The smallest positive integer by using the trial and error method will be 47.
What is meant by trial and error method?
Trial and error is a fundamental method of Problem solving. It is characterized by repeated, varied attempts which are continued until success, or until the agent stops trying. Until getting the right answer the problem is repeated through various steps. This type of problem solving is called trial and error method.
Now
since the numbers are small, trial and error works.
Consider those numbers which are of the form 11x+3 :- 3, 14, 25, 36, 47, 58, 69, 80, 102, 113, 124, 146, 168, 179, 190, 212, 223
From given number find the number which when divided by 3 gives remainder 2 and when divided by 7 gives remainder 5 and the smallest number will be our answer.
From given numbers 47 is the smallest positive integer which satisfies given conditions.
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How many pints of cooking oil are needed to have 14 quarts in all?
If you have 14 quarts of cooking oil, you will need 56 pints of cooking oil.
What is quantity?Quantity is a term used to describe the amount or magnitude of something. It can refer to physical items, such as the number of apples in a bag, or abstract concepts, such as the number of people living in a city. It is a measure of how much of something exists, and it is usually expressed in units such as gallons, liters, or pounds.
14 quarts is equal to 56 pints, so 56 pints of cooking oil are needed to have 14 quarts in total. To convert quarts to pints, multiply the number of quarts by 4. Therefore, if you have 14 quarts of cooking oil, you will need 56 pints of cooking oil.
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What is value of
X+8
Enter your answer in the box
2x-5
B
10
14
The value of x is 13 in the equation x+8=2x-5.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is x+8=2x-5
x plus eight equal to two times of x minus five.
Subtract 2x from both the sides
x+8-2x=-5
-x+8=-5
Subtract 8 on both sides
-x=-5-8
-x=-13
x=13
Hence, the value of x is 13 in the equation x+8=2x-5.
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Cameron's soccer team has $168 to buy
uniforms that cost $20 each. How many uniforms can
his team buy? Will there be any money left over? Solve
this problem any way you choose.
Answer:
His team can buy 8 uniforms, and $8 will be left over.
Step-by-step explanation:
168(total amount of money) divided by 20(cost of each uniform) is 8 with a remainder of $8.
A state fair costs $25 to get in plus $ 4 per ticket to go on rides. What is the equation of this situation?
The equation of this situation is,
⇒ y = $25 + $4x
Where, y is total cost and x represent number of tickets for rides.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A state fair costs $25 to get in plus $ 4 per ticket to go on rides.
Now,
Let number of tickets = x
So, We can formulate;
The equation of this situation is,
⇒ y = $25 + $4x
Where, y is total cost and x represent number of tickets for rides.
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Write the proportion.
5.4 hours is to 9.0 hours as
3.3 hours is to 5.5 hours.
PLEASE HELP!!!
consider the equation 7x + 4 = ax + b.
for each pair of values for a and b, determine the number of solutions that the equation has.
select no solution, one solution, or infinitely many solutions for each pair of values.
1. a = 7, b = -4
2. a = 4, b = 7
3. a = 7, b = 4
4. a = -7, b = 4
Answer:
a = 7, b = -4:
This equation can be rewritten as 7x = ax + b - 4.
Since the coefficients of x on both sides are equal, the equation becomes 7x = ax - 4, we can see that the equation has only one solution.
a = 4, b = 7:
This equation can be rewritten as 7x = ax + b - 7.
Since the coefficients of x on both sides are different, the equation becomes 7x = 4x + 7, we can see that the equation has no solution.
a = 7, b = 4:
This equation can be rewritten as 7x = ax + b - 4.
Since the coefficients of x on both sides are equal, the equation becomes 7x = 7x + 4, we can see that the equation has infinitely many solutions.
a = -7, b = 4:
This equation can be rewritten as 7x = ax + b - 4.
Since the coefficients of x on both sides are different, the equation becomes 7x = -7x + 4, we can see that the equation has no solution.
