Using the z-statistic relation given, the value of the z-statistic in the scenario would be 0.61
Z - statistic relationshipThe Z-statistic relation is written thus:
z = (phat - p) / √(p * q / n)phat = 140 / 200 = 0.7
p = 0.68
q = 1 - p = 0.32
n = 200
Inputting the values into our formula
z = (phat - p) / sqrt(p * q / n)
= (0.7 - 0.68) / sqrt(0.68 * 0.32 / 200)
= 0.02 / 0.0583
= 0.61
Therefore, Z-statistic is 0.61
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9497 ÷ 16 _R_ please
Find the area of quadrilateral QUAD, whose vertices are:
Q (-4, 3), U (3, 6), 1 (6, 3), and D (1, -4).
The area of quadrilateral QUAD is 2.5 square units.
To find the area of quadrilateral QUAD with vertices Q (-4, 3), U (3, 6), 1 (6, 3), and D (1, -4), we can use the Shoelace formula (also known as Gauss's area formula or the surveyor's formula).
The Shoelace formula states that the area of a polygon with vertices (x1, y1), (x2, y2), ..., (xn, yn) can be calculated as:
[tex]Area = 1/2 * |(x1y2 + x2y3 + ... + xny1) - (x2y1 + x3y2 + ... + x1yn)|[/tex]
Using this formula, we can calculate the area of quadrilateral QUAD as follows:
Area = [tex]1/2 * |(-46 + 33 + 6*(-4) + 13) - (33 + 6*(-4) + 1*(-4) + (-4)*3)|[/tex]
Simplifying the expression, we get:
[tex]Area = 1/2 * |(-24 + 9 - 24 + 3) - (9 - 24 - 4 - 12)|Area = 1/2 * |(-36) - (-31)|Area = 1/2 * |-36 + 31|Area = 1/2 * |-5|Area = 1/2 * 5Area = 5/2[/tex]
The area of quadrilateral QUAD is 2.5 square units.
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The area of quadrilateral QUAD is 17.5 square units.
The area of quadrilateral QUAD, we can use the Shoelace Formula, also known as the Gauss's Area Formula.
The formula states that if the coordinates of the vertices of a polygon are given in order, then the area of the polygon can be calculated using the following formula:
Area = 1/2 × |(x1y2 + x2y3 + ... + xn-1yn + xny1) - (y1x2 + y2x3 + ... + yn-1xn + ynx1)|
Let's apply this formula to find the area of quadrilateral QUAD:
Q (-4, 3)
U (3, 6)
A (6, 3)
D (1, -4)
Area = 1/2 × |(-4 × 6 + 3 × 3 + 6 × (-4) + 3 × (-1)) - (3 × 3 + 6 × (-4) + (-4) × (-1) + (-1) × (-4))|
Area = 1/2 × |(-24 + 9 - 24 - 3) - (9 - 24 + 4 + 4)|
Area = 1/2 × |(-42) - (-7)|
Area = 1/2 × |-42 + 7|
Area = 1/2 × |-35|
Area = 1/2 × 35
Area = 17.5
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pls help !!!!!! geometry
How much fencing is required to enclose a circular garden whose radius is 21 m
Answer:182.12 meters of fencing required.
Step-by-step explanation:
(08.01 MC)
The function h(x) is a continuous quadratic function with a domain of all real numbers. The table
x h(x)
-6 12
-57
-4 4
-3 3
-24
-1 7
What are the vertex and range of h(x)?
The vertex of h(x) is (-3, 3), and the range is y ≥ 3.
To find the vertex of the quadratic function h(x), we can use the formula x = -b/2a, where the quadratic function is in the form [tex]ax^2 + bx + c[/tex].
From the given table, we can observe that the x-values of the vertex correspond to the minimum points of the function.
The minimum point occurs between -4 and -3, which suggests that the x-coordinate of the vertex is -3. Therefore, x = -3.
