The absolute value of the difference between the first and second numbers is 5.
Here we have to find the difference between the first and the second numbers.
There are three statements.
Let a, b, and c be the first, second, and third numbers respectively.
The first statement is that the sum of the three number is 96.
The second statement is that the first number is 6 times the third number.
a = 6c
The third statement is that the third number is 40 less than the second number.
c = b - 40
b = c + 40
The sum of the three numbers is 96.
a + b + c = 96
6c + c + 40 + c = 96
8c = 96 - 40
8c = 56
c = 7
As a = 6c and b = c + 40
Now put the value of c as 7 we have:
a = 6 × 7
= 42
b = 7 + 40
= 47
Difference between the first and second numbers= 47 - 42
= 5
Therefore the difference is 5.
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What is this shape ?
Answer:
Decagon
Step-by-step explanation:
Because it has 10 sides.
Answer:
Its a Decagon
Step-by-step explanation:
Given that
7
x
−
3
y
=
23
Find
x
when
y
=
−
2
Answer: [tex]\frac{17}{7}[/tex]
Step-by-step explanation:
7x - 3y = 23
3y = -2 × 3 = -6
7x + 6 = 23
7x = 23 - 6
7x = 17
x = [tex]\frac{17}{7}[/tex]
What is the area of the parallelogram shown?
A= In^2
A youth group is planning a trip to a local amusement park. They are taking a van which holds 10 people. It will cost $25 for parking and tickets to enter the park are $18 per person. Create a table to represent the situation, showing the possible total costs for the various numbers of people who could go?
Write
y − 2 = (x + 6) in
standard form.
Can someone pls help me with this and show your work it would mean a lot
Using the angle of elevation formula, the distance between John and Fred from the building is 1.2m and 1.67m.
What is the angle of elevation?The angular relationship between the horizontal plane and the line of sight for an object above the horizontal.The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.You may calculate the angle of elevation, for instance, by standing on the ground and looking up at the peak of a mountain.So, the distance of the building from John and Fred is:
Let, the height of the building be QR and the distance between the building and John and Fred be PR and SR.Now, we get the formula:
Tanθ = QR/PRTanθ = QR/SRCalculate as follows:
John's distance:
Tanθ = QR/PR25 = 30/PRPR25 = 30PR = 30/25PR = 6/5Fred's distance:
Tanθ = QR/SR18 = 30/SRSR18 = 30SR = 30/18SR = 15/9SR = 1.67mTherefore, using the angle of elevation formula, the distance between John and Fred from the building is 1.2m and 1.67m.
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Justify each step of the solution by stating the property that was used to get to each step. (4 points - 1 point each correct answer)
Given: 2(10 - 13x) + 9x) = -34x + 60
Step 1: 20 + 26x + 9x = -34x + 60
Step 2: -17x = -34x + 40
Step 3: 17x = 40
Step 4: x = 40/17
Sample Answer
Step 1: _____ property
Step 2: ______ property
Step 3: ______ property
Step 4: ______ property
Steven hit the ball 12 times out of 26 at bats in the first half of the season and 6 times out of 14 at bats in the second half of the season. What is his batting average for the whole season, written as a decimal?
Answer:123
Step-by-step explanation:
7328x3424
Steven battling average for the whole season he played was 0.45
How to solve an equation?An equation is an expression showing the relationship between two or more numbers and variables.
Steven hit the ball 12 times out of 26 at bats in the first half of the season and 6 times out of 14 at bats in the second half of the season.
Hence:
Batting average = (total number of time he hit the ball in both season half) / (total number of balls thrown)
Therefore:
Battling average = (12 + 6)/ (26 + 14) = 18 / 40 = 0.45
Steven battling average was 0.45
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Aiden ha $3 worth of dime and quarter. He ha 2 more dime than quarter. Determine the number of dime and the number of quarter that Aiden ha
The number of dime and the number of quarters that Aiden have are 10 and 8 respectively.