Step-by-step explanation:
1 You’re a travelling sales rep. You live in city A and need to drive to City B and then on to City C for business. You then need to drive back to city A. You will rent a new car in each city. The distance from A to B is 250 miles, from B to C is 175 miles and from A to C is 320 miles. You start at A and go the shortest route next to B then to C and then back to A. The car rented in City A gets 10 km per liter of fuel. The car rented in City B gets 18 km per liter and the car rented in city C 24 km per liter. Gas costs $4.25 US per gal. You drive From City A to City B at an average speed of 120 km per hr. You drive from City B to City C at an average speed of 100 km per hr. You drive from City C to City A at an average speed of 140 km per hr. The exchange rate is 0.85 Euro per $1. 1) How far is the total distance in Kilometers? 2) How much will you spend on gas in euros? 3) How long will it take you to make the round trip not including any rest? Driving time only in minutes. 4) Suppose that while you are in City B you find out that you do not need to go to city C and decide to keep your initial car and drive back to City A. How much will this trip cost for gas in euros?
Answer:
Total distance = 250 miles + 175 miles + 320 miles = 745 miles = 1207.2 km
Total cost = (250 miles / 10 km/L * 4.25 $/gal + 175 miles / 18 km/L * 4.25 $/gal + 320 miles / 24 km/L * 4.25 $/gal) * 0.85 Euro/$ = €113.55
Total driving time = (250 miles / 120 mph * 60 min/hr + 175 miles / 100 mph * 60 min/hr + 320 miles / 140 mph * 60 min/hr) = 5.0417 hours = 304 min
Cost of trip back to City A = 250 miles / 10 km/L * 4.25 $/gal * 0.85 Euro/$ = €52.88
Step-by-step explanation:
-
Given f(x) = x² − 8x + 8, find ƒ(−5)
A young boy living in England was asked to fill up two
jugs with water. The boy took the two jugs to the watering
hole and pumped the water out to fill up the jugs. Each
jug holds 2.5 gallons of water when the boy heads back to
his house.
Find the value of c ÷ 7 when c = 49
Answer: 7
Step-by-step explanation: Plug in 49 for c.
49 divided by 7 is 7.
Answer:
c ÷ 7 = 7
Step-by-step explanation:
because if c = 49 then 49 ÷ 7 = 7
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A rose garden is formed by joining a rectangle and a semicircle, as shown below. The retangle is 32 ft long and 24 ft wide. If the gardener wants to build a fence around how many feet of fence
The length, width, and fence of a semicircle are the parameters for the garden fence.The required fence length is 118.54 feet.
How is the fence of the semicircle calculated?As shown below, a rose garden is created by connecting a rectangle with a semicircle.The rectangle is 22 feet broad by 31 feet long.
The necessary fence is computed by multiplying the rectangle's length and width by its radius.
Radius = Diameter /2 22/2 = 11 gives the radius of the semicircle.
And the semicircle's garden fence's measurements are:
11*3.14
= 34.54
Therefore,
The length, width, and fence of a semicircle are the parameters for the garden fence.
Garden fencing is necessary and equals 22+31+31+34.54
The garden fence length is 118.54 feet.
Consequently, 118.54 feet of fence
The required fence length is 118.54 feet.
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In a shipment of computers from a manufacturer, the probability that a computer is defective is 1/50. If a computer buyer for a store selects 2 computers from a shipment, what is the probability that both computers are defective? 1/50 1/100 1/250 1/2500
Answer:
1/125
Step-by-step explanation:
multiply 1/50 by 1/50
2/2500
simplify
1/125
What place is the underlined number the number is 506.34 and the underlined digit is four
Answer:
It is the hundredth place which is underlined.
Point A is the original point before rotating. Which point represents A′ after A(4, 1) is rotated 90° counterclockwise: B, C, D, E, F, G, or H?
