The first term in this sequence is -1. Write the function that represents the sequence
Answers
Answer:
[tex]a_{n}[/tex] = 2n - 3
Step-by-step explanation:
Note the difference in consecutive terms is constant, that is
1 - (- 1) = 3 - 1 = 5 - 3 = 7 - 5 = 2
This indicates that the terms are an arithmetic sequence with
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 1 and d = 2, thus
[tex]a_{n}[/tex] = - 1 + 2(n - 1) = - 1 + 2n - 2 = 2n - 3
Related Questions
Uncle drew scored 28 points in 5 5/6 minutes. How many points did he average per minute
Answers
Answer:4.6
Step-by-step explanation:
28/6
Answer:
168/35 points per minute
Step-by-step explanation:
5 5/6=35/6
28/(35/6)=(28/1)(6/35)=168/35
for the function below, state the x-coordinate of the x-intercept that is located to the left of the origin
f(x)=4x^3-12x^2 - x + 15
Answers
Answer:
The x-coordinate of the x-intercept that is located to the left of the origin is equal to -1
Step-by-step explanation:
we have the function
[tex]f(x)=4x^3-12x^2-x+15[/tex]
we know that
The x-intercepts are the values of x when the value of the function is equal to zero
using a graphing tool
The function has three x-intercepts
The x-intercepts are the points
(-1,0),(1.5,0) and (2,5,0)
see the attached figure
The x-intercept that is located to the left of the origin is the point (-1,0)
therefore
The x-coordinate of the x-intercept that is located to the left of the origin is equal to -1
Answer:
The x-coordinate of the x-intercept is -1.
Step-by-step explanation:
A student number system for a county requires that the student number be 5 characters.
The first 4 characters are any single digit number, but no character can repeat and the last
character must be a letter. How many unique student numbers are possible?
30,240
131,040
260,000
315,160
Answers
Answer:
131040
Step-by-step explanation:
10*9*8*7*26
=131040
Final answer:
To calculate the unique student numbers possible, multiply the number of options for each character position: 10 x 9 x 8 x 7 for the digits and multiply by 26 for the final letter, yielding 131,040 unique numbers.
Explanation:
The question asks us to calculate how many unique student numbers are possible with a specific format: the first four characters must be single-digit numbers with no repeat, and the last character must be a letter.
To find the total number of unique student numbers, we multiply the possibilities for each position. For the first position, we have 10 choices (0-9), for the second position 9 choices (excluding the first digit chosen), for the third position 8 choices, and for the fourth position 7 choices. This can be calculated using factorial notation as 10 x 9 x 8 x 7. The last character is a letter and since there are 26 letters in the English alphabet, we have 26 choices for the last character. The total number of combinations is hence 10 x 9 x 8 x 7 x 26, which equals 131,040.
Two groups of students were asked how far they lived from their school. The table below shows the distances in miles:
Group A (distance in miles) 1 1.5 3 3.2 2.8 1.5 1.8 2.5 2.2
Group B (distance in miles) 2 2.5 3.23 1.8 2.4 3
Which statement best compares the mean distances for the two groups?
tie anual for Group A and Group B.
Answers
Answer:
(b) The statement : It is greater for Group B than Group A is correct.
Step-by-step explanation:
Here, the given question is INCOMPLETE.
Two groups of students were asked how far they lived from their school. The table below shows the distances in miles
Group A (distance in miles) 1 1.5 3.03 3.2 2.8 1.5 1.8 2.5 2.2
Group B (distance in miles) 2 2.5 3.23 1.3 1.8 2.4 3 1.5 1.8
Which statement best compares the mean distances for the two groups?
It is equal for Group A and Group B.
It is greater for Group B than Group A.
Its value for Group A is double the value for Group B.
Its value for Group B is double the value for Group A.
Answer:
Now,here the calculating the mean as calculated by the group A.
[tex]\textrm{Mean} = \frac{\textrm{Sum of Obseravtion}}{\textrm{ Number of Observation}}[/tex]
Mean as calculated by Group A = [tex]\frac{\textrm{1 + 1.5 +3 +3.2+ 2.8+ 1.5 +1.8+ 2.5 +2.2}}{\textrm{ Number of Observation}} = \frac{19.5}{9} =2.16[/tex]
So, mean by Group A = 2.16
Now, calculating the mean as calculated by the group B.
