The second and fifth term for the given sequence are 6 and 48 respectively and a₆ > 50.
What is an inequality expression?An inequality expression refers to the relation between an algebraic expression to some known value that contains inequality sign. Unlike an equation it can have a range of values inside an interval.
The given problem can be solved as,
(a) The nth term of the sequence is given as aₙ = 3n²/2
Then, substitute n = 2 to get second term as below,
a₂ = (3 × 2²)/2 = 6
(b) The fifth term is obtained as,
a₅ = (3 × 2⁵)/2 = 48.
(c) The inequality expression for the given case can be written as,
3n²/2 > 50
⇒ 3n² > 100
⇒ n² > 33.33
This is possible only for n = 6.
Hence, the second and fifth terms are 6 and 48 respectively. And, the 6th term will be the first to be greater than 50.
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Two fair dice are renumbered using -2, -1, 0, 1, 2, 3 instead of the
usual numbers. The two dice are thrown in the normal way.
Draw a table to show the total score for each of the possible
outcomes
(b) How many ways are there of scoring 0 ?
Pls help ASAP
Answer:
6
Step-by-step explanation:
the number of occurs over 0
Sue either travels by bus or walks when she visits the shops. The probability that she catches the bus from the shops is 0.7. Show that the probability that she walks at least one way is 0.72
Corrected Question
Sue travels by bus or walks when she visits the shops. The probability that she catches the bus to the shops is 0.4. The probability she catches the bus from the shops is 0.7. Show the probability that Sue walks at one way is 0.72
Answer:
[tex]P(A \cup B) =0.72[/tex] (Proved)
Step-by-step explanation:
Sue travels by bus or walks when she visits the shops.
Let the event that she catches the bus to the shop=A
Let the event that she catches the bus from the shop=B
P(A)=0.4
P(B)=0.7
Both A and B are independent events.
Therefore,Probability that she catches the bus to and from the shop:
P(A∩B) = 0.4 X 0.7= 0.28
Probability Sue walks at least one way [tex]P(A \cup B) = 1 - P(A \cap B)[/tex]
[tex]= 1 - 0.28\\= 0.72[/tex]
Hence, the probability that Sue walks at least one way is 0.72.
George used the diagram below to help determine 30% of 60. Which expression could George have used?
Answer:
(3)(6)
Step-by-step explanation:
1st. Find the answer(60*30%=18)
2nd. Find the option that equals 18 which was (3)(6)
Basically, for all of questions that ask for a different way to express it, multiply the total amount by the percentage(or decimal/fraction) and find the other expression with the same answer.
Answer:
(3)(6)
Step-by-step explanation:
i did the test
City Middle School held its annual musical production last weekend. Of the 700 tickets sold, 55% were for the Saturday performance. How many tickets were sold for the Saturday show?City Middle School held its annual musical production last weekend. Of the 700 tickets sold, 55% were for the Saturday performance. How many tickets were sold for the Saturday show?
Answer: 385 tickets
Step-by-step explanation:
From the question, City Middle School held its annual musical production last weekend and of the 700 tickets that were sold, 55% were for the Saturday performance. The number of tickets that were sold for the Saturday show will be 55% of 700. This can be expressed mathematically as:
= 55% of 700
= 55/100 × 700
= 55 × 7
= 385 tickets
385 tickets were sold for the Saturday show.
Answer:
ITS IS A= 385
Step-by-step explanation:
Suppose figure A underwent a dilation to produce figure B. Are figure A and figure B similar?
Answer:
Figure A and B are still congruent to each other. the only change is the size of the shape.
Step-by-step explanation:
Yes, figure A and figure B similar because even though their side lengths are different, their internal angles are the same.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
Suppose figure A underwent a dilation to produce figure B.
Now, A dilation is a transformation that produces an image that is the same shape as the original, but is a different size
if Dilation factor N then image Size is multiplied by N
if Scale factor < 1 then image get reduced
if scale factor > 1 then image get enlarged
scale factor = 1 lead to Same size image
Hence, Figure A and figure B similar because even though their side lengths are different, their internal angles are the same.
