The sixth term is a₆ = 13.
What is an arithmetic sequence?A sequence in which the difference between any two consecutive terms is the same is known as an arithmetic sequence.
Given that, a₁= -12 and aₙ = aₙ₋₁ + 5.
aₙ = aₙ₋₁ + 5
Substitute n = 2 into the above equation,
a₂ = a₂₋₁ + 5
a₂ = a₁ + 5
Substitute a₁ = -12 into the above equation,
a₂ = -12 + 5
a₂ = -7
Repeating the same process, a₃ = -2, a₄ = 3, a₅ = 8, and a₆ = 13.
Hence, the sixth term is a₆ = 13.
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Reduce 75 litres of water by 15%
Answer:
63.75 litres
Step-by-step explanation:
the original amount of water is 100%
then a reduction of 15% = 100% - 15% = 85% of original
multiply 75 litres by 85% to obtain reduction
75 × 85%
= 75 × [tex]\frac{85}{100}[/tex] = 75 × 0.85 = 63.75
75 litres reduced by 15% = 63.75 litres
Triangle XYZ has vertices X: (0,2) Y: (3,8), and Z: (6,2). Show that the triangle is isosceles by determining the length of each side.
Please help!!!
Sides XY and YZ are both equal to √45 units, therefore, triangle XYZ is an isosceles triangle.
What is an Isosceles Triangle?If a triangle has two side lengths that are equal to each other, the triangle is called an isosceles triangle. Therefore, two of the sides of an isosceles triangle must be equal.
Given the vertices of triangle XYZ as:
X(0, 2)
Y(3, 8)
Z(6, 2).
Find the length of each side using the distance formula, [tex]\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex].
XY = √[(3−0)² + (8−2)²]
XY = √45
XZ = √[(6−0)² + (2−2)²]
XZ = √36
XZ = 6
YZ = √[(6−3)² + (2−8)²]
YZ = √45
The triangle has two equal sides YZ and XY, therefore it is an isosceles triangle.
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Mike and Tom are trying to make weight for wrestling. Mike weighs 200 lbs and is
losing 2 Lbs a week. Tom weighs 160 lbs and is gaining 3 pounds a week. How many
weeks will both boys weigh the same?
Answer:
8 weeksStep-by-step explanation:
Let the number of weeks be x after which both boys have same weight.
Mike's weight after x weeks:
200 - 2xTom's weight after x weeks:
160 + 3xEquate both expressions and solve for x:
200 - 2x = 160 + 3x3x + 2x = 200 - 1605x = 40x = 8Answer:
After 8 weeks, both boys weigh same.
Step-by-step explanation:
Forming the equation,
→ 200 - 2x = 160 + 3x
Now the value of x will be,
→ 200 - 2x = 160 + 3x
→ -2x - 3x = 160 - 200
→ -5x = -40
→ x = -40/-5
→ x = 40/5
→ [ x = 8 weeks ]
Hence, the value of x is 8.
During a session, a senate had a total of 112 Democrats and Republicans. There were 4 fewer Democrats than Republicans. How many members of each party were there?
Answer:
There are 54 Republicans, and 58 Democrats
Step-by-step explanation:
See the attached image
month of the gym
membership?
5. A train travels 16 miles in
20 minutes. At this rate, how
many minutes will it take to
travel 12 miles?
Answer: 15 minutes
Step-by-step explanation:
Let's make a proportion
16 miles - 20 minutes
12 miles - х minutes
Hence,
[tex]\displaystyle\\x=\frac{12(20)}{16} \\\\x=\frac{3(4)(4)(5)}{4(4)} \\\\x=3(5)\\\\x=15\ minutes[/tex]
A hopper bought a watermelon,a pack of napkin,and ome paper plate. In hi tate, there i no tax on food. The tax rate on non-food item i 15 percent. The total for the three item he bought wa $8. 25 before tax, and he paid $0. 19 in tax. How much did the watermelon cot?
The shopper bought a watermelon costing $4.45.
Let x represent the cost of watermelon
y = cost of napkin + cost of paper plates
The tax rate on non-food items is 5%, hence:
5% of y = 0.19
0.05y = 0.19
y = $3.8
The total for the three items he bought was $8.25 before tax,
x + y = 8.25
x + 3.80 = 8.25
x = 4.45
The shopper bought a watermelon costing $4.45.