How to find the number of dime and quarter?Aiden ha $3 worth of dime and quarter. Aiden has 2 more dime than quarter. The number of dime and the number of quarter that Aiden has can be calculated as follows:
let
x = number of quarter
y = number of dime
Therefore,
y = 2 + x
y - x = 2
0.1y + 0.25x = 3
Multiply equation(ii) by 10
y - x = 2
y + 2.5x = 30
subtract equation(i) from equation(ii)
3.5x = 28
x = 28 / 3.5
x = 8
Hence,
y = 2 + 8
y = 10
Therefore,
number of dime = 10
number of quarters = 8
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Students in a classroom have eaten 20% of jellybeans from a jar. There are now only 100 jellybeans left! How many jellybeans were in the jar to begin with?
Using percentages we calculate in the beginning there were 125 jellybeans in the jar.
Let the number of jellybeans in the jar was x.
Now student ate 20% of the jellybeans.
Number of jellybeans students ate = 20% of x = 0.2x
Number of jellybeans left = x - 0.2x = 0.8x
But the number of jellybeans is given as 100.
Therefore 0.8x = 100
or, x = 100 /0.8 = 125
Hence there were 125 jellybeans in the jar.
The English word "percentage" derives from the Latin phrase "per centum," which means "by the hundred." Percentages are fractions with a denominator of 100.
In other words, that is a relationship where it is always assumed that the value of the whole is 100.
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Stacy bought 8.3 pounds of fruit for a class party. The class ate 7.44 pounds of the fruit. How much fruit is left?
Answer:
0.86 pounds of fruit is left.
Step-by-step explanation:
If Stacey bought 8.3 pounds and the class ate 7.44 pounds, the amount of fruit that's left is 8.3-7.44=0.86
Find the largest area for a rectangle that is inscribed in a semicircle with radius 4 inches.
The area of the largest rectangle is 25 square units.
It is given that the radius of the semicircle is [tex]4[/tex].
It is required to inscribe a rectangle of maximum area.
Consider a rectangle of sides [tex]x[/tex], [tex]y[/tex] as shown in the given figure.
From the attached figure,[tex]AB=x[/tex], [tex]OB=r[/tex] and [tex]OB=\frac{y}{2}[/tex].
Now, in the triangle OAB, apply Pythagoras' theorem as,
[tex](OA)^{2}=(OB)^{2}+(AB)^2[/tex]
[tex]r^2=(\frac{y}{2} )^2+x^2\\\\[/tex]
[tex]16=\frac{y}{4}+x^2[/tex]
[tex]y^2=4(16-x^2)[/tex]
[tex]y=2\sqrt{16-x^2}[/tex]
So, the area of the rectangle will be,
Area,
[tex]A = 2x \times y[/tex]
= [tex]2x \times \sqrt{(16 - x^2)}[/tex]
Differentiate the area with respect to ,
[tex]A' = 2 \times \sqrt{(16 - x^2)} - 2x^2/(16 - x^2)[/tex]
Differentiate the area twice as,
When[tex]x = 0, y = 5[/tex] and when [tex]x = 5, y = 0[/tex], [tex]area = 0[/tex].
It implies that area is maximum when the value of x lies between 0 and 5.
This will occur where [tex]A'= 0[/tex].
⇒ [tex]2 \times \sqrt{(16 - x2) }- 2x^2/(16 - x^2) = 0[/tex]
⇒[tex]2 \times \sqrt{(16 - x^2)} = 2x^2/(16 - x^2)[/tex]
On simplification, we get,
⇒ [tex]2 \times (16 - x^2) = 2x^2[/tex]
⇒ [tex]16 - x^2 = x^2[/tex]
⇒ [tex]2x^2= 16[/tex]
⇒ [tex]x^2 = 16/2[/tex]
⇒ [tex]x = \sqrt{8}[/tex]
Now, [tex]y = \sqrt{(16 - x^2)}[/tex] becomes
⇒[tex]y = \sqrt{(16 - (\sqrt8)^2)}[/tex]
⇒ [tex]y = \sqrt{(16 - 8)}[/tex]
[tex]y =\sqrt{8}[/tex]
Maximum area = 2xy
[tex]=2(\sqrt{8)}(\sqrt{8})[/tex]
[tex]=16[/tex]
Therefore, the area of the largest rectangle is 16 square units.
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Helen draws a random circle.
She then measures
its diameter and circumference.
She gets a
circumference, C, of 405 mm correct to 3 significant figures.
She gets a diameter, d, of 130 mm
correct to 2 significant figures.
Helen wants to find the value of rt using the formula
T= G
Calculate the upper bound for Helen's value of TC.
