The 30th term a30 of the sequence is -1445
How to determine the value of a30?The definition of the function is given as
arithmetic sequence of 1,-4,-9,-14
The above definitions imply that we simply subtract 5 from the previous term to get the current term
Using the above as a guide,
so, we have the following representation
First term, a = 1
Common difference, d = 5
An arithmetic sequence is represented as
a(n) = a + (n - 1)d
For the 30th term, we have
a(30) = a + 29d
So, we have
a(30) = 1 + 29 * -5
Evaluate
a(30) = -144
Hence, the value of a30 is -144
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you are given a system of 4 linear equations in 3 variables x, y, z. explain why it is impossible for the system to have exactly two solutions.
A system of 4 linear equations in 3 variables x, y, z can have at most one solution.
It is because a system with more than three equations and only three variables will not have a unique solution due to the fact that the dimension of the solution space of 3-dimensional equations is three, so adding an extra equation will result in an over-determined system.
In other words, there are not enough variables in the system to meet the requirements of all the equations, which leads to an over-determined system where there is either no solution or a unique solution. If the system has exactly two solutions, it means that the solution space of the system of equations has a dimension greater than 3, which contradicts the fact that the dimension of the solution space of a system of 3-dimensional equations is 3.
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A solid metal cube of side 6 cm is recast into a solid sphere. Find the radius of the sphere.
Answer:
Answer provided in image May it help you !!!
Step-by-step explanation:
PLEASE HELP 50 POINTS
Answer:
Isosceles acute triangle
Step-by-step explanation:
angle CBD = 56 because you have to subtract 180 - 124 = 56
angle BDC = 62
add CBD = 56 and BDC = 62
56+62+c(angle c)=180
c= 62 b=56 d=62
2 angles are equal and therefore it is Isosceles
Non of the angles are obtuse and therefore it is acute triangle!
Hope I helped!
Carlos has noticed that because each of his purchases have been somewhat similar, it has been easy
figure out the cost of each item. However, his last set of receipts has him puzzled. One week he tried out
cheaper brands of cat and dog food. On Monday he purchased 3 small bags of cat food and 5 small bags of
dog food for $22.75 Because he went through the small bags quite quickly, he had to return to the store on
Thursday to buy 2 more small bags of cat food and 3 more small bags of dog food, which cost him $14.25.
Based on this information, figure out the price of each bag of the cheaper cat and dog food. Explain your
reasoning.
Price of each bag of cat food is $3 and the price of each bag of dog food is $2.75.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Let x be the cost of each small bag of cat food and y be the cost of each small bag of dog food.
Given that,
On Monday Carlos purchased 3 small bags of cat food and 5 small bags of dog food for $22.75.
3x + 5y = 22.75
On Thursday he buy 2 more small bags of cat food and 3 more small bags of dog food, which cost him $14.25.
2x + 3y = 14.25
So we have two linear equations.
3x + 5y = 22.75 and 2x + 3y = 14.25
Multiplying throughout the first equation with 2 and the second equation with 3, we get the two equations as,
6x + 10y = 45.5 and
6x + 9y = 42.75
Subtracting second from first,
y = 2.75
Substituting y = 2.75 in 2x + 3y = 14.25,
2x = 14.25 - 8.25
x = 3
Hence the the price of cat food and dog food are $3 and $2.75 respectively.
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the eleventh term of an arithmethic sequence is 69 while the sum of the first three terms is 45. find the third term
The third term of this arithmetic sequence is 21.
eleventh term of an arithmetic sequence is 69.
a₁₁ = a + 10 d = 69
also sum of the first three terms is 45
the first three terms are a, a + d, a + 2d
a + a + d + a + 2d = 45
3a + 3d = 45
a + d = 15
a = 15 - d
so, a + 10 d = 69
15 - d + 10d = 69
9d = 69 - 15
9d = 54
d = 6
a = 15 - 6 = 9
a₃ = a + 2d
= 9 + 2(6)
a₃ = 21
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rty families gathered for a fund-raising event. suppose the individual contribution for each family is normally distributed with a mean and a standard deviation of $115 and $35, respectively. the organizers would call this event a success if the total contributions exceed $5,000. what is the probability that this fund-raising event is a success?
The probability that fund-raising event is a success and total contributors exceeds $5,000 is 0.0351 or 3.51%
Number of family members = 40
Mean of individual contributions for each family is normally distributed is $115 (μ) and standard deviation(σ) is $35. It is also given that the organizers would call this event a success if the total contributions exceed $5,000
Mean = [tex]\frac{5000}{40}[/tex]
Mean = 125
P-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
P(mean > 125) = P( 2 > [tex]\frac{(125 - 115)\sqrt{40} }{35}[/tex] )
= P(2 > 1.81)
= 1 - P(2 < 1.81)
1.81 has a pvalue of 0.9649
≅ 0.0351
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if 12 bagels cost $35 how much would one cost
Answer:$2.97
Step-by-step explanation: 35 divided by 12 = 2.97
divide the sum of 11 and g by 9 in algebraic expression
The algebraic expression can be written as:
(11 + g)/9
How to write the algebraic expression?
