Answers
Given the function :
[tex]f(x)=\log _5x+2[/tex]The graph of the function will be as shown in the following picture
The function will have a vertical asymptote which is the line : x = 0
As shown in the figure :
Domain = ( 0 , ∞ )
Range = ( -∞ , ∞ ) or all real numbers
Related Questions
It takes 3/4 of an hour for an automated sprinkler to cover 2/7 of a lawn after an hour has passed what fraction of the lawn has been covered
Answers
Answer:
x=8/21
Step-by-step explanation:
(3/4)/(2/7) = 1/x
(3/4)x = (2/7)
x = (2/7) / (3/4)
x = (2/7) * (4/3)
x = 8/21
A=16xx-6use the given area to find the missing sides of the rectangle
Answers
The area of the rectangle is given as 16 units squared
The length = x
The width = x-6
The area of a rectangle is given by the formula;
A= l * w
A= x {x-6}
16 = x^2 -6x -----------form a quadratic equation as;
[tex]x^2-6x-16\text{ =0}[/tex]Find the factors of -16 that can add or subtract to give -6
The factors will be -8 and 2
Factorize the equation as ;
[tex]x^2+2x-8x-16=0[/tex][tex]x(x+2)-8(x+2)=0[/tex][tex](x+2)(x-8)=0[/tex]Finding the real values of x , take that which will result to a positive length
( x-8) = 0
x-8 = 0
x= 8 units
So ; Length = x = 8 units
Width = x- 6 = 8-6 = 2 units
Answers
Length = 8 units
Width = 2 units
Peyton go shopping she finds two shirts one cost $24.97 the other cost $13.75 she needs to know if she has enough money to buy both shirt using mental math she rounds $24.97 to $25 and add that to $13.75 to get $38.75 how does Peyton need to say to find the exact a total of 2 shirts
Answers
We know that Peyton wants to buy two shirts.
• First shirt cost $24.97.
,• Second shirt cost $13.75.
To do the mental math is ok to round $24.97 to $25, and them sum with $13.75.
However, to get the exact number, Peyton needs to subtract 3 pennies from the last amount $38.75, becuase she rounded before.
Therefore, to find the exact amount she needs to subtract 3 pennies.
2^4c^-10 to a fraction
Answers
The given expression is
[tex]2^4c^{-10}[/tex]We have to solve the power of 2.
[tex](2\cdot2\cdot2\cdot2)c^{-10}=16c^{-10}[/tex]Then, we use the property for negative exponents.
[tex]a^{-b}=\frac{1}{a^b}[/tex]This means we have to move the power to the denominator.
[tex]\frac{16^{}}{c^{10}}[/tex]Therefore, the fraction is[tex]\frac{16}{c^{10}}[/tex]What is the effect on the graph of f(x) = x2 when it is transformed toh(x) = 3x2 + 12?A. The graph of f(x) is horizontally compressed by a factor of 5 andshifted 12 units up.O B. The graph of f(x) is vertically compressed by a factor of 5 andshifted 12 units to the left.O C. The graph of f(x) is horizontally stretched by a factor of 5 andshifted 12 units to the left.O D. The graph of f(x) is vertically compressed by a factor of 5 andshifted 12 units up.SUBMIT
Answers
the fraction 1/5 horizontally expands the graph and the constant 12 move up the graph because is a sum
so the right option is the last
D. The graph of f(x) is vertically compressed by a factor of 5 and
shifted 12 units up
a regular square pyramid has base whose area is 250 cm^2. a section parallel to the base and 31.8 cm above it has an area of 40 cm^2 . find the ratio of the volume of the frustum to the volume of the pyramid.