To find the corresponding y-coordinate of the vertex, we look at the corresponding h(x) value in the table, which is 3. Hence, the vertex of the function h(x) is (-3, 3).
To determine the range of h(x), we need to consider the y-values attained by the function.
From the table, we see that the lowest y-value is 3 (the y-coordinate of the vertex), and there are no other y-values lower than 3. Therefore, the range of h(x) is all real numbers greater than or equal to 3.
The vertex of h(x) is (-3, 3), and the range is y ≥ 3.
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The vertex of the quadratic function is (-4, 12).
The range of h(x) is [3, ∞).
To find the vertex and range of the quadratic function h(x) based on the given table, we can use the properties of quadratic functions.
The vertex of a quadratic function in the form of f(x) = ax² + bx + c can be determined using the formula:
x = -b / (2a)
The domain of h(x) is all real numbers, we can assume that the quadratic function is of the form h(x) = ax² + bx + c.
Looking at the table, we can see that the x-values are increasing from left to right.
Additionally, the y-values (h(x)) are increasing from -6 to -4, then decreasing from -4 to -1.
This indicates that the vertex of the quadratic function lies between x = -4 and x = -3.
To find the exact x-coordinate of the vertex, we can use the formula mentioned earlier:
x = -b / (2a)
Based on the table, we can choose two points (-4, 4) and (-3, 3).
The difference in x-coordinates is 1, so we can assume that a = 1.
Plugging in the values of (-4, 4) and a = 1 into the formula, we can solve for b:
-4 = -b / (2 × 1)
-4 = -b / 2
-8 = -b
b = 8
The equation of the quadratic function h(x) can be written as h(x) = x² + 8x + c.
Now, let's find the y-coordinate of the vertex.
We can substitute the x-coordinate of the vertex, which we found as -4, into the equation:
h(-4) = (-4)² + 8(-4) + c
12 = 16 - 32 + c
12 = -16 + c
c = 28
The equation of the quadratic function h(x) is h(x) = x² + 8x + 28.
The range of the quadratic function can be determined by observing the y-values in the table.
From the table, we can see that the minimum y-value is 3.
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I don’t understand can I get answers please
Answer:
c=25
Step-by-step explanation:
Since you are given [tex]x^{2}[/tex]+10x+c
We know that in an equation of [tex]ax^{2}+bx+c[/tex], when a = 1, c can be found by [tex](\frac{b}{2})^{2}[/tex]
So c = [tex](10/2)^{2}[/tex]=[tex]5^{2}[/tex]=25
A sixth-grade class recorded the number of letters in each student's first name.
The results are shown in the dot plot.
A dot plot titled lengths of student names show the number of students with a certain number of letters in their name. The data is as follows. 1 dot above 3, 2 dots above 4, 4 dots above 5, 7 dots above 6 and 7, 3 dots above 8, 1 dot above 9, 2 dots above 10, and 3 dots above 11.
Which is the best representation of the center of this data set?
A. 8
B. 5
C. 7
D. 6
A bacteria culture triples every 5 minutes. At 4:27 P.M. the population is . Determine what the population was 27 minutes earlier, at 4:00 P.M.
The population at 4:00 P.M., 27 minutes earlier, is[tex]3^3[/tex] times the initial population P.
To determine the population of a bacteria culture 27 minutes earlier, we need to calculate the population growth from 4:00 P.M. to 4:27 P.M. given that the bacteria culture triples every 5 minutes.
Let's break down the time period into intervals of 5 minutes:
From 4:00 P.M. to 4:05 P.M., the population triples once.
From 4:05 P.M. to 4:10 P.M., the population triples again.
From 4:10 P.M. to 4:15 P.M., the population triples for the third time.
From 4:15 P.M. to 4:20 P.M., the population triples for the fourth time.
From 4:20 P.M. to 4:25 P.M., the population triples for the fifth time.
From 4:25 P.M. to 4:27 P.M., the population undergoes partial growth.