[tex]\textrm{Mean} = \frac{\textrm{Sum of Obseravtion}}{\textrm{ Number of Observation}}[/tex]
Mean as calculated by Group B = [tex]\frac{\textrm{2 + 2.5 +3.23 +1.3 + 1.8+ 2.4 +3 +1.5 +1.8}}{\textrm{ Number of Observation}} = \frac{14.93}{9} =2.48[/tex]
So, mean by Group B = 2.17
Hence, the statement : It is greater for Group B than Group A is correct.
Answer:
The correct answer is B. It is greater for Group B than Group A.
Step-by-step explanation:
The values are not equal and the difference just isn't enough for it to be any of the other answers making B the right option.
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solve the systems of equations using elimination
3x-5y=-2
4x-7y=-3
a.(-1,-1)
b.( -7/3, -1)
c. (-7/3, 1)
d.(1, 1)
Answers
Answer:
x=1, y=1. (1, 1). The answer is D).
Step-by-step explanation:
3x-5y=-2
4x-7y=-3
--------------
4(3x-5y)=4(-2)
-3(4x-7y)=-3(-3)
------------------------
12x-20y=-8
-12x+21y=9
--------------------
y=1
3x-5(1)=-2
3x-5=-2
3x=-2+5
3x=3
x=3/3
x=1
Select the equation of the line that passes through the point (3, 5) and is
perpendicular to the line x= 4
O 1) y = 5
O2)x= 5
O3) y = 4
O4) x = 3
Answers
Answer:
1) y = 5Step-by-step explanation:
x = 4 it's a vertical line.
Perpendicular line to a vertical line is a horizontal line.
A horizontal line has equation y = a.
A horizontal line passes through the point (3, 5) → x = 3 and y = 5.
Therefore the equation is y = 5
Stephanie left Riverside, California, driving her motorhome north on Interstate 15 towards Salt Lake City at a speed of 56
miles per hour. Half an hour later, Tina left Riverside in her car on the same route as Stephanie, driving 70 miles per hour.
Solve the system
Answers
Answer:
2.5
Step-by-step explanation:
56(t+1/2)=70 t
56T + 28= 70T
28=70T-56T
28=14
2=T
s=T+ 1/2
S=2+ 1/2
S=2.5 hours
Tina traveled for 2 hours at a speed of 70 miles per hour, covering a distance of 140 miles.
Stephanie traveled for 2.5 hours at a speed of 56 miles per hour, also covering a distance of 140 miles.
What's the expression about?The distance traveled by a vehicle is given by the formula: distance = speed × time.
For Stephanie:
Distance_stephanie = Speed_stephanie × Time_stephanie
Distance_stephanie = 56 × (t + 0.5)
For Tina:
Distance_tina = Speed_tina × Time_tina
Distance_tina = 70 × t
Since both Stephanie and Tina are traveling the same route, the distances they travel should be equal:
Distance_stephanie = Distance_tina
Substitute the expressions for distances:
56 × (t + 0.5) = 70 × t
Now solve for "t":
56t + 28 = 70t
28 = 14t
t = 28 / 14
t = 2
So, Tina traveled for 2 hours.
Now we can find the distance traveled by both Stephanie and Tina:
Distance_tina = 70 × t
Distance_tina = 70 × 2
Distance_tina = 140 miles
Distance_stephanie = 56 × (t + 0.5)
Distance_stephanie = 56 × (2 + 0.5)
Distance_stephanie = 56 × 2.5
Distance_stephanie = 140 miles
Both Stephanie and Tina traveled a distance of 140 miles.
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A rational function is a function whose equation contains a rational
expression.
A. True
B. False
Answers
Answer:
True
Step-by-step explanation:
Answer:
true
Step-by-step explanation:
What is the following product square root 10* square root 10
Answers
Answer: 10
Step-by-step explanation:
Answer:
The answer would be ten.
Step-by-step explanation:
I plugged it into my TI-84 plus calculator.
PLEASE HELP ASAP!!! heres the screenshot... please answer with two senteces! srry it is sideways :(
Answers
Answer:
jo mamma
Step-by-step explanation:
One third of a store’s inventory is children’s clothing. Two fifths of its inventory is women’s clothing. What fraction of the total inventory is children’s or women’s clothing?
Answers
Women : 4/15
I’m sorry if it’s incorrect :(
Answer:
11/15
Step-by-step explanation:
To answer this, add (combine) 1/3 and 2/5.