Give your answer correct to 3 decimal places.
If Helen wants to find the value. the upper bound for Helen's value of TC is 3.123 and lower bound is 3.092.
How to find upper and lower bound?Upper bound
405 = 405.999
130 =130.99
Lower bound
405 = 405.001
130 =130.01
Now let find the upper and lower bound
Upper bound = 405.999/130.01
Upper bound =3.123
Lower bound = 405.001 /130.99
Lower bound = 3.092
Therefore the upper bound is 3.123.
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a group of five friends goes to the state fair. each friend pays the entrance fee and buys one booklet of ride tickets and a meal ticket. the entrance fee is d dollars. a booklet of ride tickets costs 2.5 times the entrance fee. a meal ticket costs $4 less than the entrance fee.
Answer: What do you need the total or the equation? I am going to write the equation.
Step-by-Step Solution: (5)(d)+(5)(d)(2.5)+ (5)(d)-4
How much water must be added to 14 liters of a 90%
acid solution to obtain a 40% acid solution?
17.5 litres of must be added to 14 litres of a 90% acid solution to obtain a 40% acid solution.
What is percentage?A percentage is a number or ratio expressed as a fraction of 100.
Given that, there are 14 litres of a solution which is 90% acidic,
Let water added be x, then according to question,
0.90*14 = 0.40(x+14)
12.6 = 0.40x + 5.6
0.40x = 7
x = 17.5
Hence, 17.5 litres of must be added to 14 litres of a 90% acid solution to obtain a 40% acid solution.
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a salesman keeps 20% of his sales as a commission. how much does he have to sell to earn $1,000?
Answer:
He has to sell 5000 to earn $1000
Step-by-step explanation:
1000/0.2 = 5000
whats the equation of a line that passes through the points
(12,12) and (20,6)
PLEASE HELP!!!!!!!!!!!!!
A handicapped ramp is being constructed for the front entrance of First National Bank in Springfield. ADA guidelines requires a rise angle from the foot of the ramp (point furthest from the entrance) not to exceed 4.8 degrees. This means the vertical to horizontal ratio cannot exceed 1:12. If the handicapped ramp must start 15 feet away from the front entrance, contractors estimate the rise to be about 3 feet.
Part A: Explain thoroughly whether or not these ramp dimensions meet the ADA guidelines.
Part B: If the rise estimate does not meet ADA requirements, provide a measurement that would meet the guidelines.
a) These ramp dimensions do not meet the ADA guidelines.
b) A measurement that would meet the guidelines is the ramp starting 39 feet away, with a height of 3 meters.
What is a slope?The slope of a situation is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
For the ramp in this problem, we have that the vertical change and the horizontal change are given as follows:
The vertical change is of: 3 feet.The horizontal change is of: 15 feet.The ratio between the vertical change to the horizontal change is of:
3/15 = 1/5.
Which is greater than 1/12, hence the ramp does not meet the ADA guidelines.
If the horizontal change was 13 times the vertical change, it would meet the ratio, hence a possible measurement is of:
3 feet vertical.39 feet horizontal.As the ratio would be of:
3/39 = 1/13 < 1/12.
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graph the solution of the inequality x ≤ 3
The solution of x ≤ 3 depicts that all the value of x is either less than 3 or equal to 3, so option C is correct.
What is number line?In mathematics, numbers are shown visually as a straight line on a number line. The numerals on a number line are positioned in a specific order and spaced out equally throughout its length. Since it can go on forever in any direction, it is frequently presented horizontally.
The expression x ≤ 3 depicts that the value of x is less than 3 or equal to 3, this can be represented in the image attached below.
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The cost of the Gas is 11p for each unit
there is also a fixed charge of £25.57
calculate the cost of the gas
you must show your working
The cost of the gas will be equal to £67.81 p.