Here we want to write:
"divide the sum of 11 and g by 9"
As an algebraic expression.
The sum of 11 and g can be written as:
(11 + g)
Where g is the variable in this problem.
And now we just divide that by the number 9, then the algebraic expression is the next one:
(11 + g)/9
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Kayla is looking at a graph that has a parabola on it. The parabola touches the x-axis at 3 and 9. Which of the following functions could have been graphed on her paper?
The function graphed on the paper could be a quadratic function which has the two real roots equal to 3 and 9.
What is Parabola?A parabola is a two dimensional figure on a plane which is U shaped and any point on the parabola is at an equal distance from a fixed point called focus and a fixed line called directrix.
The graph of a function is parabola when the function is quadratic.
Quadratic functions are of the form f(x) = ax² + b x + c.
Given that, the parabola touches the x-axis at 3 and 9.
This indicates that roots of the quadratic equation are 3 and 9.
That is, f(x) = 0, when x = 3 and x = 9.
It may be of the form f(x) = (x - 3)(x - 9) = x² - 3x - 9x + 27 = x² - 12x + 27.
So the function representing the graph on the paper is a quadratic function whose roots are 3 and 9 and the function could be of the form f(x) = x² - 12x + 27.
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100 is no less than 20 times a number t
Answer:
You can put this solution on YOUR website!
100 >= 20t (that's "more than or equal to")
Divide each side by 20
5 >= t [5 is more than or equal to t]
or, conversely, t <= 5 [t is less than or equalequal to 5]
A 20-minute TV program consists of two commercials, each 13 over 4 minutes long, and three equal-length entertainment segments. How long is each entertainment segment? Enter your answer as a decimal.
The length of each entertainment segment written as a decimal is 4.5 minutes
How long is each entertainment segment?Total time of the TV program= 20 minutes
Number of commercials= 2
Time taken for each commercial= 13/4 minutes
Total time taken for 2 commercials= 2(13/4)
= 26/4
= 13/2 minutes
Number of minutes remaining after commercials= Total time of the TV program - Total time taken for 2 commercials
= 20 - 13/2
= (40-13) / 2
= 27/2 minutes
Number of entertainment segment = 3
Time spent on each entertainment segment= Number of minutes remaining after commercials / 3
= 27/2 ÷ 3
multiply by the reciprocal of 3
= 27/2 × 1/3
= 27/6 minutes
= 4.5 minutes
Therefore, each entertainment segment will take 4.5 minutes from the 20 minutes TV program.
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while attending school, you work part time at a coffee shop. last year, you made $8,700. why might you still file your taxes, even though you made less than the standard deduction?
Even if we earned less than the standard deduction, we nonetheless file taxes since, regardless of their income, freelancers are always required to pay tax on their earnings.
What is a freelancer?Freelancer, freelancer, or freelance worker are phrases frequently used to describe someone who is self-employed and isn't necessarily long-term dedicated to a certain employer.
Others work independently or use websites or professional associations to find work.
Freelancers are occasionally represented by a business or a temporary agency that resells their services to clients.
Independent contractors must always pay taxes on their wages, regardless of how much they make.
The term "freelancing" is most frequently used in the culture and creative industries, and use of this term may indicate participation in these sectors, even though the term "independent contractor" would be used in a different register of English to designate the tax and employment classes of this type of worker.
Therefore, even if we earned less than the standard deduction, we nonetheless file taxes since, regardless of their income, freelancers are always required to pay tax on their earnings.
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Answer below i really really need help with this
Answer: 1/5
Step-by-step explanation:
help meeeeh please with this question
a) This can't be correct because we will see that she found 6.7 animals, and that can't be.
b) in this case the fraction of plants ios 2/5, then the number of plants is 8.
Can Jill's statement be correct?a) We know that she found 20 species of animals and plants, so, if she says that a fraction of 1/3 of these are animals, then the number of animals will be:
A = (1/3)*20 = 20/3 = 6.7
That is not a whole number, so it isn't correct.
b) If 3/5 of the species were animals, then 2/5 were plants, so the number of plants is given by:
P = (2/5)*20 = 2*20/5 = 2*4 = 8
There are 8 plants in this case.
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What is the answer to both parts of the question
19.Viktor's skating rink is 1.2 miles from his house. If he has practice at 7:00 am and can
walk at an average speed of 3.0 mph, what is the absolute latest he can leave to
arrive on time?