A tax is a compulsory monetary charge or a few other sorts of levy imposed on a taxpayer (a man or woman or criminal entity) by using a governmental agency if you want to fund authorities' spending and numerous public expenses (regional, neighborhood, or countrywide), and tax compliance refers to coverage movements and character behavior geared toward making sure that taxpayers are paying the right amount of tax on the proper time and securing the right tax allowances and tax reliefs. the first known taxation passed off in historical Egypt around 3000–2800 BC. A failure to pay in a well-timed way (non-compliance), together with evasion of or resistance to taxation, is punishable by means of regulation. Taxes consist of direct or oblique taxes and may be paid in cash or as its labor equivalent.
Maximum nations have a tax system in the region, so as to pay for public, common societal, or agreed-on country-wide needs and for the capabilities of the presidency. a few levies a flat percentage rate of taxation on private annual profits, however, maximum scale taxes are modern and based on brackets of annual earnings amounts. most nations charge a tax on a character's profits as well as on corporate earnings. nations or subunits regularly additionally impose wealth taxes, inheritance taxes, estate taxes, gift taxes, property taxes, sales taxes, use taxes, payroll taxes, duties, and/or tariffs.
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If one or more data items are much greater than the other items, the mean, rather than the median, is more representative of the data.
a. True
b. False
The given statement is FALSE.
If one or more data items are much greater than the other items, the median, rather than the mean, is more representative of the data.
When one or more data items are much greater than the other items, these extreme values can greatly influence the mean.
When you have a skewed distribution, the median is a better measure of central tendency than the mean
The median and mean can only have one value for a given data set. The mode can have more than one value
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the sum of two numbers is 61, if the larger number is seven less than three times the smaller number, find both numbers
Answer:
The two numbers are 17 and 44.
Step-by-step explanation:
x --> smaller number
y --> larger number
x + y = 61
y = 3x - 7
x + 3x - 7 = 61
4x - 7 = 61
4x = 68
x = 17
y = 3(17) - 7
y = 51 - 7
y = 44
Find the value of y.
M
51
12y+7
L
Q
51
43
P
Answer:
y = 3Step-by-step explanation:
Given is a kite because:
one pair of congruent sides ML and LP,second pair of sides also congruent since OQ is perpendicular bisector of angle Q, making MPQ an isosceles triangle, hence MQ = QP.Since MQ and QP are congruent, set equation and solve for y:
12y + 7 = 4312y = 36y = 3Answer:
y = 3
Step-by-step explanation:
Forming the equation,
→ 12y + 7 = 43
Now the value of y will be,
→ 12y + 7 = 43
→ 12y = 43 - 7
→ 12y = 36
→ y = 36/12
→ [ y = 3 ]
Hence, the value of y is 3.
Write a numerical expression to model the situation Kristen read her book for 2 hours after school.Then she read for another hour before she went to sleep.
The numerical expression to model the situation when Kristen read her book is 2 + 1.
What is a numerical expression?A numerical expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
In this case, Kristen read her book for 2 hours after school, then she read for another hour before she went to sleep. The expression will be:
= 2 + 1
= 3
She read for 3 hours.
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NEED HELP PLEASEEEEEEEE
Answer:
- 3/4
PLEASE GIVE BRAINLIEST THANK YOU!!!
Write the equation of a line that i parallel to y=1/2x4 and goe thru the point(-3,4)
what is the volume of the following rectangular prism? 1 1/3 units 4 1/2 units2
Answer: 6 units^3
Step-by-step explanation:
using the volume of a rectangular prism formula:
L*W*H
We are already given the AREA which is the part L*W of the previous formula.
Now we multiply:
1 1/3 units * 4 1/2 units^2
Convert the fractions into 4/3 * 9/2 for an easier multiplication.
Resulting in 36/6 which is equivalent to 36 divided by 6.
Which gives us our answer of 6.
1000 to the power of m divided by 100 to the power of n can be written as 10 to the power of z.
Express z in terms of m and n.