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,
Initial gas reading = 8247
Final gas reading = 8631
The total consumed gas is given by,
Final gas reading - Initial gas reading → 8631 - 8247 = 384
Since the cost of gas is 11p per unit we have, the total cost of the gas consumed is given by
Cost of consumed gas = Units of gas consumed × Unit cost of gas
= 384 × 11p = 4224 p
100 p ≡ £ 1
4224 p = £42.24 p
The total cost of the gs is obtained by adding the fixed charge to the cost of gas consumed as follows,
£25.57 + £42.24 = £67.81 p
The cost of the gas = £67.81 p
The complete question is given below,
The gas meter readings at the beginning and end of a period were: 8247 = 8631 the cost of the gas is 11p for each unit. there is also a fixed charge of £25.57. calculate the cost of the gas. you must show your working
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What is the value of y?
y =
Find the following angle measures.
mAngleJKM = °
mAngleMKL = °
Applying the definition of linear pair angles, the measures are:
y = 10
m∠JKM = 106°
m∠MKL = 74°
What is the Linear Pair?A linear pair involves two angles that lie adjacent to each other on a straight line. The sum of their measures is equal to 180 degrees, this is because linear pair angles are supplementary to each other.
Given the following:
Measure of angle JKM = (10y + 6)°
Measure of angle MKL = (8y - 6)°
Therefore:
m∠JKM + m∠MKL = 180 [linear pair angles are supplementary]
Substitute
10y + 6 + 8y - 6 = 180
Combine like terms
18y = 180
18y/18 = 180/18
y = 10
Plug in the value of y to find the measures:
Measure of angle JKM = (10y + 6)° = 10(10) + 6 = 106°
Measure of angle MKL = (8y - 6)° = 8(10) - 6 = 74°
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g(a)=3a+2; find g(-3) HELP PLEASE!!
The output value of g( -3 ) in the function g( a ) = 3a + 2 is -7.
What is the output value of g( -3 ) in the given function?A function is simply a relationship that maps one input to one output. For relation to qualify as a function, each x-value can only have one y-value.
Given the data in the question;
g( a ) = 3a + 2g( -3 ) = ?To determine the output value of g( -3 ), replace all the occurrence of 'a' with -3 in the function and simplify.
g( a ) = 3a + 2
g( -3 ) = 3( -3 ) + 2
Multiply 3 and -3
g( -3 ) = -9 + 2
Add -9 and 2
g( -3 ) = -7
Therefore, the output value is -7, this forms an ordered pair of (-3,-7).
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Matilda walks from a castle's tower to its drawbridge by heading 624 m due
east and then heading due south.
The straight-line distance from the tower to the drawbridge is 927 m.
Work out the bearing of the drawbridge from the tower.
Give your answer to the nearest degree.
Answer:
138° (nearest degree)
Step-by-step explanation:
Bearing: The angle (in degrees) measured clockwise from north.
The given scenario can be modelled as a right triangle (see attachment).
Therefore, the bearing is 90° + θ (shown in green on the attached diagram).
To find angle θ, use the cosine trigonometric ratio:
[tex]\implies \cos{\theta}=\dfrac{A}{H}[/tex]
[tex]\implies \cos{\theta}=\dfrac{624}{927}[/tex]
[tex]\implies \theta=\cos^{-1}\left(\dfrac{624}{927}\right)[/tex]
[tex]\implies \theta=47.69018863...[/tex]
[tex]\implies \theta=48^{\circ}\; \; \sf (nearest\;degree)[/tex]
Therefore, the bearing of the drawbridge from the tower is:
[tex]\begin{aligned}\implies \sf Bearing&=90^{\circ}+\theta\\&=90^{\circ}+48^{\circ}\\&=138^{\circ} \end{aligned}[/tex]
Answer:
The bearing of the drawbridge from the tower is 138° SE-----------------------------
The segments that are formed by Matilda walking from the tower to drawbridge form a right triangleHorizontal leg = 624 m,Hypotenuse = 927 m.Find the angle x between the two segmentscosine = adjacent / hypotenusecos x = 624/927x = arccos (624/927)x = 48° (rounded to the whole degree)Find the bearing of the drawbridge from the towerAdd 90° to the angle measure we just found, since bearing is counted from the north direction:
48° + 90° = 138° SE
Write the number below as a fraction in its simplest form
0.538
Answer:
0.538 as a fraction in its simplest form is 269/500
Step-by-step explanation:
We all know that 0.538 can be written as 0.538/1
Multiply the numerator and denominator by 1000 which comes out to 538/1000
Divide the numerator and denominator by 2 which comes out to 269/500
Since 269 is a prime number 269/500 is 0.538 in its simplest form
equivalent expressions
it’s due tmr and i don’t understand
thank you if you are willing to help
Answer:
c) x+4
Step-by-step explanation:
1. The original expression can be re-written as (I just rewrote each fraction so that there are no mixed numbers):
[tex]\frac{x}{2}+\frac{9}{2}+\frac{x}{2}-\frac{1}{2}[/tex]
2. Next, you want to group all the terms with the variable x, and all the terms without a variable. All the fractions should be rearranged:
[tex]\frac{x}{2}+\frac{x}{2}+\frac{9}{2}-\frac{1}{2}[/tex]