Since the population triples every 5 minutes, we can express the population at 4:27 P.M. as 3^5 times the initial population at 4:00 P.M.
Let's denote the initial population at 4:00 P.M. as P. Then, the population at 4:27 P.M. is [tex]3^5[/tex] * P.
To find the population 27 minutes earlier, we need to reverse the growth from 4:27 P.M. to 4:00 P.M. Since the population triples every 5 minutes, we need to divide the population at 4:27 P.M. by [tex]3^{(27/5).[/tex]
Therefore, the population at 4:00 P.M., 27 minutes earlier, can be calculated as:
Population at 4:00 P.M. = (Population at 4:27 P.M.) / [tex]3^{(27/5)[/tex]
[tex]= (3^{5} * P) / 3^{(27/5)\\\\\\\\= 3^{(25/5)} * P\\= 3^5 * P / 3^2\\= 3^3 * P[/tex]
Hence, the population at 4:00 P.M., 27 minutes earlier, is 3^3 times the initial population P.
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Reynold’s company has a product with fixed costs of $334,000, a unit selling price of $22, and unit variable costs of $19. The break-even sales (units) if the variable costs are decreased by $4 is
The break-even sales (units) when the variable costs are decreased by $4 is approximately 47,714 units.
To find the break-even sales (units) when the variable costs are decreased by $4, we need to calculate the new unit variable costs and then use the break-even formula.
Fixed costs (F) = $334,000
Unit selling price (P) = $22
Unit variable costs (V) = $19
Change in unit variable costs = $4
New unit variable costs (V') = V - Change in unit variable costs
= $19 - $4
= $15
Now, let's calculate the break-even sales (units) using the formula:
Break-even sales (units) = Fixed costs / (Unit selling price - Unit variable costs)
Break-even sales (units) = $334,000 / ($22 - $15)
= $334,000 / $7
= 47,714.29
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Which function is graphed ?
Select the correct answer. Which fraction converts to a terminating decimal number? A. 1\6 B. 2\9 C. 3\8 D. 4\7
The fraction that converts to a terminating decimal number is C. 3/8.
To determine which fraction converts to a terminating decimal number, we need to analyze the denominator of each fraction. A fraction will result in a terminating decimal if its denominator has only prime factors of 2 and/or 5.
Let's examine each option:
A. 1/6: The denominator is 6, which can be factored into 2 * 3. Since 3 is not a factor of 2 or 5, this fraction does not convert to a terminating decimal.
B. 2/9: The denominator is 9, which can be factored into 3 * 3. Since 3 is not a factor of 2 or 5, this fraction does not convert to a terminating decimal.
C. 3/8: The denominator is 8, which can be factored into 2 * 2 * 2. Since all the factors are 2, this fraction does convert to a terminating decimal.
D. 4/7: The denominator is 7, which cannot be factored into 2 or 5. Therefore, this fraction does not convert to a terminating decimal.
Based on our analysis, the fraction that converts to a terminating decimal number is C. 3/8.
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find the value of b
A. 14
B. 15
C. 64
D. 289
[tex] \sf \hookrightarrow \: {8}^{2} + {b}^{2} = {17}^{2} [/tex]
[tex] \sf \hookrightarrow \: 8 \times 8 + {b}^{2} = 17 \times 17[/tex]
[tex] \sf \hookrightarrow \: 8 \times 8 + {b}^{2} = 289[/tex]
[tex] \sf \hookrightarrow \: 64 + {b}^{2} = 289[/tex]
[tex] \sf \hookrightarrow \: {b}^{2} = 289 - 64[/tex]
[tex] \sf \hookrightarrow \: {b}^{2} = 225[/tex]
[tex] \sf \hookrightarrow \: b = \sqrt{225} [/tex]
[tex] \sf \hookrightarrow \: b = \sqrt{15 \times 15} [/tex]
[tex] \sf \hookrightarrow \: b = 15[/tex]
B) b = 15 ✅The first three steps in determining the solution set of
the system of equations algebraically are shown.
y=x²-x-3
y=-3x + 5
Step
1
2
3
Equation
x²-x-3=-3x+5
0=x²+
+2x-8
0=(x-2)(x+4)
What are the solutions of this system of equations?