Answers
We are given that the area of the base of a pyramid is 250 cm^2. We are asked to determine the ratio of the volumes of the frustum and the volume of the pyramid. To do that, let's remember that the volume of a pyramid is given by:
[tex]V=\frac{1}{3}A_bh[/tex]Where:
[tex]\begin{gathered} A_b=\text{ area of the base} \\ h=\text{ height} \end{gathered}[/tex]Now, the volume of the frustum is given by:
[tex]V_f=\frac{1}{3}h_f(A_b+A_f+\sqrt[]{A_bA_f})[/tex]Where:
[tex]\begin{gathered} h_f=\text{ height of the frustum} \\ A_f=\text{ area of the base of the frustum} \end{gathered}[/tex]Now, the ratio of between the volume of the frustum and the volume of the pyramid is:
[tex]\frac{V_f}{V_{}}=\frac{\frac{1}{3}h_f(A_b+A_f+\sqrt[]{A_bA_f})}{\frac{1}{3}A_bh_{}}[/tex]We can cancel out the 1/3 and we get:
[tex]\frac{V_f}{V_{}}=\frac{h_f(A_b+A_f+\sqrt[]{A_bA_f})}{A_bh}[/tex]Now, we need to determine the heights. To do that we will use the fact that the ratio of the squares of the height of the pyramid and the height to the top of the pyramid is equivalent to the ratio of the areas, therefore, we have:
[tex](\frac{h}{h_t})^2=\frac{A_b}{A_f}[/tex]Now we substitute the areas:
[tex](\frac{h}{h_t})^2=\frac{250}{40}[/tex]Taking square root we get:
[tex]\frac{h}{h_t}=\sqrt[]{\frac{250}{40}}[/tex]Solving the operations:
[tex]\frac{h}{h_f}=2.5[/tex]Now we multiply by the height of the frustum on both sides:
[tex]h=2.5h_t[/tex]Now, let's look at the following diagram:
This shows us that the height of the frustum plus the height to the top must be equal to the height of the pyramid, therefore:
[tex]h=h_t+31.8[/tex]Substituting the relationship we determined for the height to the top we get:
[tex]h=\frac{h}{2.5}+31.8[/tex]Now we solve form the height "h" first by subtracting h/2.5 from both sides:
[tex]\begin{gathered} h-\frac{h}{2.5}=31.8 \\ \end{gathered}[/tex]Solving the operations:
[tex]\frac{1.5h}{2.5}=31.8[/tex]Now we multiply both sides by 2.5:
[tex]\begin{gathered} 1.5h=31.8\times2.5 \\ 1.5h=79.5 \end{gathered}[/tex]Now we divide by 1.5:
[tex]h=\frac{79.5}{1.5}=53[/tex]Therefore, the height of the pyramid is 53 cm. Now we substitute in the ratio of the volumes and we get:
[tex]\frac{V_f}{V_{}}=\frac{h_f(A_b+A_f+\sqrt[]{A_bA_f})}{A_bh}[/tex]Substituting the values:
[tex]\frac{V_f}{V_{}}=\frac{(31.8)(250+40+\sqrt[]{(250)(40)})}{(250)(53)}[/tex]Solving the operations:
[tex]\frac{V_f}{V}=0.936_{}[/tex]Therefore, the ratio is 0.936
Write T for true or F for false. 6. The number 14 is a multiple of 4. 7. The Identity Property says that any number times 1 equals the number itself. 8. A bar diagram can be used to show 3 X 6.
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In the number 6, it says the number 14 is a multiple of 4. It means there would be an integer number X which when multiplied by 4 would result in the number 14. To check it, we can perform the following calculation.
[tex]14=X\times4\to X=\frac{14}{4}=3.5[/tex]Because the value of X found is not an integer, 6. is FALSE
In the number 7, it says the Identity Property rays that any number times 1 equals the number itself. This property says that there is a number that, when multiplied by any number will always equal the number itself, and this is the number 1. From this, 7 is TRUE
Number 8 says a bar diagram can be used to show 3X6. This technique can be used to show any multiplication by an integer number. Because both. 3 and 6, are integer, 8 is TRUE
your dinner bill was $21.00 if you leave a 20% tip, how much will the tip be?
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As given by the question,
There are given that the total bill was $21.00
Now,
If leave a 20% tip,
Then,
[tex]\begin{gathered} 21\times\frac{20}{100}=21\times\frac{1}{5} \\ =4.2 \end{gathered}[/tex]Hence, the tip
The question is in the image. Answer question 20 only.
