5 additional trees give maximum yield and 35 trees per acre will give largest crop of apple.
Let's assume that, we are planting x apple trees extra per acre. So, net 10x apple will be less.
Let say, total number of apples = y
Then, y = (30+x)×(400–10x)
For, optimum number of trees, let's do the differentiation of the above equation with respect to x.
d(y)/d(x) = (400–10x)×1 + (30+x)×(-10)
= 400–10x-300–10x
= 100–20x …………..(1)
For mimima or maxima, the above equation must be equal to 0.
So, 0 = 100–20x
=> x=5
Let's do the second differentiation of equation (1) and substitute the the value of x I.e x=5
[tex]d^2(y)/d(x^2) = -20[/tex]
The above equation is negative for all values of x which indicates that at x=5 we will have the maximum value.
So, the number of trees for maximum apple will be (30+x)
So, 30+5 = 35 trees per acre will give the largest crop of apple.
Hence 5 additional trees give maximum yield and 35 trees per acre will give largest crop of apple.
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It says that raise school is 1. 7 miles from his house I did that problem so the challenge says how many miles does he walk in a 5-day school week
It says that raise school is 1. 7 miles from his house the student walks 17 miles in a 5-day school week
If the school is 1.7 miles from the student's house, then the round trip distance between the house and school is 2 times 1.7 miles, or 3.4 miles per day.
A mile is defined as the unit of length, which is exactly equal to 5280 feet, or 1760 yards, and standardized as exactly 1609.344 meters by the International agreement in 1959. It is the largest unit that is commonly used to measure the distance between places that are far from each other.
To find out how many miles the student walks in a 5-day school week, we can multiply the daily distance by the number of school days in a week:
3.4 miles/day x 5 days/week = 17 miles/week
Therefore, the student walks 17 miles in a 5-day school week
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Triangle QRS triangle TUV.
Q
117⁰
V
30°
R
S
What is the measure of LQ and the measure of LS?
U
T
Answer: Since triangle QRS and triangle TUV are both triangles, we can use the fact that the sum of the interior angles in a triangle is 180 degrees.
In triangle QRS, the measure of angle Q is 117 degrees and the measure of angle R is 180 - 117 = 63 degrees. The measure of angle S is 180 - 63 = 117 degrees, since the angles in a triangle add up to 180 degrees.
In triangle TUV, the measure of angle T is 180 - 30 = 150 degrees and the measure of angle U is 30 degrees. The measure of angle V is 180 - 150 = 30 degrees, since the angles in a triangle add up to 180 degrees.
The measures of LQ and LS can be found using the fact that the exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it.
The measure of LQ is equal to the sum of the measures of angles R and T:
LQ = 63 + 150 = 213 degrees
The measure of LS is equal to the sum of the measures of angles Q and U:
LS = 117 + 30 = 147 degrees
So the measure of LQ is 213 degrees and the measure of LS is 147 degrees.
Step-by-step explanation:
which of the following shows 87 and 1/2% as a fraction? 7/8, 5/8, -8/75, none of these
Answer: none of these
Step-by-step explanation:
87 and 1/2% should be written as 87.5%
The second smallest number that has 1,2,3,4 and 5 in them
12354 is the second smallest number that contains the digits 1, 2, 3, 4 and 5 in that order. It can be used in a variety of ways, such as counting, addition, subtraction, multiplication and division, as well as to represent dates and times.
The second smallest number that has 1,2,3,4 and 5 in them is 12354. This number is made up of the digits 1, 2, 3, 4, and 5 in that order. It is the second smallest number because the smallest number that contains these digits is 12345.
To form this number, we start by arranging the digits in descending order, from the largest to the smallest, 5, 4, 3, 2 and 1. We then combine the digits together to form 12354.
12354 is the second smallest number because it contains all the digits 1, 2, 3, 4 and 5 in that order. This number can be used in different ways, such as counting, addition, subtraction, multiplication and division. For example, 12354 divided by 4 equals 3088.75.
The number 12354 can also be used in other ways, such as to represent a date or time. For example, the number 12354 can represent the date 12/3/54, which is December 3, 1954.