First we must rewrite these fractions with the same denominator, the LCD.
The LCD here is obtained by multiplying the denominators 3 and 5 together, obtaining 15.
Thus, 1/3 + 2/5 becomes 5/15 + 6/15, which, in turn, is 11/15.
The fraction of the total inventory that is children’s or women’s clothing
is 11/15.
A = {1, 2, 5, 7} B = {3, 4, 6, 7} C = {0, 5, 8, 9} Find A U B U C. A) {0,1,2,3,4,5,6,7,8,9} B) {1,2,3,4,5,6,7} C) {3,4,5,6,7} D) {3,4,7}
Answers
A) {0,1,2,3,4,5,6,7,8,9} is the right answer
Step-by-step explanation:
Given
A = {1, 2, 5, 7}
B = {3, 4, 6, 7}
C = {0, 5, 8, 9}
We hvae to find the union of all thre sets. In union, the elements of involved sets are combined. The repating elements are only written once
So,
[tex]AUBUC = \{1, 2, 5, 7\}U\{3, 4, 6, 7\}U\{0, 5, 8, 9\}\\= \{0,1,2,3,4,5,6,7,8,9\}[/tex]
Hence,
A) {0,1,2,3,4,5,6,7,8,9} is the right answer
Keywords: Sets, Union
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×/76 = 4/12
Solving proportions
Answers
Answer:
x = 25.33333333
Step-by-step explanation:
x = 4
76 12
Cross multiply:
x * 12 = 76 * 4
Simplifying
x * 12 = 76 * 4
Reorder the terms for easier multiplication:
12x = 76 * 4
Multiply 76 * 4
12x = 304
Solving
12x = 304
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Divide each side by '12'.
x = 25.33333333
Simplifying
x = 25.33333333
A garden patio is covered with grey slabs and yellow slabs
1/5 of the slabs are grey
The ratio of grey to yellow slabs are 1:4
There are 55 slabs in total
Work out number of yellow slabs
Answers
Answer:
There are 44 yellow slabs.
Step-by-step explanation:
Multiply 1/5 x 55. This gives you 11. 55 - 11 = 44.
The number of yellow slabs in a garden patio is 44.
Given that, a garden patio is covered with grey slabs and yellow slabs 1/5 of the slabs are grey.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
The ratio of grey to yellow slabs are 1:4.
There are 55 slabs in total.
Number of grey slabs =1/5 ×55
= 11
So, the number of yellow slabs
= 55-11
= 44
Therefore, the number of yellow slabs in a garden patio is 44.
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Evaluate n+2x2 when n=3 and x=−2.
Answers
Answer:
When n=3 and x=−2 the answer is 11.
Step-by-step explanation:
Given:
Let p (n,x) be the function such that
[tex]p (n,x) = n + 2x^{2}[/tex]
To Find:
p (n,x) = p ( 3, -2) = ?
Solution:
[tex]p (n,x) = n + 2x^{2}[/tex]
Substituting n = 3 and x = -2 we get
[tex]p (3, -2) = 3 + 2(-2)^{2}[/tex]
Negative square gives positive number therefore (-2)²=4
[tex]p (3, -2) = 3 + 2\times 4[/tex]
[tex]p (3, -2) = 3 + 8\\p (3, -2) = 11[/tex]
When n=3 and x=−2 the answer is 11.
Final answer:
When evaluating the expression n+2x^2 with n=3 and x=-2, we substitute the values to get 3 + 2(-2)^2, which simplifies to 3 + 8. The final evaluated expression is 11.
Explanation:
To evaluate the expression n+2x² with given values for n and x, we need to substitute the values into the expression and simplify it.
In this case, n = 3 and x = -2. Substituting these values in, we get:
3 + 2(-2)²
First, we calculate the square of -2:
3 + 2(4)
Now, we multiply 2 by 4:
3 + 8
Finally, we add 3 and 8 together:
11
Therefore, the evaluated expression is 11.
Marcela estimates the distance between the library and town hall is 735 ft. The actual distance is 612 ft.
What is the percent error in Marcela's estimate?
Round your answer to the nearest tenth of a percent.
Enter your answer in the box.
Answers
Answer:
20.1%.
Step-by-step explanation:
(735 - 612 = 123 ft.