Answers
To convert radians to degrees we use the formula:
[tex]\theta\cdot\frac{180}{\pi}[/tex]In this case the angle is 12 radians, then we have:
[tex]12\cdot\frac{180\degree}{\pi}=687.55[/tex]Therefore, the angle in degrees is 687.55°
The measures of the angles of a triangle are shown in the figure below. Find the
measure of the smallest angle.
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The smallest measure of the angle in the given triangle is 3x - 15 which is 33°.
What are triangles?A triangle is a polygon with three edges and three vertices. It belongs to the basic geometric shapes. A triangle having vertices A, B, and C is known as triangle ABC. Any three locations in Euclidean geometry that are not collinear result in a distinct triangle and a distinct plane.So, the measure of the smallest angle in the triangle is:
90 + 4x - 7 + 3x - 15 = 1807x + 68 = 1807x = 180 - 68x = 112/7x = 16Now,
4x - 7 = 4(16) - 7 = 57°3x - 15 = 3(16) - 15 = 33°Therefore, the smallest measure of the angle in the given triangle is 3x - 15 which is 33°.
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please help me with this question and explain it so I can understand. thank you!
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We can solve this question using trigonometric functions. Here, we use the tangent of the angle of elevation to find the height of the tree.
[tex]\begin{gathered} \tan 40^o=\frac{h}{35} \\ 0.839=\frac{h}{35} \\ 0.839\times35=h \\ 29.36=h \end{gathered}[/tex]Thus, the height of the tree is 29 feet (to the nearest foot).
how do I find the value of x so f(x)=7
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We have a function for which we only have the chart.
We need to find the value of x so that f(x)=7.
NOTE: As we are lookin for the value of x that makes the value of f(x) = 7, we are able to see it in the graph directly:
If we start at y=7, we can draw a line until we intersect the line for f(x). When this happens we draw a vertical line towards the x-axis until we intersect it.
The value of x at that point is the one that makes f(x)=7.
If we can not find the solution by graph, we have to find the equation of the line and clear x for f(x)=7.
SOLUTION WITH EQUATION:
With the information from the chart we have to find the equation.
We can identify two points in the function: (2,0) and (5,7).
Using the 2 known points, we calculate the slope of the line as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{7-0}{5-2}=\frac{7}{3}[/tex]Then, we can write the slope-point equation as:
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-0=\frac{7}{3}(x-2) \\ y=\frac{7}{3}x-\frac{14}{3} \end{gathered}[/tex]Then, if we know that y=7, we can replace y with this value and calculate x as:
[tex]\begin{gathered} y=7=\frac{7}{3}x-\frac{14}{3} \\ 7\cdot3=7x-14 \\ 21=7x-14 \\ 7x=21+14 \\ 7x=35 \\ x=\frac{35}{7} \\ x=5 \end{gathered}[/tex]Answer: the value of x so that f(x)=7 is x=5.
4-Which turkey is the better deal? * Sarah Lee Turkey $6.58 per lb O Butterball Turkey $11.16 for 2 lbs 4b-What is the Unit Price for the better deal? Round to the nearest hundredth) Put your answer in the form 0.00 or .00, so if answer is 43 cents, its 0.43 or.43, if there is a dollar amount like 1.50, do not add zeros in front).
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We will determine the best deal as follows:
We divide 11.16 by 2 to obtain the value per Lb, and we get that for each Lb the price is $ 5.58.
So, the best deal is Butterball Turkey at a price of $5.58 per Lb.
please help i dont know to do it please help
Answers
Given:
0.5
Let's write the decimal in form of a fraction a/b using integers.
To write the number in fractional form, we have:
[tex]0.5=5\times10^{-1}[/tex]Since the exponent is the negative of 1, using the definition of negative exponent, we have:
[tex]5\times10^{-1}=\frac{5}{10^1}=\frac{5}{10}[/tex]Therefore, the correct fraction is:
[tex]\frac{5}{10}[/tex]ANSWER:
[tex]\frac{5}{10}[/tex]I don't even get like what a mean and a median is can you explain?