In conclusion, 12354 is the second smallest number that contains the digits 1, 2, 3, 4 and 5 in that order. It can be used in a variety of ways, such as counting, addition, subtraction, multiplication and division, as well as to represent dates and times.
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n a certain culture of bacteria, the number of bacteria is increased sixfold in 10 hours. how long did it take for the population to double? [use the
The time taken by population of bacteria to be doubled whose normal growth is six fold in 10 hours is equal to 3.87 hours.
Let us consider 'n' is the time taken by the bacteria populations.
And P(n) represents the population of the bacteria in time 'n'
Using exponential growth function we know,
P(n) = K e^(a× n)
Where K and 'a' are the constants.
From the given condition we have :
P(10 ) = 6 P(0)
⇒ K e^ (10a) = 6k e^(0 × a )
⇒ e^(10a) = 6
⇒ 10a = log 6
⇒ a = ( log 6 ) / 10
Now required time when population is double :
P(n ) = 2P(0)
⇒ K e^ (n × a) = 2k e^(0 × a )
⇒ e^ [ n ×( log 6 ) / 10 ] = 2
⇒ n ×( log 6 ) / 10 = log 2
⇒ n = ( 10 × log 2 ) / log 6
⇒ n = ( 10 × 0.3010 ) / 0.7782
⇒ n = 3.8679 hours
⇒ n = 3.87 hours
Therefore, the population of the bacteria will take 3.87 hours to get double.
The above question is incomplete , the complete question is:
A bacteria population increases sixfold in 10 hours. Assuming normal growth, how long did it take for their population to double?
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PLEASE HELP!
Mrs. Harris is in the 20% income tax bracket. Last year, her taxable income was $75,400. How much did she need to pay in taxes?
A. $1,508
B. $15,080
C. $60,320
D. $73,892
Answer: B: 15,080
Step-by-step explanation:
Alright, let's convert 20% into a decimal: 0.20
Then multiply 0.20 x 75,400 which gets you to 15080
So she needed to pay $15,080 in taxes
Write the scale factor of abcde to zyxwv
The scale factor of abcde to zyxwv is obtained dividing one side length of zyxwv by the equivalent side length of abcde, for example:
k = zy/ab.
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
The figures for this problem are given as follows:
Original: abcde.Dilated: zyxwv.Hence the scale factor of abcde to zyxwv is obtained dividing one side length of zyxwv by the equivalent side length of abcde, for example:
k = zy/ab.
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all ratios equivalent to 5:8
answer:
if you multiply the 2 sides of the ratio by a number it will give you an equivalent ratio
5:8 = 10:16 multiplying by 2
5:8 = 15:24 multiplying by 3
5:8 = 20:32 multiplying by 4
5:8 = 25:40 multiplying by 5
5:8 = 30:48 multiplying by 6
5:8 = 35:56 multiplying by 7
and so on ...
Find the missing side length using trig
Answer:
29.22
Step-by-step explanation:
54 is what percent of 200?
PLEASE GIVE BRAINLIEST!
thank you and have a good day :)
Answer:
27%
Step-by-step explanation:
a percent is a part of 100
so if we get the denominator to 100, the numerator is the percent of the equation
54/200
in order to get 200 to 100, we have to divide by 2.
however we have to divide the numerator aswell as if we don't, we simply just half the equation.
54/2 = 27
200/2 = 100
27/100 is the new equation. referring back to the first statement, i made, the numerator would be the percent of the equation that is a part of 100
27%.
54/200 is equal to 27/100. all we did was divide both the numerator and denominator by 2.
7. A storage shed is shown below. How many cubic feet will the storage shed hold? 13 ft 13.6 ft 5 8 ft 13.6 ft 6 ft
The amount of cubic feet that the storage shed can hold is 168 ft³
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
The volume of the storage shed is the product of the base area and the height. It is given by:
Volume = base area * height
From the diagram, the base is a triangle. Hence:
Area of base = (1/2) * base * height = (1/2) * 8 ft * 7 ft = 28 ft²
Volume = base area * height = 28 ft² * 6 ft. = 168 ft³
The volume of the storage shed is 168 ft³
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How to find the semicircle and quarter circle.