With his average speed of 3mph, Viktor should leave his house by 6:36 am to arrive at the skaring rink on time.
From the case, we know that:
Average speed = 3.0 mph
Distance = 1.2 miles
Arrival time = 7:00 am
Departure time?
Using the average speed concept, we know that average speed can be calculated by dividing the travel distance with the travel time, or it can be formulated as:
Average speed = distance : travel time
3.0 = 1.2 : travel time
travel time = 0.4 hours
After finding the travel time Viktor spend to go from his house to the skating rink, we need to find the departure time for him to arrieve at the skating rink on time. However, we need to convert the travel time into minutes first.
Travel time = 0.4 hours
Travel time = 0.4 x 60 minutes
Travel time = 24 minutes
Arrival time = Departure time + Travel time
7:00 = Departure time + 24 minutes
Departure time = 6:36 am or 24 minutes before 7:00 am
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Name the following triangles
Answer:
7-isoceles, 8- equilateral 9-scalene
Step-by-step explanation:
isoceles have 2 identical sides unlike scalene, where all sides have different lengths.
is obtuse and acute I think
plssssss help me! i don’t understand.
Line p intersects lines a and b. a b. By which theorem is ∠1 ≅ ∠8?
The transversal Alternate Interior Angle Theorem is the theorem for which ∠1 ≅ ∠8
What is the theorem?If line p intersects lines a and b and angles 1 and 8 are opposite angles, then they are congruent (equal) by the Transversal-Alternate Interior Angle Theorem.
The Transversal-Alternate Interior Angle Theorem states that if a transversal intersects two lines, then alternate interior angles are congruent. In other words, if a transversal line (such as line p in this case) cuts two other lines (lines a and b), then the angles on one side of the transversal will be equal to the corresponding angles on the other side. These corresponding angles are called alternate interior angles.
So, in this case, angle 1 and angle 8 are alternate interior angles and are equal to each other as per the Transversal-Alternate Interior Angle Theorem.
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the unit kilowatt-hour is a measure of the unit kilowatt-hour is a measure of power. the amount of power used per second. an amount of energy. the rate at which energy is transformed.
The unit kilowatt-hour measures the amount of energy used or produced, whereas the rate at which energy is transformed is measured in kilowatts.
The unit kilowatt-hour (kWh) is a measure of energy, not power. Energy is a measure of the amount of work that can be done, and is usually measured in joules. Power, on the other hand, is a measure of the rate at which energy is transformed, and is usually measured in watts.
A kilowatt-hour is the amount of energy used or produced when a power of one kilowatt is used for one hour. For example, if a 100-watt light bulb is left on for 10 hours, it will have used
100 * 10 = 1000 watt-hours or 1 kilowatt-hour of energy.
So to summarize, the unit kilowatt-hour measures the amount of energy used or produced, whereas the rate at which energy is transformed is measured in kilowatts.
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One angle of a quadrilateral is 160 degrees. The other angles are all the same size. Work out the size of the other three angles
Answer:
Step-by-step explanation:
can you include a picture please
Working together, two pumps can drain a certain pool in 3 hours. If it takes the older pump 12 hours to drain the pool by itself, how long will it take the newer pump to drain the pool on its own?
if it take 12 hours for a older pump and 3 hours for 2 pumps you would multiply 3x2 witch equals 6 and 6÷12 equals 3
a class has 10 boys and 12 girls. 3 students are chosen at random to clean the classroom each day. how many unique cleaning teams exist?
The number of different unique cleaning teams should be 1540.
What are permutation and combination?A permutation is an arrangement of things where order matters, AB and BA are two different permutations.
The combination is a selection of things where order does not matter, AB and BA are the same combinations.
Given, A class has 10 boys and 12 girls and 3 students are chosen at random.
So, the team of 3 can be chosen as 3 boys, 3 girls, 1 boy 2 girls, and 1 girl and 2 boys and the total teams will be the sum of different combinations which is,
= [tex]^{10}C_3 + ^{12}C_3 + ^{10}C_1\times^{12}C_2 + ^{12}C_1\times^{10}C_2[/tex].
= (10×9×8)/6 + (12×11×10)/6 + 10×(12×11)/2 + 12×(10×9)/2.
= 120 + 220 + 660 + 540.
= 1540.
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A 5 kilograms bag of beans cost $18.50. At the same rate, what amount of money would 9 kilograms bag of beans cost?
Answer: $33.3
Step-by-step explanation:
1kg of beans cost $3.70 then $3.70x9= $33.3.
Hope this helps.
In the inequality 3x + 4y ≤ 5, which of the following ordered pair is the solution?
A. (7,2)
B. (2,-1)
C. (5,-1)
D. (6,1)
Answer: (2, -1)
Step-by-step explanation:
To determine if an ordered pair is a solution to an inequality, we substitute the values of x and y into the inequality and see if the resulting expression is true or false.
