The given expression is
[tex](6^2)^4[/tex]We would apply the rule of indices or exponent which is expressed as
[tex]\begin{gathered} (a^b)^c=a^{bc} \\ \text{Therefore, the expression would be } \\ 6^{2\times4} \\ =6^8 \end{gathered}[/tex]set up a trigonometric ratio for angle H and solve for X
According to the picture, it is necessary to use cosine, which is the ratio between the side that is adjacent to a given angle and the hypotenuse.
In this case, the angle would be H, the adjacent side to it would be x and the hypotenuse 14. It means that cos H is the ratio between x and 14:
[tex]\cos H=\frac{x}{14}[/tex]2) seperate 90 into two parts (the sum of two numbers is 90)so that one part Cone number) is four times the other part (the other number)
The sum of two parts equal 90.
Also,
one part is 4 times the other part.
Let the normal part be "x", so the 4 times part would be "4x".
Their sum is 90, thus we can write:
[tex]x+4x=90[/tex]Solving for x (a part):
[tex]\begin{gathered} x+4x=90 \\ 5x=90 \\ x=\frac{90}{5} \\ x=18 \end{gathered}[/tex]The other part is:
90 - 18 = 72
So,
The two parts we separate 90 into are "18 and 72".
Suppose medical records indicate that the length of newborn babies (in inches) is normally distributed with a mean of 20 and a standard deviation of 2.6. Find the probability that a given infant is longer than 20 inches. [? ]%
To find the probability we need to use the z score formula, given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where x is the value we like, mu is the median and sigma is the standard deviation.
Then the z score is:
[tex]z=\frac{20-20}{2.6}=0[/tex]Then we have to look for the proability:
[tex]P(z>0)=0.5[/tex]Therefore the probability that a given infant is longer than 20 inches is 0.5 or 50%.
if you could please answer quickly my brainly app keeps crashing
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
diagram:
circle and chords
Step 02:
congruent chords:
Congruent chords are equidistant from the center of a circle.
x = 7 + 7
x = 14
The answer is:
x = 14
write the expression using exponents 7•7•7•7•7•7• (–3)•(–3)•(–3)•(–3)
We have the number 7 multiplying itself 6 times, and the number (-3) multiplying itself 5 times, so writing the expression using exponents, we have:
[tex]\begin{gathered} 7\cdot7\cdot7\cdot7\cdot7\cdot7=7^6 \\ (-3)\cdot(-3)\cdot(-3)\cdot(-3)\cdot(-3)=(-3)^5 \\ \\ 7\cdot7\cdot7\cdot7\cdot7\cdot7\cdot(-3)\cdot(-3)\cdot(-3)\cdot(-3)\cdot(-3)=7^6\cdot(-3)^5 \end{gathered}[/tex]So the final expression is 7^6 * (-3)^5
Amy's cookie shop had expenses of the following: flour $45.00sugar $92.00butter $53 she earns $12 per dozen. what is her profit,if she sells 9 dozen?what is the total dollar amount for expenses?what is the total dollar amount for earnings or revenue?
If she earns $12 per dozen, the following will be the profit if she sells 9 dozen:
[tex]9\cdot12=108[/tex]Profit would be $108.
*The dollar amount of expenses would be:
[tex]e=\frac{190\cdot108}{12}\Rightarrow e=1710[/tex]The expenses would be $1710 if she were to sell 9 dozen.
*The total amount of revenue would be $108 for the 9 dozen sold.
A Ferris wheel at a carnival has a diameter of 72 feet. Suppose a passenger is traveling at 5 miles per hour. (A useful fact: =1mi5280ft.)
(a) Find the angular speed of the wheel in radians per minute.
(b) Find the number of revolutions the wheel makes per hour. (Assume the wheel does not stop.)
a) The Ferris wheel has an angular speed is 12.222 radians per minute.
b) The Ferris wheel makes 116.712 revolutions in an hour.
How to understand and analyze the kinematics of a Ferris wheel
Kinematics is a branch of mechanical physics that studies the motion of objects without considering its causes. In other words, kinematics studies displacements, velocities and accelerations in translation, rotation and combined motion. In this case we find a Ferris wheel rotating around its axis at constant rate.
a) Then, the angular speed (ω), in radians per minute, is determined by the following product:
ω = v / R
Where:
v - Linear velocity at the rim of the Ferris wheel, in feet per second.R - Radius of the Ferris wheel, in feet.Please notice that the length of the radius is the half of the length of the diameter.