# Distance and No. of turns.
Answer:
A semicircle can be drawn by first drawing a diameter of a circle, which is a line segment connecting two points on the circumference that passes through the center of the circle. Then, the semicircle can be constructed by drawing an arc that is half of the circumference of the circle and connecting the ends of the arc to the endpoints of the diameter.
A quarter circle can be drawn in a similar way, but instead of drawing an arc that is half of the circumference, you would draw an arc that is a quarter of the circumference. To do this, you would need to find the central angle that subtends the arc and divide it by 4. The quarter circle can then be constructed by drawing an arc with this central angle and connecting the ends of the arc to the endpoints of a radius of the circle, rather than the diameter.
In both cases, you can use a compass or a protractor to accurately draw the arcs.
2. How can the term unit square help you to remember
that area is measured in square units?
When ever the area is calculated the units will have a degree of two.
What is an area?The area is defined as the space covered by any two-dimensional body. The unit if the area is calculated as square units. The square units come because the area is calculated by the two parameters of length.
The area of the rectangle is calculated by the multiplication of the two lengths like length and width.
Similarly, the area of the circle is calculated by taking the square of the radius of the circle it means that the length here is also multiplied by two times.
Therefore, the area is calculated in an square units.
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The "hang time" of a football is the amount of time the football stays in the air after being kicked. Zara kicks a football, and the height (in meters) of the football above the ground at t seconds is shown in the graph below.
The completed statements with regards to the projectile motion of the football are presented as follows;
This graph is a nonlinear function
The hang time of the football is 3 seconds
The football reaches its maximum height when t = 1.5 seconds
The maximum height is about 11 meters
For t between t = 0 and t = 1.5, the height is increasing
What is a projectile motion?The motion of a projectile is one that involves an object thrown into the air or into space, which is acted upon by only gravitational force.
The graph in the question, showing the scale on the x-axis obtained from a similar question on the internet, indicates that we get;
The x-intercept of the graph are; (0, 0), and (3, 0)
Therefore;
The time the football is in the air, which is the hang time of the football can be obtained from the difference between the x-values of the x-intercept as follows;
Hang time = 3 - 0 = 3
The hang time of the football is 3 secondsThe graph indicates that the coordinates of the maximum height is (1.5, 11). Therefore;
The football reaches the maximum height when t = 1.5 second(s)The maximum height reached, obtained from the coordinate of the maximum height is 11 metersThe height at t = 0 is 0 meters, and the height at t = 1.5 seconds is 11 meters, therefore; the height is increasing between t = 0 and t = 1.5 seconds
For t between t = 0 and t = 1.5, the height is increasing
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Answer:
Nonlinear
3
1.5
11
increasing
Step-by-step explanation:
I NEED HELP, THIS IS DUE TODAY AND IM CONFUSED.
The value of x that makes the shape a parallelogram is 2/3
What is a quadrilateral?A quadrilateral is a polygon that has four sides and four angles. Types of quadrilaterals are kite, square, rectangle, parallelogram and so on.
A parallelogram is a quadrilateral with two pairs of parallel sides. Each parallel sides are equal. Also, the diagonals of a parallelogram bisect each other.
From the diagram, the diagonals bisect each other in other to be a parallelogram, hence:
6x = 3x + 2
3x = 2
x = 2/3
The value of x is 2/3
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the pew research center internet project conducted a survey of 1,057 internet users. this survey provided a variety of statistics on them. if required, round your answers to four decimal places. (a)the sample survey showed that 90% of respondents said the internet has been a good thing for them personally. develop a 95% confidence interval for the proportion of respondents who say the internet has been a good thing for them personally.
variety of statistics for 1057 inernet users are = (0.9180, 0.8998) solve by given question .
population proportion is the share of a population that belongs to a particular category. Confidence intervals are used to estimate population proportions.
Let p be the population proportion of respondents who say the Internet has been a good thing for them personally.
=p +- z*[tex]\sqrt{p*(1-p)/n}[/tex]
where z* = Critical value p = Sample proportion,n = sample size.