Z in terms of m and n is z = [tex]3^{m} -2^{n}[/tex]
Exponentiation is the process of expressing large numbers in terms of powers. That is, exponent refers to the number of times a number has been multiplied by itself. For example, 6 is multiplied by itself four times, yielding 6 6 6 6. This is written as [tex]6^{4}[/tex]. The exponent is 4 and the base is 6.
Given that 1000 to the power of m divided by 100 to the power of n
When powers of the equal base are divided, the same base is placed and the exponents are subtracted, which is an important mathematical property of powers.
Then, as powers of the same base, we can write 1000m and 100n:
1000m = [tex](10^{3})^{m}[/tex] = [tex]10^{3m}[/tex]
100n= [tex](10^{2)^{n} }[/tex] = [tex]10^{2n}[/tex]
Now we perform the division of powers of the same base (10)
103m/102n
= 103m-2n
Finally
103m-2n = 10z
z = 3m-2n
Therefore Z in terms of m and n is z = [tex]3^{m} -2^{n}[/tex]
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Simon drives 75 km at an average speed of 120 km/h and then 9 km at 70 km/h without stopping. What is the average speed for the whole journey to 1 dp?
95km/h is the average speed for the whole journey
What is Speed?Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object's movement
Given,
Simon drives 75 km at an average speed of 120 km/h
9 km at 70 km/h without stopping.
We need to find the average speed.
Average speed = Total distance/Total time
The total distance is 75km+9km
84 km
The average speed is sum of speeds by two
120+70=190/2=95km/h
Hence, 95km/h is the average speed for the whole journey
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Khadija is blocking off several rooms in a hotel for guests coming to her wedding. The hotel can reserve small rooms that can hold 3 people, and large rooms that can hold 4 people. Khadija reserved 2 more small rooms than large rooms, which altogether can accommodate 48 guests. Graphically solve a system of equations in order to determine the number of small rooms reserved, x, and the number of large rooms reserved, y.
There are 8 small rooms and 6 large rooms.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Let s be the number of small rooms reserved.
Let l be the number of large rooms reserved.
Each small room can accommodate 3 guests, hence s small rooms can hold 3s guests.
Each large room can accommodate 4 guests, so all large rooms can hold 5l guests.
Thus, the total number of guests
48 =3s+4l
3s+4l=48
3s+4l=48
as, Khadija reserved 2 more small rooms than large rooms,
So, s=l+2
s=l+2
Now, solving the equations
3s+5l= 54
s=l+2
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Coupon B: 30% off of $63 shoes
suppose that a set of scores has a mean of 5 and standard deviation of 2. what score corresponds to a z score of -2.0?
The set of scores has a mean of 5 and a standard deviation of 2. The score which corresponds to a z score of -2.0 is 1.
Given in the question,
Mean (m) = 5
Standard deviation σ =2
Z-score = -2
The score x,
= Z = x - m / σ
= -2 = x - 5 / 2
= -4 = x - 5
= x = 1
Standard deviation in statistics means the amount of dispersion or variations in the set of values. A lower standard deviation means the value is closer to the mean while a higher standard deviation means the value is farther away from the mean.
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Write 480 ml as a fraction of 3 litres
Give your answer in its simplest form
Answer:
Step-by-step explanation:480/3000
147,21,3 Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form.
The sequence is geometric and the common ratio is 1/7
How to determine if the sequence is arithmetic or geometric?An arithmetic sequence is a sequence of numbers in which each differs from the preceding one by a constant value e.g 2, 4, 6, etc. That is: 6-4 = 4-2 = 2
A geometric sequence is a sequence of numbers with a constant ratio between each number and the one before e.g. 9, 27, 81, etc. That is: 81/27 = 27/9 = 3
Given: 147, 21, 3
This sequence does not have a common difference. Thus, it is not arithmetic
This sequence has a common ratio. Thus, it is geometric
common ratio = 21/147 = 1/7 or 3/21 = 1/7
Therefore, the sequence is geometric and has a common ratio of 1/7
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The longet ide of an acute triangle meaure 30 inche. The two ide are congruent, but their length i unknown. What i the mallet poible perimeter of the triangle, rounded to the nearet tenth?
The smallest possible perimeter of the triangle is, 72.4 inches.
What is perimeter?