If we know that v = 5 mi / h and R = 36 feet, then the angular speed of the wheel is:
ω = [(5 mi / h) · (1 h / 60 min) · (5280 ft / 1 mi)] / [(0.5) · (72 ft)]
ω = 12.222 rad / min
The angular speed is 12.222 radians per minute.
b) A revolution is equal to an angular displacement of 2π radians and an hour is equal to 60 minutes. Then, we can derive the number of revolutions in an hour by dimensional analysis:
n = (12.222 rad / min) · (1 rev / 2π rad) · (60 min / h)
n = 116.712 rev / h
There are 116.712 revolutions in an hour.
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Good morning, I need help on this questions. Thanks :)
The observed values are given in the table shown in the question. The line of best fit is given to be:
[tex]y=-1.1x+90.31[/tex]where x is the average monthly temperature and y is the heating cost.
A residual is a difference between the observed y-value (from scatter plot) and the predicted y-value (from regression equation line). The formula will be:
[tex]Residual=Observed\text{ }y\text{ }value-Predicted\text{ }y\text{ }value[/tex]QUESTION A
The average monthly temperature is 24.9:
[tex]x=24.9[/tex]Observed cost:
[tex]y=51.00[/tex]Predicted cost:
[tex]\begin{gathered} y=-1.1(24.9)+90.31=-27.39+90.31 \\ y=62.92 \end{gathered}[/tex]Residual:
[tex]\begin{gathered} R=51.00-62.92 \\ R=-11.92 \end{gathered}[/tex]QUESTION B
The average monthly temperature is 35.9:
[tex]x=35.9[/tex]Observed cost:
[tex]y=67.00[/tex]Predicted cost:
[tex]\begin{gathered} y=-1.1(35.9)+90.31=-39.49+90.31 \\ y=50.82 \end{gathered}[/tex]Residual:
[tex]\begin{gathered} R=67.00-50.82 \\ R=16.18 \end{gathered}[/tex]Answer: Hl
Step-by-step explanation:
Solve the equation for y in terms of x. After that, replace y & solve with function notation f(x). Once you solve that, find f(4).y+3x^2=4f(x)=____f(4)=____
Given:
[tex]y+3x^2=4[/tex]We have that y f(x), so solve for f(x):
[tex]\begin{gathered} y+3x^2-3x^2=4-3x^2 \\ y=4-3x^2 \\ f(x)=4-3x^2 \end{gathered}[/tex]And for f(4):
[tex]f(4)=4-3(4)^2=4-3(16)=4-48=-44[/tex]Answer:
[tex]\begin{gathered} f(x)=4-3x^{2} \\ f(4)=-44 \end{gathered}[/tex]The diagram has a hollow cylindrical tube, of internal radius 4cm and external radius 6cm. How can I determine the area of an external curved surface, how can I get the area of the inner curved surface and how can I get the total surface area of the tube?
Given:
internal radius = 4cm
External radius = 6cm
Height = 20cm
Curved surface area of the external surface
The formula for the curved surface is:
[tex]\begin{gathered} =2\pi rh \\ \text{Where r is a radius} \\ \text{and h is the height of the cylinder} \end{gathered}[/tex]Hence, the curved surface area:
[tex]\begin{gathered} C\mathrm{}S\mathrm{}A\text{ of external surface = 2}\times\pi\times6\times20 \\ =753.982cm^2 \end{gathered}[/tex]Curved surface area of the inner surface:
[tex]\begin{gathered} C\mathrm{}S\mathrm{}A\text{ of inner surface = 2 }\times\pi\times4\times\text{ 20} \\ =502.654cm^2 \end{gathered}[/tex]The total surface area of the tube :
The total surface area can be found using the formula:
[tex]\text{Total Surface area = }2\pi(R^2-r^2)\text{ + }2\pi h(R\text{ + r)}[/tex]Where R is the radius of the external surface and r is the radius of the inner surface
Hence:
[tex]\begin{gathered} \text{Total Surface area = 2}\times\pi\times(6^2-4^2)\text{ + 2}\times\pi\times20\times(6\text{ + 4)} \\ =\text{ }1382.3cm^2 \end{gathered}[/tex]Solve the system by substitution:y=-6x-77x+y=-3(__ , __)
Substitute -6x-7 for y in the equation 7x+y=-3 to obtain the value of the of x.
[tex]\begin{gathered} 7x-6x-7=-3 \\ x=-3+7 \\ =4 \end{gathered}[/tex]Substitute 4 for x in the equation y=-6x-7 to obtain the value of the y.