As per given , we have
n= 1057 By z-table , Critical value for 95% confidence interval : z*= 1.96
Then, the 95% confidence interval for the proportion of respondents who say the Internet has been a good thing for them personally. will be :
=p +- z*[tex]\sqrt{p*(1-p)/n}[/tex]
=0.9+-1.96[tex]\sqrt{.9*(1-.9)/1057}[/tex]
=0.9180, .8998
Hence, the required 95% confidence interval for the proportion of respondents who say the Internet has been a good thing for them personally = (=0.918, .881)
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State how the triangles are congruent using SSS, SAS, ASA, AAS, or
HL. If they are not congruent, type NOT.
Answer:
NOT
Step-by-step explanation:
There are no pairs of congruent sides.
What is the length of the hypotenuse of a 30-60-90 triangle if the short leg has a length of 10?
Answer: 20
Step-by-step explanation:
30-60-90 triangles are special: Their side lengths fall in a ratio of 1:2:[tex]\sqrt{3}[/tex], in order of Shortleg : hypotenuse : longleg
Since we know the short leg is 10, the hypotenuse must be double, or 20.
In AOPQ, m/O = (6x – 14)°, m/P = (2x + 16)°, and m/Q = (2x + 8)°.
Find m/Q.
The required measure of angle m∠Q is 42 degrees, as of the given condition.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should equal to 180°
Here,
In a triangle, the sum of the angles is always equal to 180 degrees. Therefore, for triangle OPQ,
m∠O + m∠P + m∠Q = 180°
Using the given information,
m∠O = (6x - 14)°
m∠P = (2x + 16)°
m∠Q = (2x + 8)°
(6x - 14)° + (2x + 16)° + (2x + 8)° = 180°
10x + 10 = 180°
10x = 170
x = 17
Substituting the value of x back into the expression for m∠Q,
m∠Q = (2x + 8)°
m∠Q = (2 * 17 + 8)°
m∠Q = 42°
So the value of m∠Q is 42 degrees.
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Jayden has some dimes and some quarters. He has at most 25 coins worth at least $4.60 combined. If Jayden has 7 dimes, determine all possible values for the number of quarters that he could have. Your answer should be a comma separated list of values.
The possible values of the number of quarters are at least 14 and more.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
1 dime = $0.10
1 quarter = $0.25
Number of dimes = x
Number of quarters = y
Now,
He has at most 25 coins worth at least $4.60 combined.
This means
we can write two inequalities.
x + y ≤ 25 ____(1)
0.10x + 0.25y ≥ 4.60 _____(2)
Now,
From (1) and (2).
x ≤ 25 - y
Substituting in (2).
0.10x + 0.25y = 4.60
0.10 (25 - y) + 0.25y ≥ 4.60
2.5 - 0.10y + 0.25y ≥ 4.60
2.5 + 0.15y ≥ 4.60
0.15y ≥ 4.60 - 2.5
0.15y ≥ 2.1
y ≥ 2.1/0.15
y ≥ 14
This means,
y is at least 14.
Thus,
The possible values of the number of quarters are at least 14 and more.
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Benjamin invests $400 in a savings account that earns 5\%5% interest each year. Which expression does not give the correct balance in the account after 33 years?
If Benjamin invests $400 in a savings account that earns 5% interest each year, the expression that shows the correct balance is A = 400(1 + 0.05)(1 + 0.05)(1 + 0.05)
The principal amount = $400
interest rate = 5%
The equation of the simple interest
A = P (1+ rt)
Where A is the final amount
P is the principal amount
r is the interest rate
t is the time period
The final amount after one year
= 400( 1 + 0.05×1)
= 400(1 + 0.05)
The final amount after two year
= 400(1 + 0.05)(1 + 0.05)
The final amount after three year
= 400(1 + 0.05)(1 + 0.05)(1 + 0.05)
Therefore, the balance amount after three years is A = 400(1 + 0.05)(1 + 0.05)(1 + 0.05)
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Throwing the stone horizontally at 1.5 times the previous speed multiplies the time to reach the ground by what factor?
a construction crew is lengthening a road. the road started with a length of miles, and the crew is adding miles to the road each day. let represent the total length of the road (in miles), and let represent the number of days the crew has worked. write an equation relating to . then use this equation to find the total length of the road after the crew has worked days.
The necessary equation is [tex]L= 52+2D[/tex], and the necessary overall length is [tex]114 miles[/tex].