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In the picture above, parallel lines p and q are cut by transversal line t. If the measure of angle 1 is 11x+7 and the measure of angle 8 is x+17, then x is equal to _____ and the measure of angle 1 is_____ degrees. The measure of angle 8 is _____ degrees.
Answer:
-11
Step-by-step explanation:
Evaluate and Solve 6x + 4 > 7
Answer:
x>1/2
Step-by-step explanation:
6x>3
x>1/2
Answer:
X>1/2
Step-by-step explanation:
6x + 4> 7
-4 on each side
6x > 3
Divide 6 on each side
X>1/2
Hope this helps plz mark brainliest!
Which statement is true about the right traingle
Answer:
Its 90 degrees
idk if this helps but i hope it does :)
Step-by-step explanation:
Fitness Classes cost £6 per person. The table shows the number of people who go to the classes on Thursday, Friday and Saturday.
The teacher earns 90% of the total paid.
How much does the teacher earn altogether on these days?
(4 marks)
Answer:
£216
Step-by-step explanation:
Cost = £6 per personTeacher earns = 90% of totalTotal number of people:
13 + 11 + 16 = £40Total payment:
40*6= £240Teacher earns in total per given week:
240*90/100 = £216What is the slope and y intercept of the following linear equation:y=1/3×-2
Answer:
Step-by-step explanation:
The general formula for slope-intercept form is y = mx + b
We can see that m (slope) equals 1/3 here. We can also see that the y-intercept (b) is -2. Another way to find the y intercept is to make x equal to 0. You get 0 - 2 which equals -2
Note:
If youre ever asked for the x-intercept, make y equal to zero and solve for x.
A student is running a 3 km race he runs 1 km every two minutes. Select the function that describes distance from the finish line after X minutes
x - number of minutes;
f ( x ) - the distance from the finish line.
x : 0 2 4 6
f ( x ) : 3 2 1 0
f ( x ) = 3 - x/2
Answer: B ) f ( x ) = -1/2 x + 3
Volume of a triangular prism 4 cm 9 cm and 5 cm
Answer:
180 cm³
Step-by-step explanation:
Volume = base area x height
4x9x5
Answer:
180 cm^3
Step-by-step explanation:
Vol = base time height times length
4 times 9 times 5 = 180
Officer Brimberry wrote 32 tickets for traffic violations last week, but only 12 tickets this week. What is the percent decrease? Give your answer to the nearest tenth of a percent.
Answer:
62.5 %
Step-by-step explanation:
Take the original amount and subtract the new amount
32-12 = 20
Divide by the original amount
20/32 =.625
Multiply by 100 to get to percent form
62.5 %
write the equation in vertex form: Vertex is (1.-3) and passes through the point (-1,5)
Answer:
y = 2(x - 1)² - 3
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (1, - 3), thus
y = a(x - 1)² - 3
To find a substitute (- 1, 5) into the equation
5 = a(- 1 - 1)² - 3
5 = (- 2)²a - 3 ( add 3 to both sides )
8 = 4a ( divide both sides by 4 )
a = 2
Thus
y = 2(x - 1)² - 3 ← in vertex form
Please answer correctly !!!!!! Will mark brainliest !!!!!!!!!!!
Answer:
1 A
2 A
Step-by-step explanation:
1. steps can be positive whole numbers only
2. there is 15 steps
L+S = 17 3L + 2S=46
Please show your work
Answer:
S= 5, L= 12
Step-by-step explanation:
To find the value of L and S, we need to first label the 2 equations.
L +S= 17 -----(1)
3L +2S= 46 -----(2)
From (1):
L= 17 -S -----(3) (-S on both sides)
Subst. (3) into (2):
3(17-S) +2S= 46
3(17) -3S +2S= 46 (expand)
51 -S= 46
-S= 46 -51 (-51 on both sides)
-S= -5
S= 5 (divide by -1 throughout)
Subst. S=5 into (3):
L= 17 -5
L= 12
The two triangles below are similar. What is the similarity ratio of AABC to ADEF? (5 points)
2:1
1:2
2:5
5:2
Solve for x.
7x+ 3
3x + 35
x = [?]