[tex]\begin{gathered} y=-6\cdot4-7 \\ =-24-7 \\ =-31 \end{gathered}[/tex]So solution of the equation is (4,-31).
Let MF = 3x - 4 and BM = 5x - 5
Answer:
Explanation:
a)Here, we want to get the value of x
Mathematically, we know that for a triangle with median M, the length of one of the sides is two times the length of the other side of the median
We have this as:
[tex]BM\text{ }=\text{ 2MF}[/tex]Using the side lengths given, we have it that:
[tex]\begin{gathered} 5x-5\text{ = 2(3x-4)} \\ 5x-5\text{ = 6x-8} \\ 6x-5x=8-5 \\ x\text{ = 3} \end{gathered}[/tex]b) We want to find the length of MF. We just have to substitute the value of x in the expression for MP
Mathematically, we have this as:
[tex]MF\text{ = 3(3)-4 = 9-4 = 5}[/tex]c) We want to find the length of BM
[tex]5x-5\text{ = 5(3)-5 = 15-}5\text{ = 10}[/tex]d) Here, we want to find the length of BF
[tex]\begin{gathered} BF\text{ = BM + MF} \\ BF\text{ = 10 + 5 = 15} \end{gathered}[/tex]Mario ordered a pizza for dinner. WHEN IT Came Mario quickly ate 1/8 of the pizza. While Mario was getting napkins, his pet poodle ate 1/3 of the pizza.
Mario ordered a pizza for dinner. when pizza came, Mario quickly ate 1/8 of the pizza and his pet ate 1/3 of the pizza, then the remaining fraction of pizza left is 13/24
The fraction of pizza that Mario eat = 1/8
The fraction of pizza that his pet eat = 1/3
Total fraction = (1/8) + (1/3)
= 11/24
The remaining fraction of pizza = 1 - 11/24
= 13/24
Hence, Mario ordered a pizza for dinner. when it came, Mario quickly ate 1/8 of the pizza and his pet ate 1/3 of the pizza, then the remaining fraction of pizza left is 13/24.
The complete question is :
Mario ordered a pizza for dinner. When it Came Mario quickly ate 1/8 of the pizza. While Mario was getting napkins, his pet poodle ate 1/3 of the pizza. What is the fraction of pizza that left?
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If f(x) = -3 and g(x) = 4x + 2x - 4, find (* + )(x).O A. 4x2 + x +1OB. 432 + x ->C.X2-12OD. 4x2+2x-7
You have the following functions:
[tex]\begin{gathered} f(x)=\frac{x}{4}-3 \\ g(x)=4x^2+2x-4 \end{gathered}[/tex]In order to find (g + f)(x) add like terms of each function. Remind that like terms are those terms with the same variable and same exponent.
Then, you have:
[tex]\begin{gathered} (f+g)(x)=4x^2+2x+\frac{x}{4}-3-4 \\ (f+g)(x)=4x^2+\frac{9}{4}x-7 \end{gathered}[/tex]Hence, the answer is
4x^2 + 9/4 x - 7
–2(1 – 5x) = 4 – 4(-2x)
-2(1 - 5x) = 4 - 4(-2x)
First, we eliminate the parentheses and solve the multiplications
-2*1 - 2*(-5x) = 4 + 8x
-2 + 10x = 4 + 8x
Now, we subtract 8x from both sides and add 2 to both sides
-2 + 10x - 8x + 2 = 4 + 8x - 8x + 2
2x = 6
Then, we divide both sides by 2
2x/2 = 6/2
x = 6/2
x = 3
a bottle of juice is 2/3 full the bottle contains 4/5 cup of juice write division problem that represents the capacity of the bottle
Answer:
x = ( 6 / 5 )y
Step-by-step explanation:
Identify the equaiton.
let x = bottle;
let y = cups;
( 2 / 3 )x = ( 4 / 5 )y;
Multiply both sides by ( 3 / 2 ).
( 3 / 2 )( 2 / 3 )x = ( 3 / 2 )( 4 / 5 )y;
x = ( 12 / 10 )y;
Write the fraction in its simplest form.
x = ( 6 / 5 )y;
It takes 1 + ( 1 / 5 ) of a cup to fill the bottle.
in a hurry! have to finish the practice test in 30mins, so I can take the real one!(CHECKING AWNSERS, SO ONLY NEED AWNSERS TO I CAN COMPARE)
The expression can be simplified as,
[tex]\begin{gathered} \frac{3}{x+2}+\frac{2}{x-3}=\frac{3(x-3)+2(x+2)}{(x-3)(x+2)} \\ =\frac{3x-9+2x+4}{(x-3)(x+2)} \\ =\frac{5x-5}{(x-3)(x+2)} \end{gathered}[/tex]Thus, option (D) is the correct option.