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The mean is an average of a set of numbers, where in order to calculate it, we sum all the numbers and divide by the amount of numbers.
For example, in the set {2, 5, 7, 10}, the mean is:
[tex]\frac{2+5+7+10}{4}=\frac{24}{4}=6[/tex]The median is the middle term of the set when it's put in the crescent order.
For example, in the set {4, 7, 2, 10, 5}, the median is:
[tex]\begin{gathered} \text{crescent order}\to\mleft\lbrace2,4,5,7,10\mright\rbrace \\ \text{middle term}\to5 \end{gathered}[/tex]If the number of elements in the set is even, the median will be the average of the two middle terms. For example, in the set {4, 7, 2, 10, 5, 3}, the median is:
[tex]\begin{gathered} \text{crescent order}\to\mleft\lbrace2,3,4,5,7,10\mright\rbrace \\ \text{middle terms}\to4\text{ and 5} \\ \operatorname{median}\to\frac{4+5}{2}=4.5 \end{gathered}[/tex]in ABC, G is the centroid. If BF=48 find BG
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Recall that the centroid of the triangle is the intersection point of its medians, which are the lines that are formed by joining the midpoint of one side with the remainding vertex of the triangle. This point has the property that for each median it splits it in two smaller segments, one of which has the double of the length of the other.
We are given the following picture
Let us call the lenght of GF x. Since G is the centroid, then the length of BG is 2x. Note that the sum of the length of BG plus the length of GF should be BF. So we have the following equation
[tex]x+2x=48[/tex]Now, we should solve this equation for x. First we add the x terms on the left. So we get
[tex]3x=48[/tex]Finally, we divide by 3 on both sides, so we get
[tex]x=\frac{48}{3}=16[/tex]so the lenght of GF is 16. Now, si BG has the double length of FG, then the length of BG is 16*2 = 32.
Use the Distributive Property to find each missing factor.6 x 8 = ( 4 x ____) + ( 2 x 8 )10 x 3 = (___ x 3 ) + ( 2 x 3 )(___ X 7 ) = ( 3 x 7 ) + ( 2 x ___)( 8 X ___) = (___ x 8 ) + ( 4 X 8 )3rd grade subject Distributive property
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The question is given below as
[tex]6\times8=(4\times\ldots)+(2\times8)[/tex]The distributive property of multiplication states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately, then adding the two products together for the same result as multiplying the first number by the sum.
[tex]a(b+c)=a\times b+a\times c[/tex]Let the missing factor in the question be x
[tex]\begin{gathered} 6\times8=(4\times\ldots)+(2\times8) \\ 6\times8=(4\times x)+(2\times8) \end{gathered}[/tex]By multiplying,
We will have
[tex]\begin{gathered} 6\times8=(4\times x)+(2\times8) \\ 48=4x+16 \end{gathered}[/tex]Collect like terms,by subtracting 16 from both sides
[tex]\begin{gathered} 48=4x+16 \\ 48-16=4x+16-16 \\ 32=4x \end{gathered}[/tex]Divide both sides by 4
[tex]\begin{gathered} 4x=32 \\ \frac{4x}{4}=\frac{32}{4} \\ x=8 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} 6\times8=(4\times8)+(2\times8) \\ 6\times8=8(4+2) \\ 6\times8=6\times8 \end{gathered}[/tex]Therefore,
The missing factor = 8