O (-2,-1) and (4, 17)
O (-2, 11) and (4, -7)
O (2, -1) and (-4, 17)
(2, 11) and (-4,-7)
The solutions of the system of equations are (2, -1) and (-4, 17)
The given system of equations is:
y = x² - x - 3
y = -3x + 5
To find the solutions, we need to solve these equations simultaneously.
Set the equations equal to each other:
x² - x - 3 = -3x + 5
Simplify and rewrite the equation in standard form:
x² - x + 3x - 3 - 5 = 0
x² + 2x - 8 = 0
Factor the quadratic equation:
(x - 2)(x + 4) = 0
Now we can solve for x by setting each factor equal to zero:
x - 2 = 0 or x + 4 = 0
Solving for x, we get:
x = 2 or x = -4
To find the corresponding y-values, we substitute these x-values into either of the original equations. Let's use equation 1):
For x = 2:
y = (2)² - 2 - 3 = 4 - 2 - 3 = -1
For x = -4:
y = (-4)² - (-4) - 3 = 16 + 4 - 3 = 17
As a result, the system of equations has two solutions: (2, -1) and (-4, 17).
The right responses are therefore (2, -1) and (-4, 17).
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(-14)+x=14[/tex] what is the answer
The equation (-14) + x = 14 is solved by adding 14 to both sides of the equation, resulting in x = 28. This means that 28 is the value of x that satisfies the equation and makes it true.
To solve the equation (-14) + x = 14, we need to isolate the variable x on one side of the equation. Let's go through the steps:
Step 1: Add 14 to both sides of the equation to eliminate the -14 on the left side.
(-14) + x + 14 = 14 + 14
x = 28
The solution to the equation (-14) + x = 14 is x = 28.
In this equation, we start with (-14) on the left side, and we want to determine the value of x that makes the equation true. To do that, we need to isolate x. By adding 14 to both sides of the equation, we cancel out the -14 on the left side, leaving us with just x. On the right side, 14 + 14 simplifies to 28.
Therefore, the solution to the equation is x = 28. This means that if we substitute 28 for x in the original equation, (-14) + 28 will indeed equal 14. Let's verify this:
(-14) + 28 = 14
14 = 14
The left side of the equation simplifies to 14, and the right side is also 14. Since both sides are equal, it confirms that x = 28 is the correct solution to the equation.
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Find the local and absolute maximum and minimum points in (x, y) format for the
function f(x) = 3/5x^5 - 9x^3 + 2 on the closed interval [-4,5]. Answer the following
questions.
a) Find all critical numbers (x- coordinates only)
b) Find the intervals on which the graph is increasing Mark critical numbers
8. Amy has $30 to spend. She wants to buy pounds of lemons at $2 per pound, a box for $4, and 7 frozen dinners for $3 each Choose True or False for each statement. A She will not have enough money to buy everything O True O False 8 She will have $1 left over. O True O False C The total cost is $39. O True O False
Answer:she will actually need 1 dollar because all of that would be 31 dollars.
Step-by-step explanation:
3 pounds of lemons= $6
1 box of rice= $4
7 frozen diners= $21
6+4=10
10+21=31
a) Write a linear system to model the situation:
For the school play, the cost of one adult ticket is $6 and the cost of one student ticket is $4. Twice as many student tickets as adult tickets were sold. The total receipts were $2016.
b) Use substitution to solve the related problem:
How many of each type of ticket were sold?
Answer:
There were 126 student tickets sold and 252 adult ticket sold.
Step-by-step explanation:
Let x be the number of adult tickets sold
y be the number of students tickets sold
Twice as many student tickets as adult tickets were sold
a.
x = 2y ---equation 1
6x + 4y = 2016 ---equation 2
b.