% error = (123/612) * 100
= 20.1%.
please solve the equation (15m + 3)/2 = -6
Answers
Answer:
m = - 1
Step-by-step explanation:
Given
[tex]\frac{15m+3}{2}[/tex] = - 6
Multiply both sides by 2 to clear the fraction
15m + 3 = - 12 ( subtract 3 from both sides )
15m = - 15 ( divide both sides by 15 )
m = - 1
[tex]\text{Solve:}\\\\\frac{15m+3}{2}=-6\\\\\text{Multiply both sides by 2}\\\\15m+3=-12\\\\\text{Subtract 3 from both sides}\\\\15m=-15\\\\\text{Divide both sides by 15}\\\\\boxed{m=-1}[/tex]
What is the volume of this rectangular prism?
4.8 cm
4.1 cm
15 cm
Answers
Answer:
those are the dimentions
Step-by-step explanation:
Solve the system of linear equations. 2x + 5y = 12 4x − y = 2
Answers
Answer:
x=1, y=2. (1, 2).
Step-by-step explanation:
2x+5y=12
4x-y=2
--------------
y=4x-2
2x+5(4x-2)=12
2x+20x-10=12
22x-10=12
22x=12+10
22x=22
x=22/22
x=1
4(1)-y=2
4-y=2
y=4-2=2
y=2
Answer:
x = 1, y = 2 → (1, 2)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}2x+5y=12\\4x-y=2&\text{multiply both sides by 5}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}2x+5y=12\\20x-5y=10\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad22x=22\qquad\text{divide both sides by 22}\\.\qquad x=1\\\\\\\text{Put the value of}\ x\ \text{to the second equation:}\\\\4(1)-y=2\\4-y=2\qquad\text{subtract 4 from both sides}\\-y=-2\qquad\text{change the signs}\\y=2[/tex]
P(A) = 8/15
P(B) = 6/15
P(A n B) = 1/5
Find P(AUB)
A. 2/15
B. 11/15
C. 1/15
D. 4/15
Answers
Answer:
Step-by-step explanation:
note : P(AUB) = p(A)+p(B) - p(A∩B)
P(AUB) = 8/15+6/15- 1/5 = 8/15+6/15-3/15 = 11/15 answer : B
Probability helps us to know the chances of an event occurring. The correct option is B.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Given that P(A) = 8/15, P(B) = 6/15, and P(A n B) = 1/5. Therefore, the value of P(AUB) will be,
P(AUB) = P(A) + P(B) + P(A n B)
= 8/15 + 6/15 - 1/5
= 11/15
Hence, the correct option is B.
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1. Two pieces of equipment were purchased for a total of $4000. If one piece cost $850 more fean
the other, find the price of the less expensive piece of equipment. Assume all data ze 2002
to two significant agits unless grezier 20curacy is given
Answers
Answer:
$1,575
Step-by-step explanation:
x = the cost of the less expensive piece of equipment
x+850 = the cost of the more expensive piece of equipment
x + (x+850) = 4,000 the. two pieces together cost 4,000, so I added up the cost of the less expensive piece and the more expensive piece, and equaled it to 4,000
solve the equation:
x + (x+850) = 4,000
2x+850=4,000
2x=3,150
÷2
x=1,575
The ballpark made a total of $15,000 from ticket sales at Wednesday's game. The ballpark
charges $20 for each adult ticket and $10 for each child's ticket. They sold 3 times as many
children's tickets as adult tickets.
Write a system of equations that can be used to determine the number of adult ar
child tickets sold.
Answers
Answer:
The number of adult tickets sold was 300 and that of child's ticket sold is 900.
Step-by-step explanation:
Let us assume that the ticket sales at Wednesday's game are x number adult and y number child's tickets.
Therefore, as per given conditions, we can write, y = 3x .......... (1)
Again, each adult ticket cost $20 and each child's ticket costs $10 and there was a $15000 ticket sale.
So, 20x + 10y = 15000
⇒ 2x + y = 1500 ......... (2)
Now, solving equations (1) and (2) we get,
2x + 3x = 1500
⇒ 5x = 1500
⇒ x = 300 and y = 3x = 900
Therefore, the number of adult tickets sold was 300 and that of child's ticket sold is 900. (Answer)
PLEASE HELP QUICKLY 25 POINTS
What is the common difference,d,of the sequence ?