Unit 5 Project 1. A projectile is fired upward from the ground with an initial velocity of 300 feet per second. Neglecting air resistance, the height of the projectile at any time I can be described by the polynomial function P(t) = -16ť + 3000 a. Find the height of the projectile when t = 1 second. b. Find the height of the projectile when t = 5 seconds. c. How long will it be until the object hits the ground? 2. A board has length (3x + 6x - 18) meters and width of 2x + 1 meters. The board is cut into three pieces of the same length a. Find the length of each piece. b. Find the area of each piece. c. Find the area of the board before it is cut. d. How is the area of each piece of the board related to the area of the board before it is cut? 3. A cubic equation has zeros at -2, 1, and 3. a. Write an equation for a polynomial function that meets the given conditions. b. Draw the graph of a polynomial function that meets the given conditions. 4. Alice was having a conversation with her friend Trina, who had a discovery to share: 10
Answers
1)
The polynomial modelling this scenario is expressed as
P(t) = - 16t^2 + 300t
where
P(t) represents the height at time t
a) To find the height of the projectile when t = 1 second, we would substitute
t = 1 into the equation. Thus,
P(1) = - 16(1)^2 + 300(1)
P(1) = - 16 + 300 = 284
Height of projectile when t = 1 second is 284 feet
b) To find the height of the projectile when t = 5 second, we would substitute
t = 5 into the equation. Thus,
P(1) = - 16(5)^2 + 300(5)
P(1) = - 400 + 1500
Height of projectile when t = 5 second is 1100 feet
c) At the time when the object hits the ground, the height would be zero. This means that p(t) = 0
Thus, the equation would be
0 = - 16t^2 + 300t
Factoring out 4t from the right, we have
0 = - 4t(4t - 75)
- 4t = 0 or 4t - 75 = 0
t = 0/-4 or 4t = 75
t = 0 or t = 75/4
t = 0 or t = 18.75
It will take 18.75 seconds until the object hits the ground
What are the solutions of 3x^2 - x + 4 = 0
Answers
ANSWER
[tex]x\text{ = 0.167 + }1.142i\text{ and x = 0.167 }-\text{ 1.142i}[/tex]EXPLANATION
We want to find the solutions of the equation.
The solutions of the equation are the values of x that make that equation equal to zero (0).
The equation given is:
[tex]3x^2\text{ - x + 4}[/tex]We need to use the quadratic formula.
For a quadratic equation:
[tex]ax^2\text{ + bx + c}[/tex]the quadratic formula is:
[tex]x\text{ = }\frac{-b\text{ }\pm\text{ }\sqrt[]{b^2\text{ - 4ac}}}{2a}[/tex]So, we have that:
a = 3, b = -1, c = 4
So::
[tex]\begin{gathered} x\text{ = }\frac{-(-1)\text{ }\pm\sqrt[]{(-1)^2_{}-\text{ 4(3)(4)}}}{2(3)}\text{ = }\frac{1\text{ }\pm\text{ }\sqrt[]{1\text{ - 48}}}{6} \\ x=\text{ }\frac{1\text{ }\pm\text{ }\sqrt[]{-47}}{6}\text{ = }\frac{1\text{ }\pm\text{ }\sqrt[]{47}\cdot\text{ }\sqrt[]{-1}}{6}\text{ = }\frac{1\text{ }\pm\text{ }\sqrt[]{47}\text{ i}}{6} \\ x\text{ = }\frac{1\text{ + 6.86i}}{6}\text{ and x = }\frac{1\text{ - 6.86i}}{6} \\ x\text{ = 0.167 + }1.142i\text{ and x = 0.167 }-\text{ 1.142i} \end{gathered}[/tex]The equation has complex solutions.
What is (a+b) (a+b) =?What is (a+1) (a+1) = ?What is (a+3) (a+3)=?What is (x+5) ^2=?
Answers
SOLUTION:
Case: Expansion
Method:
[tex]\begin{gathered} a^2+b^2=(a+b)^2 \\ R.H.S\text{ }expansion \\ (a+b)^2 \\ (a+b)(a+b) \\ a(a+b)+b(a+b) \\ a^2+ab+ab+b^2 \\ a^2+2ab+b^2 \end{gathered}[/tex]Final answer:
FALSE
[tex]a^2+b^2\ne(a+b)^2[/tex]what digit is in the
Answers
Given:
[tex]\frac{13}{7}+\frac{9}{14}[/tex]Find LCM of the denominators.
LCM (7, 14)=14.
Multiply the numerator of each fraction by the LCM 14 and divide by 14.