Substitute equation 1 to equation 2
6(2y) + 4y = 2016
12y + 4y = 2016
16y = 2016
Divide both sides of the equation by 16
16y/16 = 2016/16
y = 126
Substitute y = 126 to equation 1
x = 2y
x = 2(126)
x = 252
CAPM Elements
Value
Risk-free rate (rRF
)
Market risk premium (RPM
)
Happy Corp. stock’s beta
Required rate of return on Happy Corp. stock
An analyst believes that inflation is going to increase by 2.0% over the next year, while the market risk premium will be unchanged. The analyst uses the Capital Asset Pricing Model (CAPM). The following graph plots the current SML.
Calculate Happy Corp.’s new required return. Then, on the graph, use the green points (rectangle symbols) to plot the new SML suggested by this analyst’s prediction.
Happy Corp.’s new required rate of return is .
The new required rate of return for Happy Corp. can be calculated using the Capital Asset Pricing Model (CAPM). The formula for CAPM is:
Required rate of return = Risk-free rate + Beta * Market risk premium
Since the analyst believes that the market risk premium will be unchanged, the only factor that will affect the new required return is the risk-free rate.
Given that the analyst predicts a 2.0% increase in inflation, the risk-free rate will also increase by that amount. Therefore, the new required rate of return for Happy Corp. will be the current risk-free rate plus the product of Happy Corp.'s beta and the market risk premium.
To plot the new Security Market Line (SML) on the graph, we would use the new required return calculated above and plot it against the corresponding beta values. The SML represents the relationship between risk (beta) and return (required rate of return).
By incorporating the new required return, we can determine the new expected returns for various levels of beta and create the updated SML.
It is important to note that without specific values provided for the risk-free rate, market risk premium, and Happy Corp.'s beta, it is not possible to calculate the exact new required return or plot the new SML accurately.
These values are crucial in determining the precise position of the SML on the graph.
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How do you find the circumference of a circle with a diameter of 6 inches. Use 3.14 as estimate of tt that's correct to two decimal places
Answer: 18.84
Step-by-step explanation : To find the circumference you use the formula:
2πr
Since we have the diameter (6), divide by 2 to find the radius, or r.
So (2)(3.14)(3)
What is the radius of a circle that has a circumference of 68 cm
Step-by-step explanation:
The formula to calculate the circumference (C) of a circle is C = 2πr, where r represents the radius of the circle.
In this case, the given circumference is 68 cm. Plugging this value into the formula, we can solve for the radius (r):
68 = 2πr
To find the radius, we can divide both sides of the equation by 2π:
r = 68 / (2π)
Using an approximate value of π ≈ 3.14159, we can calculate the radius:
r ≈ 68 / (2 × 3.14159) ≈ 10.8419 cm
Therefore, the radius of the circle, which has a circumference of 68 cm, is approximately 10.8419 cm.
Therefore, The Radius of the Circle is 10.8 cm.
Find the measure of the indicated angle.
20°
161°
61°
73°
H
G
F
73 ° E
195 °
Answer:
(c) 61°
Step-by-step explanation:
You want the measure of the external angle formed by a tangent and secant that intercept arcs of 73° and 195° of a circle.
External angleThe measure of the angle at F is half the difference of intercepted arcs HE and EG.
(195° -73°)/2 = 122°/2 = 61°
The measure of angle F is 61°.
<95141404393>
what is the midpoint of 70 and 90
Answer:
80
Step-by-step explanation:
Just average the two numbers to get (70+90)/2 = 160/2 = 80
Answer:
Step-by-step explanation:
To find the midpoint between two numbers, you add them together and divide the sum by 2.
In this case, the midpoint between 70 and 90 would be:
(70 + 90) / 2 = 160 / 2 = 80.
Therefore, the midpoint between 70 and 90 is 80.
recursive formula for an=1/8(2)n-1
Answer:
The recursive formula for an=1/8(2)n-1 is:
a1=1/8 an+1=1/8(2)(n)
This formula defines a sequence where each term is equal to 1/8 of the previous term multiplied by 2.