(a) The perimeter of a rectangular garden is 312 m.If the length of the garden is 89 m, what is its width?Width of the garden: ]וח(b) The area of a rectangular window is 6205 cm?If the width of the window is 73 cm, what is its length?Length of the window: 7 cm
EXPLANATION
Let's see the facts:
Perimeter = P = 312 m
Length = l = 89m
Width = w = unknown
The perimeter of a rectangle is given by the following relationship:
[tex]P=2(w+l)[/tex]Replacing terms:
[tex]312=2(w+89)_{}[/tex]Applying the distributive property:
[tex]312=2w\text{ + 178}[/tex]Subtracting 178 to both sides:
[tex]312-178=2w[/tex][tex]134=2w[/tex]Dividing 2 to both sides:
[tex]\frac{134}{2}=w[/tex]Simplifying:
[tex]67=w[/tex]Switching sides:
[tex]w=67[/tex]The width of the garden is 67 meters.
write each decimal in word form 302.78 and 15.023
Answer and Explanation:
302.78 can be written as THREE HUNDRED AND TWO AND SEVENTY EIGHT HUNDREDTHS or THREE HUNDRED AND TWO POINT SEVEN EIGHT.
15.023 can be written in word as FIFTEEN AND TWENTY THREE THOUSANDTHS or FIFTEEN POINT ZERO TWO THREE.
What is the quotient of 2.592 x 10^7 and 7.2 x 10^4 expressed in scientific notation?
Answer:
Explanation:
Given the expression:
[tex]\frac{2.592\times10^7}{7.2\times10^4}[/tex]We can rewrite it as:
[tex]\frac{2592\times10^{-3}\times10^7}{72\times10^{-1}\times10^4}[/tex]Combine all powers of 10:
[tex]\begin{gathered} =\frac{2592\times10^{-3+7}}{72\times10^{-1+4}^{}} \\ =\frac{2592\times10^4}{72\times10^3} \\ =\frac{2592}{72^{}}\times\frac{10^4}{10^3} \\ =36\times10 \\ =3.6\times10^1\times10^1 \\ =3.6\times10^{1+1} \\ =3.6\times10^2 \end{gathered}[/tex]The quotient expressed in scientific notation is 3.6 x 10².
Consider the following data. The expected value is -2.1.Find the variance, standard deviation, P(X ≥ -1), and P(X ≤ -3).
Given
The data,
To find:
The variance, standard deviation, P(X ≥ -1), and P(X ≤ -3).
Explanation:
It is given that,
Then,
The variance is,
[tex]\begin{gathered} Var[x]=(-4-(-2.1))^2\times0.2+(-3-(-2.1))^2\times0.3+(-2-(-2.1))^2 \\ \times0.1+(-1-(-2.1))^2\times0.2+(0-(-2.1))^2\times0.2 \\ =(-4+2.1)^2\times0.2+(-3+2.1)^2\times0.3+(-2+2.1)^2\times0.1+(-1+2.1)^2 \\ \times0.2+(2.1)^2\times0.2 \\ =3.61\times0.2+0.81\times0.3+0.01\times0.1+1.21\times0.2+4.41\times0.2 \\ =0.722+0.243+0.001+0.242+0.882 \\ =2.09 \end{gathered}[/tex]And the standard deviation is,
[tex]\begin{gathered} SD=\sqrt{Var[x]} \\ =\sqrt{2.09} \\ =1.45 \end{gathered}[/tex]Also,
[tex]\begin{gathered} P\left(X≥-1\right)=P(X=-1)+P(X=0) \\ =0.2+0.2 \\ =0.4 \\ P\left(X≤-3\right)=P(-4)+P(-3) \\ =0.2+0.3 \\ =0.5 \end{gathered}[/tex]Hence, the answers are,
Variance is 2.09
Standard deviation is 1.45
P(X ≥ -1) is 0.4
P(X ≤ -3) is 0.5.
Determine the probability of the given opposite event.What is the probability of rolling a fair die and not getting an outcome less than 3?
The Opposite Event rule is the probability that event A happens is equal to one minus the probability that A does not happen.
If P(A) is the probability of A happening, and N(A) is the probability of A don't happen, we can write:
[tex]P(A)=1-N(A)[/tex]Now we can see:
[tex]N(A)=1-P(A)[/tex]This, we if we calculate the probability of getting less than 3, ve can calculate the probability of not getting less than 3.
Then, what are the results that are less than 3? Those are 1 and 2. Thus are the favorable outcomes, and since is a fair dice, there are 6 total possible outcomes.
The probability of A = getting less than 3, is:
[tex]\begin{gathered} P(A)=\frac{2}{6} \\ P(A)=\frac{1}{3} \end{gathered}[/tex]
Now we can calculate the probability of not getting less than 3:
[tex]\begin{gathered} N(A)=1-\frac{1}{3} \\ \end{gathered}[/tex][tex]N(A)=\frac{2}{3}[/tex]
The probability of not getting less than 3 is:
[tex]Probability=\frac{2}{3}\approx0.666[/tex]Or in percentage:
[tex]Probability=66.67\%[/tex]Hello good night everyone I need help with number 6 I’m so lost I’m abt to cry
We have to add and substract this complex numbers.
In this type of problems, where we have to add or substract complex numbers, we need to have the real and imaginary terms separated.
In this case, we already have all the terms as real or imaginary.
Then, we can group the real terms on one side and the imaginary terms on the other side and simplify them. We can do it like this:
[tex]\begin{gathered} (7-2i)-(-1-4i)+3 \\ 7-2i+1+4i+3 \\ (7+1+3)+(-2i+4i) \\ 11+2i \end{gathered}[/tex]Answer: 11 + 2i
The perimeter of a rectangle is 36 cm and the length is twice the width. What are the dimensions of this rectangle? What’s the length and width?
Chen is opening a new account with a $1,200 deposit. She will be keeping money in the account, compounded monthly for no more than 3 years. the formula gives the value, V, of the account as a function of time, t. Which is a reasonable domain of this function?V(t)= 1,200(1 + 0.02)^t/12A) 0< or equal to t < or equal to 36B) 0C) 0 < or equal to t < or equal to 1,273.45D) 1,200 < or equal to t < or equal to 1,273.45
The Solution:
Given the function:
[tex]V(t)=1200(1+0.02)^{\frac{t}{12}}[/tex]We are required to find a reasonable domain for the given function.
The domain of the function V(t) is the range of values for t.
The question says Chen is will continue to keep money in the account for not more than 3 years, but the interest will be compound monthly.
Recall:
1 year = 12 months
So,
3 years will be
[tex]12\times3=36\text{ months}[/tex]This means that the range of values for t is:
[tex]0\leq t\leq36[/tex]Therefore, the correct answer is [option A]
A ball is shot from a cannon into the air with an upward velocity of 40 ft/sec. The equation that give the height (h) of the ball at any time (t) is: h(t)= -16t^2 + 40t + 1.5. Find the maximum height attained by the ball. I need a clear explanation because I have to expose this
The height of the ball at any time t is given by
[tex]h(t)=-16t^2+40t+1.5[/tex]This is a quadratic equation, which attains its maximum value at time:
[tex]t=\frac{-b}{2a}[/tex]In the given equation, a = -16 and b = 40. substitute these values in the formula:
[tex]t=\frac{-40}{-16\times2}=\frac{-40}{-32}=\frac{5}{4}[/tex]Therefore, the ball attains its maximum height at t=5/4 seconds which is given below:
[tex]\begin{gathered} h(\frac{5}{4})=-16(\frac{5}{4})^2+40(\frac{5}{4})+1.5 \\ =-25+50+1.5 \\ =26.5 \end{gathered}[/tex]Thus, the maximum height attained by the ball is 26.5 feet.
Today's previewYou can solve this by rearranging to create asituation to use the method from the previouslesson, or you can solve this by thinking a littledifferently about how the variables below mightalso be described.... so solve it.y = 2x + 4x + y = 7
A hummingbird's brain has a weight of approximately 2.94 x 10- ounces. An elephant's brain has a weight ofapproximately 1.76 x 102 ounces.Approximately how many times heavier is the elephant's brain than the hummingbird's brain?A) 60B) 600C) 6,000D) 60,000
Given the information on the problem,we have to divide the weight of the elephant's brain by the weight of the bird's brain, then, using the rules of exponents, we have the following:
[tex]undefined[/tex]in the sophomore class at Summit High School the number of students taking French is 2/3 of the number taking Spanish. how many students are studying each language if the total number of students in French and Spanish is 310 ?This is Homework
From the information given in the statement let be
[tex]\begin{gathered} f=\frac{2}{3}s\text{ (1)} \\ f+s=310\text{ (2)} \end{gathered}[/tex]Where
*f: number of students taking a French class
*s: number of students taking a Spanish class
So, you have a system of linear equations, which you can use the substitution method.