[tex]\begin{gathered} \frac{1}{14}(\frac{14\times13}{7}+\frac{9\times14}{14}) \\ =\frac{1}{14}(2\times13+9) \\ =\frac{1}{14}(26+9) \\ =\frac{35}{14} \\ =\frac{5}{2} \end{gathered}[/tex]Therefore, the result of the sum is 5/2.
Can someone please help me with this I really need help
Please
Answers
The complete table is as follows:
x = 0, p(x) = 0x = 1, p(x) = 4x = 2, p(x) = 8x = 3, p(x) = 12x = 4, p(x) = 16x = 5, p(x) = 20x = 6, p(x) = 24The equation that represent the function is p(x) = 4x.
How to represent equation of a table?Function p represents the perimeter in inches of a square with side length x inches.
Therefore,
perimeter of a square = 4l
where
l = side lengthHence, x represent the side length and p(x) is the perimeter of the square.
Therefore, the equation that represent the situation is as follows;
p(x) = 4x
Let's fill the table as follows:
x = 0, p(x) = 0x = 1, p(x) = 4(1) = 4x = 2, p(x) = 4(2) = 8x = 3, p(x) = 4(3) = 12x = 4, p(x) = 4(4) = 16x = 5, p(x) = 4(5) = 20x = 6, p(x) = 4(6) = 24learn more on equation here: https://brainly.com/question/29326385
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The answer is 139 ft provided by my teacher, I need help with the work
Answers
Answer:
139 ft
Explanation:
Given below is the diagram of the situation
the tangent ratio fo 24 degrees gives
[tex]\tan 24=\frac{h}{300}[/tex]multiplying both sides by 300 gives
[tex]300\cdot\tan 24=h[/tex][tex]h=133.57ft[/tex]We have to remember here that the measuring device was 5 ft above the ground; therefore,
[tex]\text{height}=133.57+5[/tex][tex]\text{height}=138.57ft[/tex]rounding to the nearest integer gives
[tex]\text{height}=139ft[/tex]which is our answer!
Which of these describes the function graphed below? 6 2 8 6 2 8 -2 -6 -8 There is a nonlinear relationship between x and y when x is less than 1 and a linear relationship when x is greater than 1 O There is a linear relationship between x and y when x is less than 1 and a nonlinear relationship when x is greater than 1 There is a linear relationship between x and y when x is less than 0 and a nonlinear relationship when x is greater than 0. There is a nonlinear relationship between x and y when x is less than 0 and a linear relationship when x is greater than 0
Answers
Answer
Option C is correct.
There is a linear relationship between x and y when x is less than 0 and a nonlinear relationship when x is greater than 0.
Explanation
From the graph, we can see that at values of x less than 0, the graph indicates a very straight line that translates to a linear relationship.
But at values of x greater than 0, the graph begins to curve showing that the relationship is no longer linear.
So, option C is correct.
Hope this Helps!!!
10. The graph of y=f(x) is given below.y!24168848 xWhat is the possible degree of f?A. 4IB. -3C. 2D. 3E. -1
Answers
Answer:
The degree of the function is;
[tex]3[/tex]Explanation:
From the given graph, we can observe that the function has two extremum (one minima and one maxima).
The degree of the function will be the number of extremum plus 1;
[tex]\text{degree}=n+1[/tex]Since there are two extremum on the graph then;
[tex]\begin{gathered} \text{degree}=2+1 \\ \text{degree}=3 \end{gathered}[/tex]Therefore, the degree of the function is;
[tex]3[/tex]The top of a desk would be a representation ofO a pointO a planeO a lineO none of the above
Answers
Given
The top of a desk.
To find:
The top of a desk is a representation of _____.
Explanation:
It is given that,
The top of a desk.
That implies,
Since,
The plane is a flat surface that extends infinitely in all directions.
Then, the top of a desk represents a plane.
Answer:
B-Plane tep-by-step explanation:
there are 7 Red 3 blue and 5 green marbles in a bag what is the probability that the first three chosen will not be red?
Answers
Determine the total number of marble in the bag.