3. You can now simplify and add the variable terms and the non-variable terms.
[tex]\frac{x+x}{2}+\frac{9-1}{2}[/tex]
Simplify further:
[tex]\frac{2x}{2}+\frac{8}{2}[/tex]
[tex]x+4[/tex]
So your answer is choice c
Two cyclists are 7 miles apart when they begin biking away from each other in opposite directions. The speed of the first cyclist is 12 miles per hour. The speed of the second cyclist is b miles per hour greater than the speed of the first cyclist.
How many miles apart are the cyclists in 45 minutes?
PLEASE HELPPPPPP!!!!!!!!!!!
The distance between two cyclists after 45 minutes as described in the task content is; 7 + 0.75 (12) + 0.75 (b + 12) miles.
Speed, distance and time.It follows from the task content that the distance between the two cyclists after 45 minutes is to be determined from the given parameters.
Given; the speed of the first cyclist is; 12 miles per hour, while the speed of the second cyclist is b miles per hour greater than that of the first.
The speed of the second cyclist is therefore; (b + 12).
On this note, since the distance covered by each cyclist is given by;
Distance = Speed × Time where, Time = 45 minutes = 0.75 hours.
Therefore, the total distance between the two cyclists can be determined from the expression as follows;
7 + 0.75 (12) + 0.75 (b + 12).
Therefore, the distance between the two cyclists as required in the task content is; 7 + 0.75 (12) + 0.75 (b + 12) miles.
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The graph below plots the values of y for different values of x:
plot the ordered pairs 1, 8 and 2, 3 and 3, 0 and 4, 1 and 5, 2 and 6, 1
What does a correlation coefficient of −0.2 say about this graph?
x and y have a strong, positive correlation
x and y have a weak, positive correlation
x and y have a strong, negative correlation
x and y have a weak, negative correlation
A correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables.
Hence, the correlation coefficient is [tex]-0.9[/tex], i.e., [tex]x[/tex] and [tex]y[/tex] have a strong, negative correlation
What is a correlation coefficient?
A correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables.
The variables may be two columns of a given data set of observations, often called a sample or two components of a multivariate random variable with a known distribution.
As we know that the correlation coefficient is a measure of the strength of the straight line or linear relationship between two variables. Correlation coefficients are expressed as values between [tex]+1[/tex] and [tex]-1[/tex].
So,
[tex](1,8),(2,3),(3,0),(4,1),(5,2),(6,1)[/tex]
As per the Excel tools i.e., CORREL function the correlation coefficient is [tex]-0.9[/tex].
Hence, the correlation coefficient is [tex]-0.9[/tex], i.e., [tex]x[/tex] and [tex]y[/tex] has a strong, negative correlation.
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Sophia spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -2.1°F. Between 9am and noon, the temperature increased by 10.8°F. Between noon and 3pm, the temperature decreased by 13°F. Between 3pm and 6pm, the temperature dropped 18.4°F. What was the temperature at 6pm? PLEASE
Answer:
Step-by-step explanation:
-22.7
A manager of a fast food chain wants to know how his customers rate their service at the restaurany that day. after randomly picking the 9th customer, he surveys every 5th customer that exits the restaurant. which sampling method? your answer: simple random systematic stratified cluster volunteer
The sampling method used in this scenario is random Systematic random sampling
Systematic random sampling
Systematic sampling is a form of probability sampling technique in which sample members are chosen from a wider population using a defined, periodic interval but a random beginning point. By dividing the population size by the desired sample size, this interval, also known as the sampling interval, is computed.
If the periodic interval is predetermined and the starting point is random, systematic sampling is still regarded as random even though the sample population has been chosen in advance.
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based on the graph what is the rate of the change for an airplane approaching an airport for landing
Answer:
(8, 9 000)
Step-by-step explanation:
