The common difference of the AP is 4.33 and its first term is 30.
What is the formula to calculate the nth term of an Arithmetic Sequence ?
The formula to calculate the nth term of an Arithmetic Sequence is -
a(n) = a + (n - 1)da - first term of A.P.
d - Common difference of A.P.
n - position of term
Given is the 1st term of an AP as 30 while the Sum of the its first 7 terms is 56.
We have -
[a] = 30
and -
a + (7 - 1)d = 56
30 + (6)d = 56
6d = 56 - 30
6d = 26
d = 26/6
d = 13/3
d = 4.33
and
the first term of the AP is 30.
Therefore, the common difference of the AP is 4.33 and its first term is 30.
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The babysitter charges $8 per hour plus $4 for gas to come to the house. If the babysitter earned $36, how many hours did the sitter work?
Answer: 8x + 3, where x is the number of hours
The maximum slope of a wheelchair ramp is 1:12. For a wheelchair ramp made with these specifications, what angle does the ramp make with the ground? Round your answer to the nearest hundredth.
a
8.24
b
4.76
c
6.91
d
5.39
Answer: B
Step-by-step explanation: Maximum slope for hand-propelled wheelchair ramps should be 1" of rise to every 12" of length (4.8 degree angle; 8.3% grade). To the nearest hundredth would be 4.76 so, B.
(3x³+4x² − x + 7) ÷ (x + 2)
Answer:
I think this is the answer
Step-by-step explanation:
Please help me find the equation of the parallel line.
Given: 5x-2y=10, (3,-5)
I know that the formula is y-y1=m(x-x1) but what do I do with the 2y?
Thank you!
Answer:
mperpendicular = −2/5
Step-by-step explanation:
The perimeter of a college basketball court is 96 meters and the length is 14 meters more than the width. What are the dimensions?
The dimensions of the college basketball court with a perimeter of 96 meters are:
Length = 31 metersWidth = 17 meters.What are the dimensions of a perimeter?The dimensions of a rectangular perimeter, like a basketball court, are the two sides (length and width).
The perimeter of a rectangle measures the four sides, that is, the two long sides and two wide sides.
The perimeter is given by the perimeter equation, P = 2(a+b).
The perimeter of the basketball court = 96 meters
The perimeter = 2(Length + Width)
2(Length + Width) = 96 meters
Length = 14 meters more than the width
The total difference of the two lengths = 28 meters (14 x 2)
Width = 17 meters (96 - 28)/2
Length = 31 meters (17 + 14)
Check:
Perimeter = 2(Length + Width)
96 meters = 2(31 + 17)
96 = 62 + 34
96 = 96
Thus, the college basketball court with a perimeter of 96 meters has the following dimensions: 31 meters in length and 17 meters in width.
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Kevin and Randy Muise have a jar containing coins, all of which are either quarters or nickels. The total value of the coins in the jar is $. How many of each type of coin do they have?
Hi! The total amount in the jar did not post properly. can you provide this?
During a journey, a motorbike travels between two sets of traffic lights. The graph shows the motorbikes velocity for this part of the journey. What is the distance between the traffic lights?
2.5 m/s² is the distance between the traffic lights .
Defining acceleration Short response?
The rate at which the speed and direction of a moving object vary over time. A point or object going straight ahead is accelerated when it accelerates or decelerates. Even if the speed is constant, motion on a circle accelerates because the direction is always shifting.The three different types of accelerated motions are uniform acceleration, non-uniform acceleration, and average acceleration. The motion in which an item moves in a straight line while increasing in velocity at regular intervals is referred to as uniform acceleration.from the picture V = 15 m/s
t = 6 sec
a = Δv/Δt = 15/6 ⇒ 2.5 m/s²
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A daycare center in Hillsdale currently has 12 assistant caregivers and 6 senior caregivers. Since demand is high, the owner is going to be hiring 1 assistant caregiver per month and 4 senior caregivers per month. Her goal is to have a larger staff, including an equal number of assistant caregivers and senior caregivers. How many of each type will there be? How long will that take?
1. Month for assistance caregivers is 14 months.
Month for senior caregivers will be 14 months.
2. After 2 month, there will be 14 of each types of caregiver.
What is an expression?
Expression in math is defined as the collection of the number, variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that;
A daycare center in Hillsdale currently has 12 assistant caregivers and 6 senior caregivers.
On high demand the owner is going to be hiring 1 assistant caregiver per month and 4 senior caregivers per month.
Let m is number of months.
Then, Each month has 12+ m for assistant caregivers and 6 + 4m for senior caregivers.
By given condition we formulate;
12 + m = 6 + 4m
12 - 6 = 4m - m
6 = 3m
3m = 6
m = 2
Thus, 12 + m = 12 + 2 = 14
And, 6 + 4m = 6 + 4 x 2 = 14
So, After 2 month, there will be 14 of each types of caregiver.
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Solve: 8a² +18a+ 4 = 0
Step-by-step explanation:
Splitting the middle term
8a^2 +16a + 2a+4 =0
8a (a+2) +2(a+2) = 0
(8a+2) (a+2)
8a=-2 , a = -2
a= -2/8
a= -1/4
a ( -1/4 , -2)
Match the trigonometry formula to its correct ratio. Reduce the ratio if necessary.
Matching the trigonometry formula to its ratio, we get
4/3 → tan A
4/5 → sin A
3/5 → cos A
Trigonometrical ratiosFrom the question, we are to match the given trigonometry formulas to their correct ratios.
From SOH CAH TOA, we have that
sin (angle) = opposite / hypotenuse
cos (angle) = adjacent / hypotenuse
tan (angle) = opposite / adjacent
Considering angle A,
Opposite = 16
Adjacent = 12
Hypotenuse = 20
Thus,
tan A = 16 / 12 = 4 / 3
sin A = 16 / 20 = 4 / 5
cos A = 12 /20 = 3 / 5
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express 30cm,1.5 as a percentage of second
The correct answer is 20%
We know,
1 m = 100 cm
thus 1.5 m will be 150 cm (1.5 x 100 = 150cm)
now, to find 30 cm as a percentage :
(30/150) x 100
=20 %
Thus, 30cm 1.5 can be expressed, as 20%.
What do you understand by percentage?
percentage- "a relative value indicating hundredth parts of any quantity." Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.
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A and B are two cylinders that are mathematically similar.
The area of the cross-section
of cylinder A is 18 cm².
Work out the volume of cylinder B.
+
18 cm2
A
5 cm
B
10 cm
The most appropriate choice for similarity of figures will be given by
Volume of cylinder B is 720 [tex]cm^2[/tex]
What is similarity of figures?
Two figures are said to be similar if they have same shape but different sizes.
Actually sides of similar figures are proportional
Ratio of heights of cylinder A and B = 5 : 10
= 1 : 2
Ratio of areas of cylinder A and cylinder B = [tex]1 ^2 : 2^2[/tex]
= 1 : 4
Area of cylinder A = [tex]18[/tex] [tex]cm^2[/tex]
Area of cylinder B = [tex]18 \times 4\\[/tex]
= [tex]72[/tex] [tex]c[/tex][tex]m^2[/tex]
Height of cylinder B = [tex]10 cm^2[/tex]
Volume of cylinder B = Area of cylinder B [tex]\times[/tex] Height ofcylinder B
= [tex]72 \times 10[/tex]
= [tex]720[/tex] [tex]cm^2[/tex]
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Complete Question
The image of the question has been attached with this question.
Which ordered pairs are in the solution set of the system of linear inequalities y > -1/3x +2 y < 2x + 3
The ordered pairs in the solution set of the system of linear inequalities y ≥ -1/3x +2 and y < 2x + 3 are (2, 2), (3, 1), and (4, 2).
What is the system of inequalities?One or more linear inequalities in each of the same two variables make up a system of linear inequalities in two variables. A linear inequality solution is an ordered pair that resolves all of the system's inequalities, and the inequality's graph is a representation of all of the system's solutions.Given linear inequalities represented in the graph are:
y ≥ -1/3x +2
y < 2x + 3
In the graph, the shaded region above the solid line denotes the inequality,
y ≥ -1/3x +2
The shaded area on the right side of the dotted line denotes the inequality's solution set,
y < 2x + 3
And the common area of these inequalities will denote the solution set of the system of linear inequalities.
Ordered pairs are (2, 2), (3, 1), and (4, 2) and will therefore be located in the shared shaded area.
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If the length of a room is 4.02m, the width of a room is 3.37m, and the height of a room is 2.35m, what is the volume of the room m^3? after figuring out the volume, then find out the mass of the air kg in the room.
The value for the volume of the room is 31. 84 cubic centimeters(cm³)
The mass of the air in the room is 41. 39 kg
How to determine the volume of the roomThe formula for calculating the volume of the room is expressed as;
Volume = l × w × h
Where;
l is the length of the roomw is the width of the roomh is the height of the roomFrom the information given, we have to substitute the values of the measurements of the room into the formula.
We have;
Volume, v = 4. 02 × 3. 37 × 2. 35
Volume, v = 31. 84 cubic centimeters(cm³)
To determine the mass of the air in the room, we use the formula for mass which is expressed as;
Mass = Density × volume
Given that;
Density of air = 1. 3kg/m³Volume of the room = 31. 84 cubic centimeters(cm³)Substitute the values
Mass = 1. 3 × 31. 84
Mass = 41. 39 kg
Hence, the volume is 31. 84 cubic centimeters(cm³)
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Mike says the opposite of 5 is –5 and the absolute value of 5 is –5. Is he correct?
Use the drop-down menus to explain your answer.
Mike
Choose...
correct.
Choose...
combine to make zero.
Choose...
is the distance from zero.
Answer:
Mike is not correct.
Step-by-step explanation:
The opposite of 5 is in fact -5, but the absolute value of 5 is not -5. The absolute value of 5 is 5.
your flight has been delayed: at denver international airport, 83% of recent flights have arrived on time. a sample of 14 flights is studied. round the probabilities to four decimal places.
1.0000 percent is the probability that all 12 flights will arrive on time.
What is probability?Simply put, the probability is the likelihood that something will occur.When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. Probability of an event P(E) = (Number of favorable outcomes)÷ (Sample space).So, the problem meets all requirements for a binomial experiment, written as:
[tex]P(X=x)\left(\begin{array}{l}n \\x\end{array}\right) p^x(1-p)^{n-x}[/tex]
Now, p=0.85 and n=14, the probability that precisely 14 people arrived on time are calculated as follows:
[tex]\begin{aligned}&P(X \geq 1)=1-P(X=0) \\&=1-\left(\begin{array}{c}12 \\0\end{array}\right) 0.85^0(1-0.85)^{12} \\&=1-1.297 \times 10^{-10} \\&=1.0000\end{aligned}[/tex]
Therefore, 1.0000 percent is the probability that all 12 flights will arrive on time.
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The complete question is given below;
Your flight has been delayed: At Denver International Airport, 85% of recent flights have arrived on time. A sample of 14 flights is studied. Round the probabilities to at least four decimal places. Find the probability that all 12 of the flights were on time.
*Similarity & transformations (practice) | Khan...
Pedro was curious if circles A and B (with X and Y being on each circle, respectively) were
similar, so he tried to map one figure onto the other using rigid transformations.p
1
Loading
COUP
Pedro concluded:
PO
X
"It's not possible to map circle A onto circle B using a sequence of rigid transformations, so
the circles are not similar."
Choose 1 answer:
What error did Pedro make in his conclusion?Perdo concluded: “it’s not impossible to map circle a onto circle b using a sequence of rigid transformations so the circles are not similar”. What error did Pedro make in his conclusion?
A round plane figure whose boundary ( circumference) consists of the points equidistant from a fixed point (the center). In the above question Pedro was wrong.
What is a circle?All the points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in plane draws to keep its distance from a specific point constant.
The tactic Pedro frequently used is ineffective since applying strict transformation to one figure and then onto another will only demonstrate whether the figures are congruent, not whether they are comparable.
Keep in mind that resemblance, as opposed to congruence, is about the proportionality between the dimensions of those figures. Therefore, when we overlay the figures, they won't match.
Pedro should divide each set of matching coordinates to demonstrate similarity; if all divisions provide the same outcome, the figures are said to be comparable.
Therefore, Pedro was not wrong.
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Please look at the photo and help me please or I’ll get a F
All you need to do is find the error out of the 3 choices and tell me what is the error
PLEASE AND THANK YOU
Answer:
It is the setup.
Step-by-step explanation:
Only 6 is negative. The 11 also needs to be negative.
A 32 ounce box of Fruit Loops cost $3.99 and a 24 ounce box of Honey Nut Cheerios cost $3.29.
Which is the better deal and why? What is the price of each
Answer:
32 ounce box of fruit loops is a better deal
Step-by-step explanation:
32 ounce of fruit loops is about $0.12 an ounce
24 ounce box of Honey Nut Cheerios is about $0.14 an ounce
(x-5)^2/8+(y+1)^2/32=1
Solve for the four vertices
Answer:
i Used the standard form to find the vertices.
Vertex
1: (5,−1+4√2)
Vertex
2: (5,−1−4√2)
Step-by-step explanation:
The force, F (Newtons), between two objects is inversely proportional to the square of the distance, d (metres), between them. The force is 0.084 Newtons when the distance between the objects is 3 metres. Work out d (rounded to 2 DP) when F = 0.029 Newtons.
The distance when F = 0.029 based on the computation is 5.1 meters.
How to calculate the distance?From the information, the force, F between two objects is inversely proportional to the square of the distance.
This willilk be illustrated as:
F = k / D²
We will find the value of k. This will be:
F = k / D²
0.084 = k / 3²
0.084 = k / 9
Cross multiply
k = 9 × 0.084 = 0.756
Therefore, the distance when F = 0.029 will be:
D² = k / F
D² = 0.756 / 0.029.
D² = 26
D = ✓26
D = 5.1
The distance is 5.1 meters.
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£12000 borrowed for 17 months at a rate of 12.5% p.a.
Answer:
1062.50
Step-by-step explanation:
Interest = PRT / 100.
= 12000 × 12.5 × 17 /100 × 24
= 1062.50
Salma fills an aquarium to a depth of 4/5 meters in 8 minutes.
What is the unit rate in minutes per meter?
The unit rate is 10 minutes per meters.
What is rate of time?
Time is in units of seconds, minutes, hours, or years. Rate is distance per time, so its units could be mph, meters per second, or inches per year.
rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute.
Given,
she fills 4/5 meters in 8 minutes.
let x be the time she fills minutes per liter.
4/5 meters ⇔ 8 minutes
1 meter ⇔ x minutes
Cross multiplying
4/5*x = 1*8
x = 5*8/4
x = 10 minutes
The unit rate is 10 minutes.
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Light travels 1.8x 10^7 kilometers in one minute. How far does it travel in 8 minutes
Answer:
Step-by-step explanation:
Distance covered in 1 minute= 1.8x 10^7 kilometers
So, by unitary method,
distance covered in 8 minutes= 1.8 x 10^7 kilometers x 8
= 14.4 x 10^7 kilometers
Can you help me with this math question
Answer:
40
Step-by-step explanation:
[tex]m \angle 2=20^{\circ}[/tex] (angle sum of triangle)
[tex]m\angle 1=40^{\circ}[/tex] (angle sum of triangle)
a sector with angle 120 degrees has a radius of r+4cm and its area is the same as the area of a circle with radius r cm.
By forming an equation in terms of 'r', show that r²-4r-8=0
Answer:
If area of sector = area of circle
1/3π(r+4)^2= πr^2
r^2-4r-8 =0
what is a sector?A sector is a cut out section of a circle. It is of two radii and an arc .
The area of a sector is angle substended/ 360 x area of a circle
area of a circle is πr^2
if area of circle is equal to the area of sector
120/360×π(r+4)^2=πr^2
divide both side by π
1/3(r+4)^2=r^2
multiply both sides by 3
(r+4)^2=3r^2
opening the bracket
(r+4)(r+4)=3r^2
r^2+ 8r +16=3r^2
3r^2-r^2- 8r -16=0
2r^2- 8r -16=0
divide all by 2
r^2- 4r -8=0
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ive been stuck on this question and i will give extra points but i just dont get this question
According to the solution Angle 3 is measured at 48 degrees.
What is a neighboring angle?Adjacent angles seem to be two angles that share a side and then a vertex but do not overlap at all (corner point). It is clear what is meant when the term "adjacent angles" is broken down; they are just two angles that seem to be close to one another.
Are the adjacent angles equal?Adjacent angles seem to be two angles that do not overlap but share a vertex and a side. In the figure, angles 1 and 2 are close by. Both their common side and vertex are the same.
According to the given data:Angle 3 and angle 132 degrees are nearby angles in this scenario.
Consequently,
angle3 plus 132 degrees equals 180 degrees.
angle 3 = 48 degree
angle 3 = 180-132 degree
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Drag the numbers below to put them in order from least to greatest:
8.66 8.6 8.611 8.641 8.63 8.691
8.6 8.63 8.66 8.611 8.641 8.691
ASAP I have a couple more minutes, please help! This lesson is called "The Pythagorean Theorem"
Answer: Number 5. is B-7CM
Number 8. is y=2/x
Step-by-step explanation:math
Write a statement and an expression to represent the tape diagram. Then evaluate your
expression.
22|9|22|9
22|9|22|9|22|9|22|9|
Statement:
Expression:
Value of Expression:
In the picture there are two tape diagram. From the tape diagram we got x as 7 and y as 18.
Given that,
In the picture there are two tape diagram.
1st diagram is A and 2nd diagram is B.
Diagram A has 3 blocks are x and the total of those diagram is 21.
We get,
x+x+x=21
3x=21
x=21/3
x=7
Now,
Diagram B has 2 blocks are y and 3 and the total of those diagram is 21.
We get,
y+3=21
y=21-3
y=18
Therefore, from the tape diagram we got x as 7 and y as 18.
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