Answer:
Point G
Step-by-step explanation:
The mapping rule for a 90° counterclockwise rotation is:
(x, y) → (-y, x)
Therefore, if A = (4, 1):
A' = (-1, 4)The point that represents A' after A(4, 1) is rotated 90° counterclockwise is:
Point GHow many solutions does -3(2x + 7) = -6x + 7 have?
Answer: No solution
Step-by-step explanation:
Expand:
-6x - 21 = -6x + 7
Add 6x to both sides
-21 = 7
No solution
A moving walkway at the airport moves at a pace of 1.8 feet per second.
If you stand on the walkway as it moves, how long will it take to transport you 270 feet?
The time taken by the walkway to cover 270 feet is 150 seconds.
What is speed?The distance that an object travels in relation to the amount of time it takes to do so can be used to define speed. In other terms, it is a measurement of an object's motion's speed without direction Velocities are what we get when speed and direction are combined.
Given the speed of the walkway = 1.8 feet per second
distance = 270 feet
speed is given by
speed = distance/time taken
time = distance/speed
substitute the values,
time taken = 270/1.8
time taken = 150 seconds
Hence it will take 150 seconds.
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Find the numbers whose sum is 9, if
three times the first number increased
by two times the second number
equals 22.
Therefore , the solution of the given problem of linear equation comes out to be the numbers are -2 and 14.
A linear equation definition.The equation y=mx+b is the basis of a linear regression model. The y-intercept is m, and the slope is B. Although y and x are different elements, the previous sentence is frequently alluded to as a "maths problem with two variables. In bivariate linear equations, there are only two variables. The solutions of the application domains of linear equations are always zero.
Here,
Let x and y be the first and second numbers, respectively. The information provided lets us know that:
=> 3x + 2y = 22
Additionally, we are aware that the two numbers add up to 9, therefore
=> x + y = 9
We can employ a strategy like substitution to discover the values for x and y. One equation with one variable can be solved, and the solution can then be used as an expression in the other equation.
The first equation for y can be solved as follows:
=> y = (22 - 3x)/2
After that, change y in the second equation to the following expression:
=> x + (22 - 3x)/2 = 9
When we simplify and find x, we obtain:
=> 2x + 22 = 18
=> x = -2
Knowing that x = -2, we may re-apply it to the initial equation to determine the y :
=> y =28/2 =14.
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Please help I’m desperate
Sets A, B, and C are subsets of the universal set U.
These sets are defined as follows.
U={f, g, h, p, q, r, x, y, z)
A = {f,g,r, x}
B={r, x, y, z}
C={g, h, q, r, z}
Find (BUA)'n C.
Write your answer in roster form or as Ø.
(BUA)' n C =
Answer:
Step-by-step explanation:
ANSWER:
(C ⋂ B) ⋃ A' = {p, q, x, y, z}
What is the angle of elevation of the sun when a 47 ft mast casts a 26 ft shadow. Round to the nearest degree.
The angle of elevation of the sun will be 61.04°.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
Given that the angle of elevation of the sun when a 47 ft mast casts a 26 ft shadow.
tanθ = 47 / 26
θ = tan⁻¹ ( 47 / 26 )
θ = 61.04°
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A holiday tree is formed by extending single strands of lights from the top of a 22 foot pole to an anchor point on the ground. Each strand's anchor point is on the circumference of a circle, where the bottom of the pole is the center of the circle. If the angle formed between the ground and a strand of lights is 5π/18
find the length of a light strand.
Round to the nearest hundredth of a foot, if necessary.
The length of a light strand is _______________
The length of the light strand is 28.72 feet.
What are trigonometric functions?Simply put, trigonometric functions—also called circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.
Given A holiday tree is formed by extending single strands of lights,
height of pole = 22 feet
angle made by strands of light = 5π/18
it forms a right angle with the ground,
with the sine function, we can calculate the length of the strand,
here height of the pole is perpendicular and strands form a hypotenuse,
sinФ = perpendicular/hypotenuse
Ф = 5π/18
sin(5π/18) = 0.766
sin(5π/18) = 22/hypotenuse
hypotenuse = 22/0.766
hypotenuse = 28.72 feet
Hence the length is 28.72 feet.