To do this, replace the value of the first equation in the second equation and solve for s
[tex]\begin{gathered} f+s=310\text{ (2)} \\ \frac{2}{3}s+s=310 \\ \frac{5}{3}s=310 \\ \text{ Multiply by }\frac{3}{5}\text{ on both sides of the equation} \\ \frac{3}{5}\cdot\frac{5}{3}s=310\cdot\frac{3}{5} \\ s=186 \end{gathered}[/tex]Now,
a test has 20 Questions worth 100 points the test consists of true or false questions worth 3 points each and multiple choice questions worth 11 points each how many multiple choice questions are on the test
A test is to be conducted with certain types of questions and each type of question weighs certain number of points.
A test would consist of two types of questions. These two types will be assigned variables that will denote the number of questions respectively as follows:
[tex]\begin{gathered} \text{True and False: x} \\ \text{MCQS : y} \end{gathered}[/tex]We are given that the entire test will consits of 20 questions. We can express the total number of questions on the test in terms of number of True and False questions ( x ) and number of MCQS ( y ) as follows:
[tex]\begin{gathered} \text{Total number of Questions = True and False + MCQS} \\ \textcolor{#FF7968}{20}\text{\textcolor{#FF7968}{ = x + y }}\textcolor{#FF7968}{\ldots Eq1} \end{gathered}[/tex]Further information is given to us in the questions regarding the number of points aloted to each type. The total weightage of each type of question on the test can be expressed as a product of ( number of each type * point weight of each type ).
The point weights for each type of questions are:
[tex]\begin{gathered} \text{True and False ( x ) : 3 points each} \\ \text{MCQs ( y ) : 11 points each} \end{gathered}[/tex]The total weights of each types of questions are:
[tex]\begin{gathered} \text{True and False ( points ) = 3}\cdot x \\ \text{MCQS ( points ) = 11}\cdot x \end{gathered}[/tex]We are given that the entire test is worth ( 100 points ). We express the total number of points of the test in terms of total weight of each type of question as follows:
[tex]\begin{gathered} test\text{ points = True and False ( points ) + MCQS ( points )} \\ \textcolor{#FF7968}{100}\text{\textcolor{#FF7968}{ = 3}}\textcolor{#FF7968}{\cdot x}\text{\textcolor{#FF7968}{ + 11}}\textcolor{#FF7968}{\cdot y\ldots}\text{\textcolor{#FF7968}{ Eq2}} \end{gathered}[/tex]We have two equations that express the total number of questions ( Eq 1 ) and total points ( Eq2 ) of the test in terms of number of True and False questions ( x ) and number of MCQs on the test ( y ).
[tex]\begin{gathered} \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ + y = 20 }}\textcolor{#FF7968}{\ldots Eq1} \\ \textcolor{#FF7968}{3x}\text{\textcolor{#FF7968}{ + 11y = 100 }}\textcolor{#FF7968}{\ldots}\text{\textcolor{#FF7968}{ Eq2}} \end{gathered}[/tex]We will solve the above two equations simultaneously using Elimination method.
Step1: Multiply Eq1 with ( -3 )
[tex]\begin{gathered} -3\cdot\text{ ( x + y ) = -3}\cdot20 \\ \textcolor{#FF7968}{-3x}\text{\textcolor{#FF7968}{ - 3y = -60 }}\textcolor{#FF7968}{\ldots}\text{\textcolor{#FF7968}{ Eq3}} \end{gathered}[/tex]Step2: Add Eq 3 into Eq 2
[tex]\begin{gathered} -3x\text{ - 3y = -60 } \\ 3x\text{ + 11y = 100} \\ =========== \\ 8y\text{ = 40 } \\ \textcolor{#FF7968}{y}\text{\textcolor{#FF7968}{ = 5}} \\ =========== \end{gathered}[/tex]Step3: Back susbtitue the value of ( y ) into ( Eq1 )
[tex]\begin{gathered} x\text{ + ( 5 ) = 20 } \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 15 }} \end{gathered}[/tex]Therefore, the number of each type of questions that must be put on the test should be.
[tex]\begin{gathered} \text{\textcolor{#FF7968}{True and False ( x ) = 15}} \\ \text{\textcolor{#FF7968}{MCQs ( y ) = 5}} \end{gathered}[/tex]