[tex]\begin{gathered} n(T)=7+3+5 \\ =15 \end{gathered}[/tex]Determine the probability for first three marbles be red.
[tex]\begin{gathered} P(R=3)=\frac{^7C_3^{}}{^{15}C_3} \\ =\frac{35}{455} \\ =\frac{7}{91} \end{gathered}[/tex]The probability for first three marble is not to be red is equal to one minus the probability for the first three marble be red.
[tex]\begin{gathered} P(R\ne3)=1-P(R=3) \\ =1-\frac{7}{91} \\ =\frac{91-7}{91} \\ =\frac{84}{91} \\ =\frac{12}{13} \end{gathered}[/tex]So answer is 12/13.
26. Find the area of the figure to the nearest tenth,165°7 inA. 13.5 in.B. 7.1 in 2C. 84.8 in 2D. 42.4 in?
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To find the area of the segment of the circle, use the following formula:
[tex]A=\frac{a}{360}\pi r^2[/tex]Where a is the angle of the segment and r is the radius of it. Replace for the given values and find the area of the segment:
[tex]\begin{gathered} A=\frac{165}{360}\pi\cdot(7)^2 \\ A=70.55 \end{gathered}[/tex]The scores of individual students on the American College Testing (ACT) composite college entrance examination have a normal distribution with mean 18.6 and standard deviation 5.9. What is the probability that the mean score of an SRS of 40 students chosen from all those taking the test is 21 or higher? Round your percentage to 2 decimals.
Answers
Given data
*The given mean is
[tex]\mu=18.6[/tex]*The given standard deviation is
[tex]\sigma=5.9[/tex]The value of the z score is calculated as
[tex]z=\frac{x-\mu}{\sigma}[/tex]Substitute the values in the above expression as
[tex]\begin{gathered} z=\frac{21-18.6}{5.9} \\ =0.41 \end{gathered}[/tex]The probability that the mean score of an SRS of 40 students chosen from all those taking the test is 21 or higher is given as
[tex]\begin{gathered} P(Z\ge21)=P(X\ge0.41) \\ =1-P(X<0.41) \end{gathered}[/tex]The corresponding probability is evaluated by the table.
Substitute the values in the above expression as
[tex]\begin{gathered} P(Z\ge21)=1-0.6591 \\ =0.34 \end{gathered}[/tex]At 6 AM today, you purchased 1 MW of electricity contract for 12 PM at a price of 100 pounds/MWh. Two hours later, the forecast for solar generation for 12 PM has changed from 4 GW to 4.5 GW. The market is currently bid at 95 pounds/MWh and offered at 105 pounds/MWh. What would you do, and why? Please answer logically, stating all assumptions. Note that no additional research is needed
Expert Answer
Answers
I will sell 1MW electricity contract for 12pm with a bid price of £95/MW. Lock in losses in the region of £5/MW.
At 6 AM today, you purchased 1 MW of electricity contract for 12 PM at a price of 100 pounds/MWh.
Solar power is more affordable, accessible, and prevalent in the United States than ever before.
From just 0.34 GW in 2008, U.S. solar power capacity has grown to an estimated 97.2 gigawatts (GW) today.
This is enough to power the equivalent of 18 million average American homes.
Today, over 3% of U.S. electricity comes from solar energy in the form of solar photovoltaics (PV) and concentrating solar-thermal power (CSP).
Solar generation implies an increase of 4 GW to 4.5 GW. Which will provide more power than expected during 12 p.m. This will likely lower the market value.
A bid-offer spread of 10 pounds/MWh is typically wide. This basically indicates that the market is liquid and volatile. The price of which might turn against me if I wait.
Some of my guesses are:
I am a risk-averse trader. Who does not want to take unnecessary
exposure to power market.
I do not have any positions or hedging strategies in the electricity
market that would influence my decisions.
I am not obliged to buy and sell electricity at 12 PM.
Market prices and forecasts are reliable, reflecting actual supply and demand conditions.
Hence the answer is I will sell 1MW electricity contract for 12pm with a bid price of £95/MW. Lock in losses in the region of £5/MW.
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