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PLEASE HELP im going to fail
Answer:
(3 m)/4 = 5/6
Step-by-step explanation:
Solve for m:
(3 m)/4 = 5/6
Multiply both sides of (3 m)/4 = 5/6 by 4/3:
(4×3 m)/(3×4) = 4/3×5/6
4/3×3/4 = (4×3)/(3×4):
(4×3)/(3×4) m = 4/3×5/6
4/3×5/6 = (4×5)/(3×6):
(4×3 m)/(3×4) = (4×5)/(3×6)
(4×3 m)/(3×4) = (3×4)/(3×4)×m = m:
m = (4×5)/(3×6)
The gcd of 4 and 6 is 2, so (4×5)/(3×6) = ((2×2) 5)/(3 (2×3)) = 2/2×(2×5)/(3×3) = (2×5)/(3×3):
m = (2×5)/(3×3)
3×3 = 9:
m = (2×5)/9
2×5 = 10:
Answer: m = 10/9
Answer:
(3 m)/4 = 5/6
Step-by-step explanation:
Which expression is equivalent to 3(5r+23s+3t)+9s?
Responses
15r+18s+9t15 r plus 18 s plus 9 t
15r+29s+9t15 r plus 29 s plus 9 t
15r+11s+9t15 r plus 11 s plus 9 t
15r+2s+9t
The required expression equivalent to the given expression is 15r + 78s + 9t.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
= 3(5r+23s+3t)+9s
Simplify,
= 15r + 69s + 9t + 9s
= 15r + 78s + 9t
Thus, the required expression equivalent to the given expression is 15r + 78s + 9t.
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Hello I need help with my math question three please thank you
The lengths of the unknown sides and angles are: 12.3, 229.6, 24.6, 53, 139, and 28 respectively
How to find lengths of triangles?We are to use the trigonometric in finding the unknown sides
1a) From the trig ratio of cosine
Cos A = opposite/Adjacent
Cos35 = a/15
a=15*cos35
a = 15*0.8192
a=12.3
1b) Cos A = opposite/Adjacent
Cos25 = a/250
a=250*cos25
a = 250*0.9063
a = 226.6
2) Using the sine ratio
sinA = opposite/hypothenuse
sin A = 5/12
Sin A= 0.4167
Taking the sine inverse we have
A=24.6 degrees
2b) Using the ration of cosine
CosX = 12/15
Cos x = 0.8000
x= Cos⁻¹0.8000
x=53 degrees
3) Using Pythagoras theorem to find length AB = c
c²=a²+b²
c²=123²+65²
c²= 15129+4225
= 19354
c=√19354
c= 139
To find the angle,
SinA = 69/139
Sin A = 0.4676
Taking the sine inverse
A= 28⁰
The second angle B is 90-28 = 62⁰
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an animal can travel 4/7 meters in 1/8 of an hour. what is the rate in meters per hour?
An animal traveling 4/7 meters in 1/8 hours has a speed rate of 32/7 meters per hour in fractional form.
What is a fraction?
In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.
The distance the animal can travel is = 4/7 meters
The time in which the animal can travel the specified distance = 1/8 hours
The distance and time is given in fractional form.
To get the speed rate follow the formula for speed -
Speed = Distance / Time
Find the value in fractional form.
Substitute the values in the equation -
Speed = (4/7) / (1/8)
The fraction in the denominator will be reciprocated and then multiplied with the fraction in the numerator.
Speed = 4/7 × 8/1
Speed = 32/7
Therefore, the speed rate is 32/7 meters per hour.
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What is the range of the given function?
h
O x 1 x=-5. 1.4.6)
4,
Oyly=-7.-1.0.9}
Ox|x=-7. -5, -1, 0, 1, 4, 6, 9}
Oyly=-7.-5. -1, 0, 1, 4, 6, 9)
The range for the given function will be B i.e. {-7, -1, 0, 9}.
what is range of a function?