The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimeters, meters, inches, and feet.
As given the longest side of an acute triangle measure 30 inches.
The two remaining sides' combined length must be longer than the opposite side.
The sum of the two remaining sides should be greater than 30 inches if the side is 30.
Assume the other two sides add up to 31 inches.
So, The perimeter of a triangle is equal to the sum of its three sides, which comes to 30 + 31 = 64 inches.
Consequently, the circumference must be greater than 64 inches.
Hence, based on the possibilities, the triangle's smallest conceivable perimeter is 72.4 inches.
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Write an equation of the line with the given slope and y-intercept
slope : 2/5
y-intercept : 0
[tex]y = \cfrac{2}{5}x + 0\implies y=\cfrac{2}{5}x\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
Directions: Tell whether each is a prime factorization. Write YES or NO in the
blank.
___________1. 3 x 2 x 9 x 5
___________2. 2 x 2 x 3 x 7
___________3. 5 x 7 x 3 x 2
___________4. 7 x 2 x 12 x 3
___________5. 3 x 2 x 7 x 2
___________6. 3 x 5 x 2 x 13
___________7. 5 x 3 x 21
___________8. 7 x 3 x 5 x 11
___________9. 2 x 5 x 4 x 2
___________10. 3 x 7 x 31 x 5
Pleedadeees helppilyyy meeelili out
Answer:
Step-by-step explanation:
Answer: I Can't Read it
Step-by-step explanation: Its to far
A biker cycles 9 miles in 2/3 of an hour. Make a chart and fill it in to show how far he will bike if he maintains the same pace for 2 hours 3 hours and 3.5 hours
Answer:
27 miles, 40.5 miles, and 47.25 miles
Step-by-step explanation:
9 miles in 2/3 hours. To get to a whole number, we can multiply by the reciprocal of 2/3, which is 3/2. 2/3*3/2=1. Now lets multiply 9 by 3/2. 9*3/2=13.5
We now have a unit rate which is 13.5 miles each hour.
Now lets solve for 2 hours.
13.5*2= 27 miles
Now lets solve for 3 hours.
13.5*3=40.5 miles
Now lets solve for 3.5
13.5*3.5= 47.25 miles
The wholesale price for a chair is $160. A certain furniture store marks up the wholesale price by 21%. Find the price of the chair in the furniture store.
Round your answer to the nearest cent, as necessary.
Answer:
$193.60
Step-by-step explanation:
160x1.21=$193.60
160+21%=$193.60
The circumference of a circle is 15 in. What is the area, in square inches? Express
your answer in terms of pie
Answer:
The area is 225/(4π) in²Step-by-step explanation:
Area of circle equation:
A = πr²Circumference of circle equation:
C = 2πrGivenC = 15 inTo Find Area of circleSolutionUse circumference equation to find the radius:
2πr = 15r = 15/(2π)Find the area:
A = π*[15/(2π)]² = 225/(4π) does the graph of a power function and the graph of its inverse demonstrate
symmetry? Explain your reasoning.
Yes, the graphs of a power function and its inverse are symmetric about the line y=x.
What is an inverse function?
A function that "undoes" another function is called an inverse. In other words, if f(x) yields y, then y entered into the inverse of f yields the output x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f⁻¹.
What is a power function?
Any function where y = xⁿ, where n is any real constant integer, is referred to be a power function. In reality, many of our parent functions, including linear and quadratic functions, are power functions.
Here,
The graphs of self-inverse functions are symmetrical about the line y=x. The domain of a one-to-one function f is the same as the range of its inverse f⁻¹ and the range of f is the same as the domain of f⁻¹.
Hence, the graphs of a power function and its inverse are symmetric about the line y=x.
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Write an equation of the line that passes through (-3,-3) and is perpendicular to the line 3x+4y=8
Answer:
[tex]5x-4y=-3[/tex]
Step-by-step explanation:
Take a look at the attachment...
Hope this helps! :)
What is the rate of change in the function?
Answer:
The rate of change, or slope, is 1/2.
To find the slope of a line, first, pick two points on the line and determine their coordinates. Then, determine the difference in y-coordinates of these two points (rise). After that, determine the difference in x-coordinates for these two points (run). Then you have your slope!