Answer:
0.03333 or 1/30
Step-by-step explanation:
Let A =" I go sailing" and B = "it does not rain"
P(A) = 0.03
P(B) =0.90
Since I never go sailing when it rains, P(A and B) =0.03.
Therefore, the (conditional) probability that I go sailing, given that it does not rain is:
[tex]P(A|B)=\frac{P(A\ and\ B)}{P(B)} \\P(A|B)=\frac{0.03}{0.90}=0.033333[/tex]
The probability is 0.03333 or 1/30.
figure out if the equation is inverse or direct
Answer:
A. Inverse variation
B. Direct variation
C. Direct variation
D. Inverse variation
Hope this helps you
Of the books in the Hogwarts Library, 1/4 came from Hermione and 8 came from Luna. Of the rest, 14 were Ron’s, 1/2 were Ginny’s. How many books are there in the library?
Will mark brainlist
Answer:
88
Step-by-step explanation:
The key to this question is combining the two fractional pieces we know about. Namely, Hermione has 1/4 of the books and Ginny has 1/2 of them. This means that between the two of them, they account for 3/4 of the library.
So what does that mean? Well, it means that the books Ron and Hermione have (22 in total) account for the remaining 1/4 of the library. So then the whole library is [tex]4*22=88[/tex].
Marguerite wants to rent a carpet cleaner. Company A rents a carpet cleaner for $15 per day. Company B rents a carpet cleaner for $100 per week, with a one-time fee of $5. The following functions represent the rate structures of the two rental companies: x = the number of weeks Company A f(x) = 15(7x) Company B g(x) = 100x + 5 The function h(x) = f(x) – g(x) represents the difference between the two rate structures. Determine which statements about h(x) and about renting a carpet cleaner are true. Check all that apply. h(x) = 5x – 5 h(x) = 5x + 5
Answer:
If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B
If Marguerite rents for 1 week, it will cost her the same at either company
h(x) = 5x - 5
Step-by-step explanation:
Marguerite wants to rent a carpet cleaner. Company A rents a carpet cleaner for $15 per day. Company B rents a carpet cleaner for $100 per week, with a one-time fee of $5. The following functions represent the rate structures of the two rental companies: x = the number of weeks Company A f(x) = 15(7x) Company B g(x) = 100x + 5 The function h(x) = f(x) – g(x) represents the difference between the two rate structures. Determine which statements about h(x) and about renting a carpet cleaner are true. Check all that apply. If Marguerite rents for 2 weeks, it will cost her more if she rents from Company B. If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B. If Marguerite rents for 1 week, it will cost her the same at either company. If Marguerite rents for 1 week, it will cost her more if she rents from Company A. h(x) = 5x – 5 h(x) = 5x + 5
Answer: Company A rents a carpet cleaner for $15 per day. Company B rents a carpet cleaner for $100 per week, with a one-time fee of $5. In one week there are 7 days, therefore in x weeks the cost of rentals are given below:
For company A: f(x) = 15(7x)
For company B: g(x) = 100x + 5
h(x) = f(x) – g(x) represents the difference between the two rate structures.
h(x) = f(x) - g(x) = 15(7x) - (100x + 5)
h(x) = 105x - 100x - 5
h(x) = 5x - 5
If Marguerite rents for 2 weeks:
The cost for company A = 15(7x) = 15(7 × 2) = $210
The cost for company B = 100x + 5 = 100(2) + 5 = 200 + 5 = $205
If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B
If Marguerite rents for 1 weeks:
The cost for company A = 15(7x) = 15(7 × 1) = $105
The cost for company B = 100x + 5 = 100(1) + 5 = 100 + 5 = $105
If Marguerite rents for 1 week, it will cost her the same at either company
Answer:
If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B.
h(x) = 5x + 5
those are the answers on edge
Step-by-step explanation:
pls i want help on this one
Answer:
1808 people
Step-by-step explanation:
Find 1% by dividing by 100.
1600/100=16
Multiply 16 by 13.
208
Add it to 1600.
1808
There are now 1808 people.
Please answer this in two minutes
Answer:
[tex] csc (R) = \frac{13}{12} [/tex]
Step-by-step explanation:
Formula for any given angle (Ѳ) is given as csc Ѳ = length of hypotenuse side//length of opposite side. It is the inverse of sin Ѳ.
In the right triangle given above, the opposite length = 24, while the length of the hypotenuse = 26
Thus,
[tex] csc (R) = \frac{hypotenuse}{opposite} [/tex]
[tex] csc (R) = \frac{26}{24} [/tex]
[tex] csc (R) = \frac{26}{24} [/tex]
[tex] csc (R) = \frac{13}{12} [/tex]
. What is half the next number in the pattern 1, 3, 9, 27, 81
A. 234
B. 67
D c. 468
0 0.76
Answer:
A. 243
Step-by-step explanation:
just multiply the next number by 3
81*3= 243
Answer:
[tex]\boxed{243}[/tex]
Step-by-step explanation:
The ratio can be found by dividing a term in the sequence by the previous term.
[tex]\frac{27}{9} =3[/tex]
Each term gets multiplied by 3 to get the next term.
[tex]81 \times 3 = 243[/tex]
How many times does the graph of the function below intersect touch the x-axis? y= -3x^2 + x + 4
Answer:
2 times
Step-by-step explanation:
Well let's first graph the quadratic equation,
Look at the image below ↓
By looking at the image below we can tell that the graph touches the x axis 2 times at,
(-1,0)
(1 1/3,0)
Thus,
the parabola touches the x axis twice.
Hope this helps :)
Answer:
3
Step-by-step explanation:
What is the name of the method for drawing a trend line for the data in a scatterplot in which an oval is drawn around all the points in the scatterplot except the outliers?
a.the oval method
b.the divide-center method
c.the area method
d.the regression calculator method
ty if you answer! :3
Answer:
c.the area method
Step-by-step explanation:
A scatterplot is a plotting of data that represents the relationship between the two variables that should be numerical in nature. The data points i.e to be shown in a horizontal and vertical axis represent that how much one variable affected by another variable.
In the area method, we plot a data and then draw a shape which can be in oval but it does not include the outliers but the other methods like oval method, divide center method, regression calculator includes the outliers
Therefore the option c is correct
Answer:
c.the area method
Step-by-step explanation:
c.the area method c.the area method c.the area method c.the area methodc.the area methodc.the area methodc.the area method c.the area method c.the area method c.the area method c.the area method c.the area method
Find the value of x for the triangle.
37
37
45°
45°
Answer:
[tex]x=37\,\sqrt{2}[/tex]
Step-by-step explanation:
Notice you are dealing with a right angle triangle, since one of the angles measure [tex]90^o[/tex]. Now, what you are asked to find is the hypotenuse of that triangle, given an angle of [tex]45^o[/tex] and the opposite side: 37 units. Then, we can use for example the sine function which relates opposite, and hypotenuse:
[tex]sin(45^o)=\frac{opposite}{hyp} \\hyp=\frac{opposite}{sin(45^o)} \\hyp=\frac{37}{\sqrt{2}/2}\\hyp=37\,\sqrt{2}[/tex]
Which best explains why the orthocenter of an obtuse triangle is outside the triangle?
Answer: All three of the altitudes lie entirely outside the triangle.
Step-by-step explanation:
The orthocenter is the center of the triangle formed by creating all the altitudes of each side.
The altitude of a triangle is formed by creating a line from each vertex that is perpendicular to the opposite side.
In acute traingle , the orthocenter lies inside it.
In right angled triangle, the orthocenter lies on the triangle.
In obtuse triangle , the orthocenter lies outside the triangle because all the three altitudes meet outside .
So, the best explains why the orthocenter of an obtuse triangle is outside the triangle : All three of the altitudes lie entirely outside the triangle.
Answer: It’s A on edge
Pls answer the 9th question...plsss fast
Answer:
i) x = 65° ii) x = 60° iii) x = 34°
y = 50° y = 80° y = 124°
Step-by-step explanation:
i) x = 180-115= 65°
y = 65+65= 130
= 180-130= 50°
ii) x = 90+30= 120
180-120= 60°
y = 60+20= 80
180-80 = 100
180-100= 80°
iii) y = 34+90= 124
x = 180-124= 56
56+90= 146
180-146= 34°
I hope this helped, mark me brainliest please :)
The Greenpoint factory produced two-fifths of the Consolidated Brick Company’s bricks in 1991. If the Greenpoint factory produced 1,400 tons of bricks in 1991, what was the Consolidated Brick Company’s total output that year, in tons?
Answer:
3500 tons
Step-by-step explanation:
The Greenpoint factory produced 2/5 of the bricks that the Consolidate Brick Company produced in 1991.
Let the amount of bricks produced by the Greenpoint factory be g and the amount of bricks produced by the Consolidated brick company be c.
Therefore:
g = 2/5 * c = 2c/5
That year, the Greenpoint factory produced 1400 tons of bricks. This implies that:
1400 = 2c/5
To find the amount that the Consolidated Brick Company produced, solve for c:
1400 = 2c/5
1400 * 5 = 2c
7000 = 2c
c = 7000 / 2 = 3500 tons
The Consolidated Brick Company had a total production output of 3500 tons in 1991.
numa prova de múltipla escolha com 30 questões, o aluno ganha 3 pontos por cada questão que acerta, mas perde 2 pontos por cada questão que erra. Marcelo resolveu todas as questões dessa prova e conseguiu 50 pontos. Quantas questões ele acertou?
Answer:
Marcelo acertou 22 questões.
Step-by-step explanation:
Vamos representar
Questões que acerta = a
Questões que erra = b
a + b = 30 .......... Equação 1
a = 30 - b
o aluno ganha 3 pontos por cada questão que realizar, mas perde 2 pontos por cada questão que ocorrerá.
Matematicamente:
3 × a - 2 × b = 50
3a - 2b = 50 pontos ............. Equação 2
Substitua 30 - b por a na Equação 2
3 (30 - b) - 2b = 50
90 - 3b - 2b = 50
90 - 5b = 50
Colete termos semelhantes
90 - 50 = 5b
5b = 40
b = 40/5
b = 8
Questões que erra = b
Marcelo, portanto, perdeu 8 questões.
Dizem-nos que ele respondeu todas as 30 questões. Portanto, se ele perdeu 8 questões, o número de questões acertadas é representado pela Equação 1
a + b = 30 .......... Equação 1
a + 8 = 30
a = 30 - 8
a = 22 questões.
Portanto, ele acertou 22 questões.
Can you help me plz
Answer:
[tex]\boxed{\sf y=6}[/tex]
Step-by-step explanation:
There are 5 identical squares.
The area of one square is [tex]\sf s^2[/tex].
[tex]\sf{y^2 } \times \sf{5}[/tex]
[tex]\sf 5y^2[/tex]
The area of the whole shape is 180 cm².
[tex]\sf 5y^2=180[/tex]
Solve for y.
Divide both sides by 5.
[tex]\sf y^2=36[/tex]
Take the square root on both sides.
[tex]\sf y=6[/tex]
Use the drawing tools to form the correct answers on the graph. Plot the vertex and the axis of symmetry of this function: f(x) = (x – 3)2 + 5.
Answer:
Axis of Symmetry: x = 3
Vertex: (3, 5)
Step-by-step explanation:
Use a graphing calc.
Answer:
3
Step-by-step explanation:
An ant needs to travel along a 20cm × 20cm cube to get from point A to point B. What is the shortest path he can take, and how long will it be (in cm)? WILL MARK BRAINLIEST
Answer:
The shortest path to take is [tex]20\sqrt{3}\ cm[/tex] or [tex]34.64\ cm[/tex]
Step-by-step explanation:
This question requires an attachment (See attachment 1 for question)
Given
Cube Dimension: 20cm * 20cm
Required
Shortest path from A to B
For proper explanation, I'll support my answer with an additional attachment (See attachment 2)
The shortest path from A to B is Line labeled 2
But first, the length of line labeled 1 has to be calculated;
This is done as follows;
Since, the cube is 20 cm by 20 cm
[tex]Line1^2 = 20^2 + 20^2[/tex] (Pythagoras Theorem)
[tex]Line1^2 = 2(20^2)[/tex]
Take square root of both sides
[tex]Line1 = \sqrt{2(20)^2}[/tex]
Split square root
[tex]Line1 = \sqrt{2} * \sqrt{20^2}[/tex]
[tex]Line1 = \sqrt{2} * 20[/tex]
[tex]Line1 = 20\sqrt{20}[/tex]
Next is to calculate the length of Line labeled 2
[tex]Line2^2 = Line1^2 + 20^2[/tex] (Pythagoras Theorem)
Substitute [tex]Line1 = 20\sqrt{20}[/tex]
[tex]Line2^2 = (20\sqrt{2})^2 + 20^2[/tex]
Expand the expression
[tex]Line2^2 = (20\sqrt{2})*(20\sqrt{2}) + 20 * 20[/tex]
[tex]Line2^2 = 400*2 + 400[/tex]
Factorize
[tex]Line2^2 = 400(2+1)[/tex]
[tex]Line2^2 = 400(3)[/tex]
Take square root of both sides
[tex]Line2 = \sqrt{400(3)}[/tex]
Split square root
[tex]Line2 = \sqrt{400} * \sqrt{3}[/tex]
[tex]Line2 = 20 * \sqrt{3}[/tex]
[tex]Line2 = 20 \sqrt{3}[/tex]
The answer can be left in this form of solve further as follows;
[tex]Line2 = 20 * 1.73205080757[/tex]
[tex]Line2 = 34.6410161514[/tex]
[tex]Line2 = 34.64 cm[/tex] (Approximated)
Hence, the shortest path to take is [tex]20\sqrt{3}\ cm[/tex] or [tex]34.64\ cm[/tex]
Answer:
44.72 cm
Step-by-step explanation:
1. This was marked correct by RSM
2. Unfold the cube, so that points A and B and on points diagonal from each other on a 40 cm x 20 cm rectangle. Now draw a line connecting points A to B. That is the hypotenuse of both triangles. Now according to the pythagorean theorem, the hypotenuse is √2000, which is equal to 5√20.
3. The answer is 44.72 cm
what describes the transformation of g(x)=3(2)-x from the parent function f(x)=2x
Answer:
Reflect across the y-axis, stretch the graph vertically by a factor of 3
Step-by-step explanation:
The question has certain errors, in fact the functions are the following:
g (x) = 3 * (2) ^ - x
f (x) = 2 ^ x
The transformation that we can do to obtain the translated graph, Are given in 2 steps, which are the following:
1. When x is replaced by -x, then it reflects the graph on the y axis.
2. 3 multiplies with the function, it means that it stretches the main function vertically in 3 units.
So to summarize it would be: Reflect across the y-axis, stretch the graph vertically by a factor of 3
Please can someone help me ASAP
a) [tex]\frac{8}{2}[/tex]
b) [tex]\frac{9}{4}[/tex]
c) [tex]\frac{3}{-1}[/tex]
If f(x)=k (square root)2+x, and f^-^1 (-15)=7, what is the value of k
There's a bit of ambiguity in your question...
We know that [tex]f^{-1}(-15)=7[/tex], which means [tex]f(7)=-15[/tex].
I see three possible interpretations:
• If [tex]f(x)=k\sqrt2+x[/tex], then
[tex]f(7)=-15=k\sqrt2+7\implies k\sqrt2=-22\implies k=-\dfrac{22}{\sqrt2}=11\sqrt2[/tex]
• If [tex]f(x)=k\sqrt{2+x}[/tex], then
[tex]f(7)=-15=k\sqrt{2+7}\implies -15=3k\implies k=-5[/tex]
• If [tex]f(x)=\sqrt[k]{2+x}[/tex], then
[tex]f(7)=-15=\sqrt[k]{2+7}\implies-15=9^{1/k}\implies\dfrac1k=\log_9(-15)[/tex]
which has no real-valued solution.
I suspect the second interpretation is what you meant to write.
On a coordinate plane, a line is drawn from point J to point K. Point J is at (negative 6, negative 2) and point K is at point (8, negative 9). What is the x-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:5? x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1 –4 –2 2 4
Answer:
-2
Step-by-step explanation:
The coordinate of a point that divides a line AB in a ratio a:b from A([tex]x_1,y_1[/tex]) to B([tex]x_2,y_2[/tex]) is given by the formula:
[tex](x,y)=(\frac{bx_1+ax_2}{a+b} ,\frac{by_1+ay_2}{a+b} )=(\frac{a}{a+b}(x_2-x_1)+x_1 ,\frac{a}{a+b}(y_2-y_1)+y_1 )[/tex]
Given that a line JK, with Point J is at ( -6, - 2) and point K is at point (8, - 9) into a ratio of 2:5. The x coordinate is given as:
[tex]x=\frac{2}{2+5} (8-(-6))+(-6)=\frac{2}{7}(14) -6=4-6=-2[/tex]
Line segments can be divided into equal or unequal ratios
The x coordinate of the segment is -2
The coordinates of points J and K are given as:
[tex]J = (-6,-2)[/tex]
[tex]K = (8,-9)[/tex]
The ratio is given as:
[tex]m : n =2 : 5[/tex]
The x-coordinate is then calculated using:
[tex]x = (\frac{m}{m + n }) (x_2 - x_1) + x_1[/tex]
So, we have:
[tex]x = (\frac{2}{2 + 5 }) (8 - -6) -6[/tex]
[tex]x = (\frac{2}{7}) (14) -6[/tex]
Expand
[tex]x = (2) (2) -6[/tex]
Open bracket
[tex]x = 4 -6[/tex]
Subtract 6 from 4
[tex]x = -2[/tex]
Hence, the x coordinate of the segment is -2
Read more about line ratios at:.
brainly.com/question/14382744
Lines e and f are parallel. The mAngle9 = 80° and mAngle5 = 55°.
Parallel lines e and f are cut by transversal c and d. All angles are described clockwise, from uppercase left. Where lines e and c intersect, the angles are: 1, 2, 4, 3. Where lines f and c intersect, the angles are 5, 6, 8, 7. Where lines e and d intersect, the angles are 9, 10, 12, 11. Where lines f and d intersect, the angles are 13, 14, 16, 15.
Which angle measures are correct? Select three options.
Answer:
Fist if all u will draw ur Parallel lines e and f are cut by transversal c and d. All angles are described clockwise, from uppercase left. Secondly u will draw ur Parallel lines or angle.
Answer:
a c e
Step-by-step explanation:
A bicycle is on sale price for $300 it can be brought through a hire purchase with a deposit of $60 and 10%
interest the outstanding balance, to prepaid in 10 monthly installments calculate:
a)the amount of each monthly instalment
b)the total cost of buying the bicycle by hire purchase
Answer:
a) $26.4
b) $324
Step-by-step explanation:
Hire purchase is the purchase of an item which can be paid instalmentally.
The bicycle costs $300 for an instant purchase.
For a hire purchase, a $60 deposit must be made and the rest paid instalmentally over 10 months. An interest of 10% is included in the outstanding balance
The outstanding balance after paying deposit= $300 - $60 = $240
Hence, 10% of 240 = 10/100 × 240 = 24
An interest of $24 is added.
Therefore, a total of $240 + $24 = $264 will be paid for the next 10 months.
a) Hence, the amount to be paid in instalment each month is $264/10 = $26.4
b) the total cost of buying the bicycle by hire purchase= deposit amount + instalment price
= $60 + $264
= $324
Hence, a total of $324 will be paid for the bicycle by hire purchase.
N.B: $300 is the sale price + $24 interest
solve the equation using square root 5x2-9=6
Answer:
Is this what you are looking for....
Answer:
x=±√3 or ±1.732
Step-by-step explanation:
5x²-9=6
5x²=6+9
5x²=15
x=±√15/5
x=±√3
What is the measure of angle x?
10
20
30
40
Answer:
20
Step-by-step explanation:
Since 30 and 3x are complementary we can write:
30 + 3x = 90
3x = 60 so x = 20°.
Answer:
20
Step-by-step explanation:
30 + 3x = 90
=> 3x = 90 - 30
=> 3x = 60
=> x = 60/3
=> x = 20
pls mark me as brainleist :)
The shortest side of a triangle is 12cm and the area of the triangle is 8 square cm. A similar triangle has an area of 18 square cm. Calculate the shortest side of this triangle
Answer:
27cm
Step-by-step explanation:
Given the following :
Triangle A:
Shortest side = 12cm
Area of triangle = 8cm^2
Triangle B:
shortest side =?
AREA of triangle = 18cm^2
If triangle A and B are similar :.
Area A / Area B = Length A / length B
8cm^2 / 18 = 12 / length B
Cross multiply :
8cm * Length B = 18 × 12
Length B = 216 / 8
Length B = 27
Therefore, the shortest of the other triangle IS 27cm
Answer:
its A C and E hope this helps
Step-by-step explanation:
ASAP!!! THIS WORTH 50 POINTS!
Answer:
90 16-oz cases and 30 20-oz cases will maximize resin and time use120 16-oz cases will maximize profitStep-by-step explanation:
Let x represent the number of cases of 16-oz cups produced.
Let y represent the number of cases of 20-oz cups produced.
The limitation imposed by available production time is ...
x + y ≤ 15·8 = 120 . . . . maximum number of cases produced in a day
The limitation imposed by raw material is ...
14x +18y ≤ 1800 . . . . . maximum amount of resin used in a day
__
The point of intersection of the boundary lines for these inequalities can be found using substitution:
14(120- y)+18y = 1800
4y = 120 . . . . . subtract 1680, simplify
y = 30
x = 120 -30 = 90
This solution represents the point at which production will make maximal use of available resources. It is one boundary point of the "feasible region" of the solution space.
__
The feasible region for the solution is the doubly-shaded area on the graph of these inequalities. It has vertices at ...
(x, y) = (0, 100), (90, 30), (120, 0)
The profit for each of these mixes of product is ...
(0, 100): 25·0 +20·100 = 2000
(90, 30): 25·90 +20·30 = 2850 . . . . uses all available resources
(120, 0): 25·120 +20·0 = 3000 . . . . maximum possible profit
The family can maximize their profit by producing only 16-oz cups at 120 cases per day.
Answer:
90 16-oz cases and 30 20-oz cases will maximize resin and time use
120 16-oz cases will maximize profit
Step-by-step explanation:
The canvas of a painting has an area of 64 ft2. What length of frame is needed for the border of the painting?
Answer:
8
Step-by-step explanation:
Assuming, the canvas has the shape of a square. By the square area formula we can derive its side:
[tex]S=l^{2}\\64=l^{2}\\l=\sqrt{64}\\ l=8\: ft[/tex]
Then Each side of the painting measures 8 feet, the length of frame must have 8 feet long, and the width is decided by the framer.
Answer:
The answer is C: 32 ft
Step-by-step explanation:
If you take the square root of the area of 64 ft ^2, you get 8. then it asks what is the length needed for the frame as in the entire frame. So you just have to multiply 8 by 4 which is the number of sides. Also, I got this right on the edg quiz.
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
2.86 seconds
Step-by-step explanation:
A graphing calculator shows the ball hits the ground at t = 2.86 seconds.
_____
You can use the quadratic formula with a=-16, b=45, c=2:
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\dfrac{-45\pm\sqrt{45^2-4(-16)(2)}}{2(-16)}=\dfrac{45\pm\sqrt{2153}}{32}\approx\{-0.0438,2.8563\}[/tex]
The ball is in the air for about 2.86 seconds.
A Pythagorean spiral is constructed by drawing right triangles on the hypotenuse of the other right triangles. Start with a right triangle in which each leg is 1 unit long. Use the hypotenuse of that triangle as one leg of a new triangle and draw the other leg 1 unit long. A spiral has been started below, continue the pattern until a spiral with 12 triangles is formed. 1. Determine the Tangent of the angle at the centre of the spiral for each of the first five triangles. 2. Use this pattern to predict the tangent of the 100th triangle.
Answer:
The angle is determined by dividing 360 by the number of vertexes that it took to complete the circle. The tangent of the 100th triangle would be the same respectively.
Step-by-step explanation:
I remember learning this in kindergarten.
Kala's final exam has true/false questions, worth 3 points each, and multiple choice questions, worth 4 points each. Let x be the number of true/false questions she gets correct, and let y be the number of multiple choice questions she gets correct. She needs at least 82 points on the exam to get an A in the class. Using the values and variables given, write an inequality describing this.
Answer:
3x + 4y ≥ 82
Step-by-step explanation:
3x + 4y ≥ 82
we can read as: 3 time of right answers of true/false plus 4 times of right answers of multiple choice must be bigger or at least 82