Given: A road is being extended by construction workers. The road already had a length of miles, and the crew is continuously extending it by miles. Let the number of days the crew has worked and the distance of the entire road (in miles) be represented by D and L respectively. Create a corresponding equation L to D.
According to the inquiry,
The road's initial length is 52 miles.
The daily length of roadways that a crew adds is 2 miles.
This number represents the number of days the crew worked.
The total length of the road that the crew built is represented by L.
A given condition-based equation can be written as [tex]L= 52+2D[/tex].
Now, the crew's total length of the road after 31 days of construction is calculated.
[tex]L= 52+2*31\\L=52+62\\L=114 miles[/tex]
As a result, the needed equation and the total length is [tex]L= 52+2D[/tex] and 114 miles respectively.
The complete question is:-
A construction crew is lengthening a road. The road started with a length of 52 miles, and the crew is adding 2 miles to the road each day. Let L represent the total length of the road (in miles), and let D represent the number of days the crew has worked. Write an equation relating L to D . Then use this equation to find the total length of the road after the crew has worked 31 days.
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Spin Master Toys would like to introduce a new battery powered adventure toy called "Bongo
Bumpers" targeted to boys aged 5-9 in Canada. It is a unique new toy that is expected to be a hit
this holiday season. The toy will sell for $25.
Using the following information, forecast the sales demand in retail dollars for the new "Bongo
Bumpers" toy in Canada for its first year of launch based on the assumptions below.
A Spin Master survey estimated that 80% of boys who saw the toy in action would ask
their parents to purchase it.
Based on their media plan the advertising agency estimates that 65% of boys in Canada
of launch.
would see the advertising and be aware of the toy within its first year
Spin Master has learned in research that approx. 50% of parents or others in the family
will purchase a Spin Master toy that their child requests within a year, as Spin Master has
a strong reputation for toys that have lasting play value.
a) Using the information provided, the sales forecast in retail dollars for the new "Bongo Bumpers" toy in Canada for its first year of launch is $6,259,500.
b) If Spin Master had an issue with the distribution and was only able to achieve 70 percent distribution, the sales forecast will be $4,381,650.
What is the sales forecast?A sales forecast is a projected future sales revenue based on estimated sales units and selling price under some predicted market situations.
The sales forecast is usually broken down into various periods, for example, a week, a month, or a year.
The purposes of a sales forecast are to:
Improve organization productivity and performance andConform to market modifications and meet customers' needs.The unit selling price per Bongo Bumpers toy = $25
The population of Canadian males aged 5 - 9 years = 963,000
The percentage of Canadian boys who would see the advertised toy = 65%
The estimated percentage of Canadian boys who would ask their parents to purchase the toy = 80%
The estimated percentage of Canadian parents who would buy the toy as requested by their male children = 50%
Estimated sales units for the toys = 250,380 (963,000 x 0.65 x 0.8 x 0.5)
Sales forecast for the Bongo Bumpers toys = $6,259,500 ($25 x 250,380)
With 70% distribution, the Sales Forecast = $4,381,650 ($6,259,500 x 70%)
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Lin and Andre start walking toward each other at the same time from opposite ends of the 22-mile walking trail. Lin walks at a speed of 2. 5 miles per hour. Andre walks at a speed of 3 miles per hour. How long will it take until Lin and Andre meet on the path?
If Lin walks at a speed of 2. 5 miles per hour. Andre walks at a speed of 3 miles per hour. It will take 4 hours until Lin and Andre meet on the path.
Lin and Andre are walking toward each other on a 22-mile trail, so they will meet when the sum of the distances they have walked is equal to 22 miles. Let's call the time they walk until they meet "t".
During this time, Lin will have walked a distance of 2.5t miles, and Andre will have walked a distance of 3t miles. The sum of these distances is equal to 22 miles, so we can set up the equation:
2.5t + 3t = 22
Combining like terms, we get:
5.5t = 22
Dividing both sides by 5.5, we get:
t = 4
So it will take Lin and Andre 4 hours to meet on the path.
