. Here are his results:
Time slot 8 a.m.-12 p.m. 12-4 p.m. 4-8 p.m.
Purchases
75
120
90
Choose 1 answer:
8-12 a.m.
15
He wants to use these results to carry out a x² goodness-of-fit test to determine
if the distribution of time slots of the purchases disagrees with his assumed
distribution.
What are the values of the test statistic and P-value for Lennox's test?
The test value and the p value for the probability are 10.5 and 0.0148.
How to illustrate the probability?Based on the information, the observed and expected values will be:
Observed. Expected
75. 75
100. 120
90. 75
15. 30
The p value based on the test statistic from the distribution table will be 0.0148.
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The function f(x) is graphed. It represents a translation of the square root function g(x) = .
What equation represents the graph of f(x)?
f(x) =
f(x) =
f(x) = – 1
f(x) = + 1
The equation that represents the graph of f(x) is [tex]f(x) = \sqrt {x - 1[/tex]
How to determine the equation of f(x)?The complete question is in the attached image
The parent square root function is:
[tex]g(x) = \sqrt x[/tex]
From the graph,
g(x) is shifted one unit right to get f(x)
This is represented as:
f(x) = g(x - 1)
So, we have:
[tex]f(x) = \sqrt {x - 1[/tex]
Hence, the equation that represents the graph of f(x) is [tex]f(x) = \sqrt {x - 1[/tex]
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2. What is the radius of a circle (rounded to the nearest tenth) that has a circumference of 87 cm?
O 10.5
27.7
13.8
5.3
3.
A = pi x r^2
48 = 3.141... x r^2
÷ by value of pi
15.278... = r^2
Square root the ans, to get r
Thus, R = 3.908..... So, radius is 3.9
2.
Circumference = pi x diameter
87. = 3.141... x d
÷ by value of pi
27.692............. = diameter
Radius is twice the diameter. So, divide diameter by 2 to find the radius.
27.692.....÷ 2 = 13.846...
Thus, radius is 13.8cm
Hope this helps!
20 points/ Brainliest!!
What set of transformations are applied to parallelogram ABCD to create A”B”C”D?
Answer:
A) Reflected over the x axis and reflected over the y-axisStep-by-step explanation:
ABCD moves 2 quadrants, so has to move over 2 axes.
So, the only option that would work is A).
Hope this helps.
What is the domain indicated on the graph for each
portion of the piecewise function?
-2,
2x + 1,
--—-x,
f(x)=
Domain 1st piece
Domain 2nd piece
Domain 3rd piece
Step-by-step explanation:
try this option, all the details are in the attachment.
The square shown has a perimeter of 32 units. The square is rotated about line k. what is the circumfrence of the base
The circumference equal to 25 units
What is perimeter of square?The perimeter of square is 4 times the side.
P= 4* side
The perimeter of the square,
4x = P
Now P is = 32 units then,
32 units = 4(x)
x = 8 inches
So, the diameter of the cylinder formed by the rotation of 8 inches
Now, the circumference of the base is
C = 2πr = πD
If r =8 inches
C = π(8 units) = 8π units
C = 8(3.14) = 25.12 units
Hence, the circumference equal to 25 units
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The following graph shows a proportional relationship.
What is the constant of proportionality between y and x in the graph?
Answer:
[tex]k=2[/tex]
Step-by-step explanation:
The constant of proportionality is given as [tex]k=\frac{y}{x}[/tex] .
Notice that when [tex]x=2[/tex] it follows that [tex]y=4[/tex].
Substitute [tex]x=2[/tex] and [tex]y=4[/tex] into the formula for the constant:
[tex]k=\frac{4}{2}=2[/tex] .
Therefore, the constant is equal to 2.
You work as an assistant for a local musical theatre group, the Main Street Theatre Company. The company is putting on a production of Les Misérables this year, and they need your help planning it.
Since the role of young Cosette is played by a child, the Main Street Theatre company must actually cast 3 girls in the role of young Cosette, and alternate girls from night to night. (This is because of restrictions on working hours for children.) You have received headshots and resumes from 25 girls who wish to audition for young Cosette.
When casting the first young Cosette, the casting director has _[blank 1]_ girls to choose from. When casting the second young Cosette, she has _[blank 2]_ girls to choose from, and when casting the third young Cosette, she has _[blank 3]_ girls to choose from.
Match each numbered blank to the answer that correctly satisfies the corresponding blank in the previous sentences.
The required blank 1, blank 2 and blank 3 would be filled with 25 girls, 22 girls, 19 girls respectively.
Theatre company must cast 3 girls.
And has 25 resumes girls who wish audition.
permutation can be defined as study of combinations.
In the question we are asked to calculate the number of girls left after the director chooses.
At first director chooses 3 from 25.
At second director chooses 3 from 22.
At third director chooses 3 from 19.
Thus, the required blank 1, blank 2 and blank 3 would be filled with 25 girls, 22 girls, 19 girls respectively.
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Really need help on this one!!