The set of all the outputs of a function is known as the range of the function or after substituting the domain, the entire set of all values possible as outcomes of the dependent variable.
Domain
The set of all possible values which qualify as inputs to a function is known as the domain of the function, or it can also be defined as the entire set of values possible for independent variables. The domain can be found in – the denominator of the fraction is not equal to zero and the digit under the square root bracket is positive. (In the case of a function with fraction values).
We can see from the image the values given for y i.e. range={-7, -1, 0, 9}.
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Jesse works for an engineering firm earning $54,000 per year. Jesse is 53 years old and plans on retiring at age 65. He's considering working part-time so that he can work on another degree. His new degree would take him 3 years to earn and cost a total of $30,000. After getting the degree, Jesse will make $75,000 per year.
Part time job want influence previous job.
What is cost?
A cost is the value of money that has been expended in the production or delivery of a good or service and is therefore no longer available for use in accounting, retail, research, or accounting. In business, the cost may be one of acquisition, in which case the cost is the sum of the money used to acquire it.
Given:
Jesse works for an engineering firm earning $54,000 per year.
Jesse is 53 years old and plans on retiring at age 65. He's considering working part-time so that he can work on another degree.
His new degree would take him 3 years to earn and cost a total of $30,000.
Let 53 - 65 he would get 12 x $54000 = $648000
Now, with part time job,
3 years to earn minus $30,000
64800 - 30000 = $618000 {total cost}
He still have 9 years to work .
he still get 75000 x 9 = $675000
Part time job want influence previous job.
Total = $618000 + $675000 = $1293
So its worth.
Hence, part time job want influence previous job.
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NO LINKS!! Use the diagram to name each of the following pairs of angles. If the name doesn't exist say "none" Part 3
k. <3 and <6
l. <2 and <12
Answer:
k) Alternate exterior angles
l) Same-side exterior angles
Step-by-step explanation:
Part k∠3 and ∠6 and alternate exterior angles.Alternate exterior angles
When two lines are intersected by a transversal, the angles that are exterior to the two lines and are on opposite sides of the transversal line are called "alternate exterior angles".
Part l∠2 and ∠12 are same-side exterior angles.Same-side exterior angles
When two lines are intersected by a transversal, the angles that are exterior to the two lines and on the same side of the transversal line are called "same-side exterior angles".
How many inches long is the radius of the largest circle that can fit inside a rectangle 18 inches long and 12 inches wide
Answer:
6 inches
Step-by-step explanation:
The diameter of the largest circle inside a rectangle of size 18" x 12" has to be 12", the smaller of the two lengths
If the diameter is 12", the radius is half of that = 12"/2 = 6"
The largest circle is inside a square of side 12.
The radius is 6√2 inches (half of the diagonal)
6th GRADE!! HELP ME ASAP PLEASEE DUE IN 20 MIN :((
A student's scores in a history class are listed.
60, 65, 65, 73, 74, 78, 83, 83, 85, 89, 91, 92, 100
Which of the following histograms correctly represents the data?
{Option 1} A histogram titled Grades in History Class. The x-axis is labeled Grade Earned and has intervals listed 41 to 50, 51 to 60, 61 to 70, 71 to 80, 81 to 90, 91 to 100. The y-axis is labeled Frequency and begins at 0, with tick marks every one unit up to 9. There is a shaded bar for 41 to 50 that stops at 1, for 51 to 60 that stops at 2, for 61 to 70 that stops at 2, for 71 to 80 that stops at 4, for 81 to 90 that stops at 2, and for 91 to 100 that stops at 3.
{Option 2} A histogram titled Grades in History Class. The x-axis is labeled Grade Earned and has intervals listed 41 to 50, 51 to 60, 61 to 70, 71 to 80, 81 to 90, 91 to 100. The y-axis is labeled Frequency and begins at 0, with tick marks every one unit up to 9. There is a shaded bar for 41 to 50 that stops at 1, for 51 to 60 that stops at 1, for 61 to 70 that stops at 4, for 71 to 80 that stops at 3, for 81 to 90 that stops at 2, and for 91 to 100 that stops at 2.
