Answer:
10
Step-by-step explanation:
so x=true/false questions
y=multiple-choice questions
2x+4y=100
2x=y
plug in 2x for y in the first equation
2x+4(2x)=100
10x=100
x=10
y=20
The total questions would include 10 true/false questions and 20 multiple-choice questions.
We have Mr. Dudley who is writing a test for his mathematics class. The test will have true/false questions worth 2 points each and multiple-choice questions worth 4 points each for a total of 100 points. He wants to have twice as many multiple-choice questions as true/false questions.
We have to determine how many true/false questions and multiple-choice questions will be on the test.
What do understand by Modelling of a Equation ?The modelling of equation is done to derive a mathematical relation among the terms defined in a mathematical statement.
According to the question -
Assume that the number of true/false questions be x.
Assume that the number of multiple-choice questions be y.
Then -
y = 2x
Points for each true/false questions - 2 points
Points for each multiple-choice questions - 4 points
Total points of test = 100 points
Now,
Model the equation on the basis of above information -
2x + 4y = 100
2x + 4 (2x) = 100
2x + 8x = 100
10x = 100
x = 10
Therefore -
y = 2x = 2 x 10 = 20
Hence, the total questions would include 10 true/false questions and 20 multiple-choice questions.
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Find the equation of the tangent line to y=sinx at x=2pie
Answer:
y = x - 2π
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate y₁ - y coordinate m - slopePre-Calculus
Unit CircleCalculus
The definition of a derivative is the slope of the tangent line.
Derivatives of Trig Functions
sin(x) = cos(x)cos(x) = -sin(x)tan(x) = sec²(x)sec(x) = sec(x)tan(x)csc(x) = -csc(x)cot(x)cot(x) = -csc²(x)Step-by-step explanation:
Step 1: Define
y = sinx
x = 2π
Step 2: Find Derivative
Take derivative: y' = cosxThis is the function of the tangent line for y.
Step 3: Find slope
Substitute in x into y': y'(2π) = cos2πEvaluate: y'(2π) = 1This tells us that the slope of the tangent line is 1 at x = 2π.
Step 4: Write equation
Find a point.
Substitute x into y: y(2π) = sin2πEvaluate: y(2π) = 0Write coordinate: (2π, 0)Write tangent function.
Substitute: y - 0 = 1(x - 2π)Simplify: y = x - 2πThis is the equation of the tangent line at x = 2π.
57x2.3 what is the anser pls help
Answer:
285.00
Step-by-step explanation:
Because you change 57 to a decimal (57.0) then you multiply.
57.0×2.3=285.00
today is my birthday wish me a happy birthday
Whoever answers correctly gets brainlist.
Answer:
1.- 4/5 + 5/12= 1 and 13/60
2.- 5/6 + 6/12= 1 and 1/3
3.- 1/3 + 2/6= 2/3
4.- 7/8 + 8/10= 1 and 27/40
ian's car can go 99 miles on 3 gallons of gas During a drive last weekend,Ian used 7 gallons of gas.How far did he drive?Use pencil and paper. Explain how the problem changes if you were given the distance Ian drove last weekend instead of how much gas He used. He drove____ miles.
Answer:
The answer would be 231 miles.
Step-by-step explanation:
This is because you have to make this into the most common ratio, which would be 1/33. To get to 7 gallons, you must multiply 33 by 7, because you multiplied 1 by 7.
Is the sum of any 2 consecutive prime numbers also prime?
Answer:
Yes! (it’s making me write 20 letters so yes is ur answer ok cool)
Use the order of operations to simplify 4 + 15 = 5
A 24 4/5
B 19 2/5
C 7 2/5
D 8
Answer:
C
Step-by-step explanation:
-3a - 4(a - 6) = 24 - 7a
Solve the equation
Thanks
-3a-4(a-6)=24-7a
-3a-4a+24=24-7a
-7a+24=24-7a
-7a+24=-7a+24
-7a+24-24=-7a+24-24
Simplify
Subtract the numbers
Subtract the numbers
−7a=-7a
Add 7a to both sides of the equation
-7a+7a =-7a+7a
Simplify
Combine like terms
Combine like terms
0=0
answer is 0=0
The store bought the bike at a wholesale price. The bike store marked up the wholesale cost of the bike by 60%. What was the wholesale cost of the bike if the store sold the bike to Andre for $160?
Answer: The wholesale cost of the bike = $100
Step-by-step explanation:
Let x = wholesale cost of the bike
As per given,
Selling price = cost price + (Mark up percent) x ( cost price) (i)
Selling price of bike = $160
Mark up percent = 60% =0.60
Substitute values in (i) , we get
[tex]160= x+0.6x\\\\\Rightarrow\ 160=1.6x\\\\\Rightarrow\ x=\dfrac{160}{1.6}\\\\\Rightarrow\ x= 100[/tex]
Hence, the wholesale cost of the bike = $100
An article on polygraph testing of FBI agents indicated that the probability of a false-positive (a trustworthy person who nonetheless fails the test) is 0.25. Let x be the number of trustworthy FBI agents tested until someone fails the test. (Round your answers to four decimal places.)(a) Describe the probability distribution of x.
normalgeometric binomial(b) What is the probability that the first false-positive will occur when the third person is tested?(c) What is the probability that fewer than four are tested before the first false-positive occurs?(d) What is the probability that more than three agents are tested before the first false-positive occurs?
Answer:
???
Step-by-step explanation:
What is a3 of the sequence 13, 18, 23, 28, 33, 38...
Answer:
23
Step-by-step explanation:
cuz it starts with 13 as a1
Tom bought a new mirror for his house. One side of the mirror is 38 inches and the other side is 30 inches. What is the length of the diagonal of the mirror? a. 68 inches b. 23 inches c. 34 inches d. 48 inches
Answer:
d. 48 inches
Step-by-step explanation:
We assume the mirror is a rectangle
We solve for the length of a diagonal using Pythagoras Theorem
a² + b² = c²
c = √a² + b²
Where c = diagonal
a = 30 inches
b = 38 inches
c = √30² + 38²
c = √2344
c = 48.414873748 inches
Approximately = 48 inches
Mr. Santiago has a flight from New York to Paris that covers a distance of 3,640 miles in 7 hours. If the plane travels at the same speed per hour, how many miles will it have traveled after 4 hours?
2. Josh watches 720 shows in one year. If he watches the same number of shows each month, how many shows does he watch in 5 months?
Answer:He traveled 2080 miles after 4 hours. He covered 3640 miles in 7 hours with a constant speed, so we can calculate the speed: 3640/7=520 miles/hour. After 4 hours, he traveled 520*4=2080 miles.
Step-by-step explanation:
Which of the following equations represent linear functions?
y=x2−3x
4x+y=5
y=|2x+1|
y=−5
Which of the following values are solutions to the inequality 5 < 7+ 5x?
Answer:
x can equal to anything that is 1 and higher
Step-by-step explanation:
The equation is already correct, you just want to get x as a number that would increase the value.
Imena earned $261 last week. If she worked 18 hours and earned the same amount each hour, how much was she paid per hour?
The amount paid to Imena per hour will be $14.5
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Imena earned $261 last week. She worked 18 hours and earned the same amount each hour.
Imena's earnings for an hour will be calculated as:-
Earning per hour = 261 / 18
Earning per hour = $14.5
Therefore, the amount paid to Imena per hour will be $14.5
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Auto sales in a country increased from 16.5 million in 2014 to 17.5 million in 2015. Find the percent increase in auto sales from 2014 to 2015. Round to the nearest tenth of a percent._______%
Answer:
6.1%
Step-by-step explanation:
Amount increase=17.5-16.5
=1million
% increase= amount increase/original×100% amount
= 1/16.5×100%
= 6.1%
The percentage increase in auto sales is 6.1 %
What is Percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
Given data ,
The auto sales of the country in 2014 = 16.5 million
The auto sales of the country in 2015 = 17.5 million
The increase in auto sales in 2015 from 2014 =
Auto sales of the country in 2015 - Auto sales of the country in 2014
The increase in auto sales in 2015 from 2014 = 17.5 million - 16.5 million
= 1 million
Now , the percentage increase in auto sales =
( Increase in auto sales / Auto sales of the country in 2014 ) x 100
The percentage increase in auto sales = ( 1 / 16.5 ) x 100
= 6.06 %
Therefore , the percentage increase is 6.1 %
Hence , the percentage increase in auto sales if 6.1 %
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What is the u equal to -4=u/2-8
Answer:12. V is not needed, and just substitute the letters with the numbers the correspond to.
Step-by-step explanation:
If a freight train travels at a speed of 20 miles per hour for 6 hours, how far will it travel? A 120 miles B 80 miles C 26 miles D 12 miles
Answer: The answer is A
Step-by-step explanation: Because 6*20= 120
Charli bought 2 3/4 pounds of pears for 0.76 per pound and 2 3/4 pounds of grapes for 1.40 per pound. how much money in dollars and cents did charli pay for the pears and grapes?
Answer:
[tex]Total = \$5.94[/tex] ---- in dollars
[tex]Total = 594\ cents[/tex] ---- in cents
5 dollars 94 cents
Step-by-step explanation:
Given
Pears
[tex]Weight = 2\frac{3}{4}\ lb[/tex]
[tex]Amount = \$0.76[/tex] per pound
Grapes
[tex]Weight = 2\frac{3}{4}\ lb[/tex]
[tex]Amount = \$1.40[/tex] per pound
Required
Determine the amount paid for the fruit in dollar and cents
First, we need to calculate the amount paid for each fruit.
This is calculated by multiplying the amount per pound by the number of pounds bought.
For Pears:
[tex]Total_{Pears} = 2\frac{3}{4} * \$0.76[/tex]
Convert fraction to decimal
[tex]Total_{Pears} = 2.75 * \$0.76[/tex]
[tex]Total_{Pears} = \$2.09[/tex]
For Grapes
[tex]Total_{Grapes} = 2\frac{3}{4} * \$1.40[/tex]
Convert fraction to decimal
[tex]Total_{Grapes} = 2.75 * \$1.40[/tex]
[tex]Total_{Grapes} = \$3.85[/tex]
Next, we add both amounts together to get the total amount spent in dollars.
[tex]Total = Total_{Pears} + Total_{Grapes}[/tex]
[tex]Total = \$2.09 + \$3.85[/tex]
[tex]Total = \$5.94[/tex]
Multiply by 100 to convert this amount to cents
[tex]Total = 5.94 * 100\ cents[/tex]
[tex]Total = 594\ cents[/tex]
And it can be represented as dollars and cents as:
5 dollars 94 cents
If a car travels 23 miles in 20 min what is the. car speed in miles per hour?
Answer:
69 miles per hour
Step-by-step explanation:
car travels 23 miles in 20 min
So 20 min=20/60hour
=1/3. hour
Speed of the car=23÷1/3
=69 miles/hour
So the final answer is 69miles/hour
Use differentials to approximate the value of the expression. Compare your answer with that of a calculator. (Round your answers to four decimal places.) (8.99)3 using differentials
Answer:
726.572699
Step-by-step explanation:
According to differentials
(x+Δx)³ = x³ + 3x²Δx + 3x(Δx)² + (Δx)³ (Using binomial expansion)
Using this formula to solve (8.99)³, this can also be written as;
(8.99)³ = (9-0.01)³ where
x = 9
Δx = -0.01
Substitute this vales into the differential expression above
(9+(-0.01))³ = 9³ + 3(9)²(-0.01) + 3(9)(-0.01)² + (-0.01)³
(9+(-0.01))³ = 729 + (243)(-0.01) + 27(0.0001) + (-0.000001)
(9+(-0.01))³ = 729-2.43+0.0027-0.000001
(9+(-0.01))³ = 729-2.43+0.0027-0.000001
(9+(-0.01))³ = 726.572699
Hence 8.99³ = 726.572699 (Using differential)
Using calculator;
8.99³ = 726.572699
the ratio 60 miles per hour is an example of a ______because it has two measurements having different units of measure
Answers:
1.Annex
2.Rate
3.Unit rate
4.Least common multiple
Answer:
3. Unit Rate
Step-by-step explanation:
The answer is Unit Rate because it is describing two units of measurements compared to one another.
Can you Explain how to do this plz
Video game system and several games are sold for $664. The cost of the games is 3 times as much is a cost in system. Find the cost of the system the cost of the games.
Answer:
games=$483
system=$161
Step-by-step explanation:
Answer: the cost of the system is $166 and the cost of the games is $498.
Step-by-step explanation:
Which equation is the inverse of y = 9x2 – 4?
Answer:
C
Step-by-step explanation:
For edge
Answer:
correct C on e2021
Step-by-step explanation:
pleas yall help me ill give a lot of points and brainiest
Answer:
Third choice.
Step-by-step explanation:
The left side is "8 less than 4 times a number"
The right side is "2 times the difference of 2 times the number decreased by 3"
Answer: Third choice.
Suppose a team is to be formed consisting of a head chef, sous chef, and dishwasher, in that order. What is the probability of forming such a team with 6 people?
Answer:
0.0083
Step-by-step explanation:
From the given information;
The total number of individual in the team = 3
The number of ways the team, which comprises of head chef, sous chef, and dishwasher can be arranged = [tex]^{6}P_3[/tex]
= (6×5×4×3!)/3!
= 6×5×4
= 120 ways
The probability of forming such a team with 6 people = 1/120
= 0.0083
wild deer population weight has standard deviation of 50 lb. What is the probability of existence of a random sample (size 100) weight within + 5 lb. of population mean weight?
This question was not written properly
Complete Question
Wild deer population weight has standard deviation of 50 lb. What is the probability of existence of a random sample (size 100) weight within ± 5 lb. of population mean weight?
Answer:
0.68269
Step-by-step explanation:
We solve using z score formula
z = (x-μ)/σ/√n where
x is the raw score
μ is the population mean
σ is the population standard deviation.
From the question:
Standard deviation = 50 lb.
Sample size = 100
The weight is within ± 5Ib
For +5 lb
Z =+ 5/50/ √100
Z = +5/50/10
Z = +5/5
Z = 1
Using the Z table to find the probability of the Z score.
P(Z = 1) = 0.84134
For - 5 lb
Z = - 5/50/ √100
Z = - 5/50/10
Z = - 5/5
Z = -1
Using the Z table to find the probability of the Z score.
P(Z = -1 ) = 0.15866
Hence,
P (-Z<x<Z)
P(Z = +1 ) - P(Z = -1)
0.84134 - 0.15866
= 0.68269
The probability of existence of a random sample (size 100) weight within ± 5 lb. of population mean weight is 0.68269
A car travels 180 miles in 4 hours. What is
the car’s speed in feet per minute?
Answer:
3,960 feet per minute, brainliest pls
Step-by-step explanation:
Answer:
3960 feet per minute
Step-by-step explanation:
1 mile = 5280 feet
Therefore,
180 miles = 180*5280
180 miles = 950400 feet
1 hour = 60 minutes
So, 4 hours = 240 minutes
Speed if the car
= 950400/240
= 3960 feet per minute
evaluate the expression for x = 3 y= 1/3 and z= 5. 12 x - 3y / 4 x - Z
Answer:
5
Step-by-step explanation:
12 x - 3y / 4 x - Z
=12×3-3×1/3÷4×3-5
=36-1/12-5
=35/7
=5
So the final answer is 5.