Note that we could have also solved this problem by using the formula:
time = distance / speed
For Lin, the time to cover the 22-mile distance would be:
time = distance / speed = 22 / 2.5 = 8.8 hours
For Andre, the time to cover the 22-mile distance would be:
time = distance / speed = 22 / 3 = 7.33 hours
Since they are walking towards each other, we can add their times to get the time it takes for them to meet:
time = 8.8 + 7.33 = 16.13 hours
However, we can see that this answer is not correct, as it is greater than the time it would take for either of them to cover the entire distance. This is because the time it takes for them to meet is less than the sum of their individual travel times, due to them moving towards each other.
So we go back to our original equation and solve for "t" to get the correct answer of 4 hours.
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2. What is the length of the unknown leg of the
right triangle rounded to the nearest tenth of
a foot?
2 ft
8.2
9 ft
Answer:
See below. The answer is 8.8 feet, but none of the options offers this value.
Step-by-step explanation:
I get 8.8 feet.
2^2 + x^2 = 9^2
4 + x^2 = 81
x^2 = 77
x = 8.77496 to be exact.
Four years ago, the sum of ages of father and his son was 27 years. After five years, the ratio of the ages of the son and father will be 2: 7. Find the present ages of father and his son. Ans: 30 yrs, 5 yrs
Step-by-step explanation:
x current age of the father
y current age of the son
first equation (x-4)+(y-4)=27 so x=27+4+4-y=35-y
second equation (y+5) : (x+5)= 2:7
so (y+5)*7=(x+5)*2
let's replace x we found at the first equation with the one at second equation
(y+5)*7=(35-y+5)*2
7y+35=(40-y)*2
7y+35=80-2y
7y+2y=80-35
9y=45
y=5
x=35-y=35-5=30
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The exponential function that best models the number of game systems sold, in million, x years since 2015 is given as follows:
y = 30.5(0.7)^x.
How to model an exponential function?The standard definition of an exponential function is given as follows:
y = ab^x.
In which:
a is the initial value, the value of y when x = 0.b is the rate of change.Considering the graph, the parameters for this problem are given as follows:
a = 30.5.b = 21.35/30.5 = 0.7.Hence the function is defined as follows:
y = 30.5(0.7)^x.
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Solve
#5
The formula below can be used to find the distance, d, a person can see to the horizon.
where d is the distance measured in miles and h is the person's height above the surface
of the Earth in feet.
d = 1.75h
The distance that a person with a height of 6 feet can see is given as follows:
10.5 feet.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The function for this problem is defined as follows:
d = 1.75h.
For the person with a height of 6 feet, the distance is obtained replacing the lone instance of h by 6, hence:
d = 1.75 x 6
d = 10.5 feet.
Missing InformationThe problem asks for the distance that a person with a height of 6 feet can see.
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Mrs. Townsend is giving you a test worth 100 points and it contains 40 questions. There are two-point and four-point questions on the test. How many of each type of question are on the test?
Answer:
[tex]10[/tex] four point questions and [tex]30[/tex] two point questions
Step-by-step explanation:
Let's say [tex]f =[/tex] [tex]\text{number of four point questions}[/tex] and[tex]t = \text{number of two point questions}[/tex]. The total number of questions is [tex]40[/tex], therefore [tex]t + f = 40[/tex]. We know the test is worth [tex]100[/tex] points so we can write [tex]2t + 4f = 100[/tex]. We have a system of equations: [tex]t + f = 40 \text{ and } 2t + 4f = 100[/tex]. We can rewrite [tex]t[/tex] as [tex]t = 40 - f[/tex]. We rewrite this in the equation [tex]2t + 4f = 100[/tex]. Since [tex]t = 40 - f[/tex], we have [tex]2 \cdot (40 - f) + 4f = 100[/tex]. Distributing & simplifying gives
[tex]2 \cdot (40 - f) + 4f = 100\\(80 - 2f) + 4f = 100,\\\text{Remove parentheses} 80 - 2f + 4f = 100,\\80 + (-2f) + 4f = 100\\80 + 2f = 100,\\\text{Subtract 80 from both sides} 2f = 20,\\\text{Divide 2 by both sides} f = 10.\\[/tex]
Since we determined [tex]t = 40 - f[/tex] and [tex]f = 10[/tex], subtracting [tex]10[/tex] from [tex]40[/tex] will give [tex]t = 30[/tex].
Therefore, there are [tex]10[/tex] four point questions and [tex]30[/tex] two point questions.
Hope that helps!