{Option 4} A histogram titled Grades in History Class. The x-axis is labeled Grade Earned and has intervals listed 41 to 50, 51 to 60, 61 to 70, 71 to 80, 81 to 90, 91 to 100. The y-axis is labeled Frequency and begins at 0, with tick marks every one unit up to 9. There is no shaded bar for 41 to 50. There is a shaded bar for 51 to 60 that stops at 1, 61 to 70 that stops at 2, 71 to 80 that stops at 3, 81 to 90 that stops at 4, and 91 to 100 that stops at 3.
{Option 3} A histogram titled Grades in History Class. The x-axis is labeled Grade Earned and has intervals listed 41 to 50, 51 to 60, 61 to 70, 71 to 80, 81 to 90, 91 to 100. The y-axis is labeled Frequency and begins at 0, with tick marks every one unit up to 9. There is a shaded bar for 41 to 50 that stops at 2, 51 to 60 that stops at 1, 61 to 70 that stops at 1, 71 to 80 that stops at 4, 81 to 90 that stops at 3, and 90 to 100 that stops at 2.
Answer:
{Option 4}
A histogram titled Grades in History Class.
The x-axis is labeled Grade Earned and has intervals listed 41 to 50, 51 to 60, 61 to 70, 71 to 80, 81 to 90, 91 to 100.
The y-axis is labeled Frequency and begins at 0, with tick marks every one unit up to 9.
There is no shaded bar for 41 to 50.
There is a shaded bar for 51 to 60 that stops at 1, 61 to 70 that stops at 2, 71 to 80 that stops at 3, 81 to 90 that stops at 4, and 91 to 100 that stops at 3.
Step-by-step explanation:
The data provided is
60, 65, 65, 73, 74, 78, 83, 83, 85, 89, 91, 92, 100
Breaking this into intervals,
we get
Interval Frequency count
51- 60 1
61-70 2
71-80 3
81-90 4
91-100 3
Out of the 4 histograms shown, 3 have a bar height of 1 for the interval 41-50
But the student has no score 50 and above
So the bar height should be zero. In other words there should be no bar corresponding to the interval 41-50 and one should start the x-axis at 51
Only one histogram corresponding to Option 4 has the interval 41-50 has no bar and that is the right answer.
There is really no need to check the other histograms. Just this fact alone can eliminate the other 3 options.
But if you look at my table above, each of the frequency counts corresponds to the height of the bar for that interval so we get the correct option as Option 4 and the correct histogram picture is as attached in my answer
Answer:
{Option 4} A histogram titled Grades in History Class.
The x-axis is labeled Grade Earned and has intervals listed 41 to 50, 51 to 60, 61 to 70, 71 to 80, 81 to 90, 91 to 100.
The y-axis is labeled Frequency and begins at 0, with tick marks every one unit up to 9.
There is no shaded bar for 41 to 50.
There is a shaded bar for 51 to 60 that stops at 1, 61 to 70 that stops at 2, 71 to 80 that stops at 3, 81 to 90 that stops at 4, and 91 to 100 that stops at 3.
A rectangle has a width of 24 inches and a height of 12 inches. A second rectangle is proportional to the first and has a width of 6 inches. What is the height of the second rectangle
The height of the second rectangle is 3 inches.
How to solve the side of a rectangle?The rectangle has a width of 24 inches and a height of 12 inches. A second rectangle is proportional to the first and has a width of 6 inches.
The height of the second rectangle can be found as follows:
Two variables have a proportional relationship if the ratios of the variables are equivalent.
Hence, using the proportion,
let
x = height of the rectangle
24 / 12 = 6 / x
24x = 12 × 6
24x = 72
divide both sides by 24
x = 72 / 24
x = 3 inches
Therefore,
height of the second rectangle = 3 inches
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