-92,-74,-54,-38,-20
Enter your answer in the box
D = [ ]
Answers
Answer:
+18
Step-by-step explanation:
what are associative on rational numbers
Answers
Answer:yo7 can add or multiply numbers regardless how they are grouped
Step-by-step explanation:
The temperature is -2∘C. If the temperature rises by 15∘C, what is the new temperature?
Answers
13 Degrees Celsius, or 55.4 degrees Fahrenheit.
-2 + 15 = 13. To find your answer in Fahrenheit, just do (Celsius here) x 9/5 + 32.
The new temperature value if an initial temperature value of - 2°C rises by 15°C will be 13°C
Using the addition operation :
Initial temperature = - 2°Temperature increase = 15°Final temperature = Initial temperature + Final temperature
Final temperature = (-2°C + 15°C) = 13°C
Therefore, the final temperature is 13°C
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The circumference of a pizza is about 38 inches. What is the diameter of the pizza? Round to the nearest tenth if necessary
Choices
6 in.
12.1 in.
12.7 in.
24.2 in.
Answers
Answer:
The diameter of the pizza is 12 inches
Step-by-step explanation:
Given:
Circumference of a pizza = 38 inches
To Find:
The Diameter of the pizza =?
Solution:
Circumference:
The distance around the edge of a circle (or any curvy shape). It is a type of perimeter.
We know that the shape of the pizza is circle.
So the given circumference is circumference of a circle.
Now,
Circumference of the circle(pizza)=[tex]2\pi r[/tex]
where r is the radius of the circle
circumference of the pizza =38
Thus
[tex]2\pi r= 38[/tex]
[tex]\pi r=\frac{38}{2}[/tex]
[tex]\pi r=19[/tex]
[tex]r=\frac{19}{3.14}[/tex]
r=6.050 inches
Now,
Diameter = [tex]2\times r[/tex]
Diameter = [tex]2\times 6.05[/tex]
Diameter=12.1 inches
Rounding to the nearest tenth
Diameter=12 inches
Final answer:
To find the diameter of a pizza with a circumference of about 38 inches, we apply the formula C = πD, leading to a calculation of 38 / 3.14, which results in approximately 12.1 inches.
Explanation:
The question is about finding the diameter of a pizza given its circumference, which is approximately 38 inches. To calculate the diameter from the circumference, we use the formula C = πD, where C is the circumference and D is the diameter. Since π (Pi) is approximately 3.14, we rearrange the formula to find the diameter: D = C / π. Thus, substituting the given value of C = 38 inches, we get D = 38 / 3.14, which is approximately 12.1 inches.
Year 11 Maths:
500ml of water is used to make 80g of pasta. How many grams of pasta could be made with 2.5 litres of water?
Answers
0.5L *5= 2.5L
80g*5=400g
With 2.5 litres of water, it can be estimated that you can make 400 grams of pasta.
Explanation:The question is asking how many grams of pasta could be made with 2.5 litres (or 2500 ml) of water. According to the initial ratio, 500 ml of water is used to make 80 grams of pasta.
To find out how many grams of pasta can be made with 2.5 liters of water, you first need to find the pasta-to-water ratio which is 80 grams pasta to 500 ml water, or 0.16 grams/ml. You then multiply this ratio by the total amount of water you have:
0.16 grams/ml * 2500 ml = 400 grams of pasta.
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in a sale normal prices are reduced by 10% nathelie bought a pair of shoes in the sale for £54 what was the original price of the shoes
Answers
Answer:
Step-by-step explanation:
10% of £54=£5.4 (price reduced by 10%)
Normal price should be £5.4 +£54= £59.4
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The third angle of a triangle is the same size as the first. The second angle is 4 times the third. Find the measure of angles.
Answers
Answer:
1st angle 30°
2nd angle 120°
3rd angle 30°
Step-by-step explanation:
Let's call
A = 1st angle
B = 2nd angle
C = 3rd angle
In every triangle it holds
A + B + C = 180°
Now, if the third angle of the triangle is the same size as the first
A = C
If the second angle is 4 times the third
B = 4C
we have then
C + 4C + C = 180° ===> 6C = 180° ===> C = 30°
If C = 30° then A = 30° and B = 120°
To the nearest hundredth, what is the value of x?
Answers
Answer:
60.42
Step-by-step explanation:
tan40 = opposite/adjascent
tan40 =x/72
x=72tan40
x = 72 * 0.8391
x = 60.42