A. For (7,2), we have:3(7) + 4(2) = 21 + 8 = 29 29 > 5, so (7,2) is not a solution to the inequality.
B. For (2,-1), we have:3(2) + 4(-1) = 6 - 4 = 2 2 ≤ 5, so (2,-1) is a solution to the inequality.
C. For (5,-1), we have:3(5) + 4(-1) = 15 - 4 = 11 11 > 5, so (5,-1) is not a solution to the inequality.
D. For (6,1), we have:3(6) + 4(1) = 18 + 4 = 22 22 > 5, so (6,1) is not a solution to the inequality.
So, the ordered pair that is a solution to the inequality is (2,-1).
a ball of radius 13 has a round hole of radius 7 drilled through its center. find the volume of the resulting solid.
The volume of the resulting solid is 3,280.953 cm3.
The volume of the resulting solid is calculated by subtracting the volume of the inner sphere (the hole) from the volume of the outer sphere (the ball). The volume of a sphere is calculated by the formula V=4/3πr3. Therefore, the volume of the outer sphere is V1=4/3π(13)3=4,714.286 cm3. Similarly, the volume of the inner sphere is V2=4/3π(7)3=1,433.333 cm3. Subtracting V2 from V1 gives the volume of the resulting solid as V3=4,714.286 - 1,433.333=3,280.953 cm3. Therefore, the volume of the resulting solid is 3,280.953 cm3.
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If f(x) = 2x² + 3 and g(x)=x2-7, find (f+ g)(x).
Answer: 3x2 - 4
Step-by-step explanation:
2x2 + 3 + (x2 - 7)
2x2 + 3 + x2 - 7
3x2 - 4
(i don't know if this is right let me know)
Haley's clothing store sold 540 shirts with the ratio o f short sleeve to long sleeve being 3:9. how many short sleeve were sold
The short sleeve shirts sold by haley were 405
What is a ratio?The quantitative relation between two amounts shows the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"
Given here: Haley's clothing store sold 540 shirts with ratio of short sleeve to long as 3:9
let 3x and 9x long and short sleeves were sold respectively
Then we have
3x+9x=540
12x=540
x=540/12
x=45
Thus 3x=135 and 9x=405
Hence, The short sleeve shirts sold by haley were 405
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(i) Express 2x² +8x-10 in the form a(x+b)² + c
Help
Answer:
2(x+2)² - 18
Step-by-step explanation:
Given
2x² +8x-10
express in the form a(x + b)² + c
Take out common factor 2 from 2x² +8x-10 ==> 2(x² + 4x -5)
x² + 4x - 5 can be converted to the form (x + b)² + c as follows using complete the square technique
(x + b)² = x² +2bx + b²
Comparing x² +2bx + b² and x² + 4x - 5 we can see that b = 2
So the expression becomes
x² + 4x - 5 = (x+2)³ + c
= x² + 4x + 4 + c
Therefore -5 = 4 - c
c = -5 -4 = -9
Therefore
x² + 4x - 5 = (x+2)³ -9
2(x² + 4x -5) = 2[(x+2)³ -9]
=2(x+2)² -18
ANSWER
Verify
2(x+2)² -18 = 2(x² +4x + 4) - 18 = 2x²+8x +8 - 18 = 2x² + 8x - 10
Thus verified
What are the coordinates of the orthocenter of triangle WXY with vertices W(2,7), X(3, 4), and Y(6, 7)?
Answer:
(3, 6)
Step-by-step explanation:
You want the coordinates of the orthocenter of triangle WXY with vertices W(2,7), X(3, 4), and Y(6, 7).
OrthocenterThe orthocenter is the point where the altitudes of the triangle meet. An altitude is the line through a vertex that is perpendicular to the opposite side.
This is an acute triangle, so the orthocenter is within the boundaries of the triangle.
AltitudesWe note that side WY of the triangle is a horizontal line, so the orthocenter will lie on the vertical line through point X. The x-coordinate of point X is 3, so that vertical line has equation x=3.
Side XY can be seen on the graph to have a slope of 1. Or, you can compute it from the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (7 -4)/(6 -3) = 3/3 = 1
Then the point-slope equation of the altitude to that line will have the opposite reciprocal slope, and will go through point W(2, 7):
y -7 = -1(x -2)
Concurrent pointThe y-value of the point of intersection of the altitude through W with the altitude through X will be the solution to ...
x = 3y -7 = -x +2Substituting for x in the second equation, we have ...
y -7 = -3 +2
y = 6 . . . . . . . . . . add 7
The orthocenter is (x, y) = (3, 6).
__
Additional comment
The orthocenter of a right triangle is the vertex where the right angle is located. The orthocenter of an obtuse triangle is outside the triangle.