Step-by-step explanation:
Determine the percentile of 6.2 using the following data set.
4.2 4.6 5.1 6.2 6.3 6.6 6.7 6.8 7.1 7.2
Your answer should be an exact numerical value.
The percentile of 6.2 is |
%.
The percentile of 6.2 in the given data set is 40%.
To determine the percentile of 6.2 in the given data set, we can use the following steps:
Arrange the data set in ascending order:
4.2, 4.6, 5.1, 6.2, 6.3, 6.6, 6.7, 6.8, 7.1, 7.2
Count the number of data points that are less than or equal to 6.2. In this case, there are 4 data points that satisfy this condition: 4.2, 4.6, 5.1, and 6.2.
Calculate the percentile using the formula:
Percentile = (Number of data points less than or equal to the given value / Total number of data points) × 100
In this case, the percentile of 6.2 can be calculated as:
Percentile = (4 / 10) × 100 = 40%
The percentile of 6.2 in the sample data set is therefore 40%.
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Algebra
Solve for k: 10-10|-8k+4|=10
Write your answer in set notation.
The solution for k in the equation 10 - 10|-8k + 4| = 10, expressed in set notation, is {1/2}.
1. Start with the equation: 10 - 10|-8k + 4| = 10.
2. Simplify the expression inside the absolute value brackets: -8k + 4.
3. Remove the absolute value brackets by considering two cases:
Case 1: -8k + 4 ≥ 0 (positive case):
-8k + 4 = -(-8k + 4) [Removing the absolute value]
-8k + 4 = 8k - 4 [Distributive property]
-8k - 8k = -4 + 4 [Group like terms]
-16k = 0 [Combine like terms]
k = 0 [Divide both sides by -16]
Case 2: -8k + 4 < 0 (negative case):
-8k + 4 = -(-8k + 4) [Removing the absolute value and changing the sign]
-8k + 4 = -8k + 4 [Simplifying the expression]
0 = 0 [True statement]
4. Combine the solutions from both cases: {0}.
5. Check if the solution satisfies the original equation:
For k = 0: 10 - 10|-8(0) + 4| = 10
10 - 10|4| = 10
10 - 10(4) = 10
10 - 40 = 10
-30 = 10 [False statement]
6. Since k = 0 does not satisfy the equation, it is not a valid solution.
7. Therefore, the final solution expressed in set notation is {1/2}.
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What is the distance between points R (5, 7) and S(-2,3)?
Answer:
d ≈ 8.1
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = R (5, 7 ) and (x₂, y₂ ) = S (- 2, 3 )
d = [tex]\sqrt{(-2-5)^2+(3-7)^2}[/tex]
= [tex]\sqrt{(-7)^2+(-4)^2}[/tex]
= [tex]\sqrt{49+16}[/tex]
= [tex]\sqrt{65}[/tex]
≈ 8.1 ( to 1 decimal place )
What is the symbol ~, if you're trying to find the probability of ~A?
the addition probability
the probability of the event not happening
the multiplication probability
None of these choices are correct.
(−x² − 1) ÷ (x + 1)
Help
determine the surface area and volume
The surface area and the volume of the rectangular prism are 280 and 300
How to determine the surface area and volumeFrom the question, we have the following parameters that can be used in our computation:
The rectangular prism
The surface area is caculated as
Surface area = 2 * (10 * 5 + 10 * 6 + 5 * 6)
Evaluate
Surface area = 280
For the volume, we have
Volume = 10 * 5 * 6
Evaluate
Volume = 300
Hence, the surface area and the volume are 280 and 300
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Please answer ASAP I will brainlist
Answer:
x = - 2 , x = 4
Step-by-step explanation:
the x- intercepts are the points on the x- axis where the graph crosses
the graph crosses the x - axis at - 2 and 4 , then
x- intercepts are x = - 2 , x = 4