Answer:
Step-by-step explanation:
7x + 3 = 3x + 35
4x + 3 = 35
4x = 32
x = 8
You inherited land that was purchased for $30,000 in 1960. The value of the land increases by approximately 5% per year. What will be the approximate value of the land 61 years later in 2021
Answer:
$91,500
Step-by-step explanation:
The land appreciates 5% of 30k which is $1,500 and multiply that by 61
The approximate value of the land in 2021 will be $588,394.356.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
Value of the land in 1960 = $30,000
Each year, the value is increasing approximately 5 % = 5/100 = 0.05.
Value of the land in 1961 = 30,000 + (30,000 × 0.05)
= 30,000 (1 + 0.05)
= 30,000 × 1.05
Value of the land in 1962 = (30,000 × 1.05) + (30,000 × 1.05 × 0.05)
= (30,000 × 1.05) (1 + 0.05)
= (30,000 × 1.05) (1.05)
= 30,000 × (1.05)²
So each year previous value is multiplied with 1.05.
Value of the land after n years = 30,000 × (1.05)ⁿ
Value of the land after 61 years = 30,000 × (1.05)⁶¹
= 588,394.356
Hence the approximate value of the land in 2021 is $588,394.356.
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Ana Maria has applied for United States citizenship. She has studied American history and government for a long time and thinks she is ready to take the citizenship test. When she took the practice test online she answered forty-seven questions correctly and only missed three. What percent of the questions did she get right?
Answer:
≈93.6
Step-by-step explanation:
percent right = answers right/ anwers wrong
Answers right= 47-3=44
%=44/47
≈93.6
Find the value of. (3° + 4 -¹) × 2²
Answer:
[tex]5[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
what is the equation of the circle that is centred at the origin and passes through the point (-3,4)
Answer:
The correct answer is (x)² + (y)² = r².
Step-by-step explanation:
The standard equation for a circle is (x - h)² + (y - k)² = r². Since our circle is centered at the origin, or (0, 0), our values for h and k are simply 0 and 0, so there is no need to list these values within the equation.
Now, it is time to determine r, or the radius of the circle. The circle passes through the point (-3, 4), so (-3)² + (4)² = 25², so r = 25.
Therefore, your equation is x² + y² = 25.
Question 1 (1 point)
Solve
- +13 > 10
(Blank 1 is <,>, S, or 2. Blank 2 the number)
Recall that < and > are on the keyboard. You can get S and respectively by doing Alt < and Alt > on the keyboard. You may also copy the
symbols from the instruction page or the Copy Symbol and Keyboard Shortcuts Page.
Blank 1:
Blank 2:
how do we calculate on sixth of 42
Answer:
1/6 of 42:
first, of is the same as multiplication so change this:
1/6 * 42
put 42 over 1 so they are both fractions:
1/6 * 42/1
Now solve:
42/6
= 7
:) brainliest?
(if u meant the sixth root of 42, it's about 1.86)
Answer:
7
Step-by-step explanation:
42/6=7
Which of the following best describes the set for {whole
*3
numbers between an
2
A) {-1, 0, 1, 2}
C) {0, 1, 2
B) {0, 1, 2, 3}
D) {1, 2}
Answer:
The whole number between 2 is {0,1,2}
Given the points (-2,-4) and (-3,-5) what is the slope
Answer:
1/1
Step-by-step explanation:
evaluate 1/2^-2x^-3y^5
A) -1/32
B) 16
C) -16
D)-4
Answer:
To answer this question you need to x and y
Step-by-step explanation:
help please, i will mark brainliest
Answer:
40
Step-by-step explanation:
We can see that at 1 minute there is 40 beats, at 2 minutes there is 80 beats, at 3 minutes there is 120 beats, at 4 minutes there is 160 beats and at 5 minutes there is 200 beats. If we divide each of the beats by its corresponding minute we will get 40
40 beats at 1 minute → 40 ÷ 1 = 40
80 beats at 2 minutes → 80 ÷ 2 = 40
120 beats at 3 minutes → 120 ÷ 3 = 40
160 beats at 4 minutes → 160 ÷ 4 = 40
200 beats at 5 minutes → 200 ÷ 5 = 40
What is Three-fourths divided by one-sixth?
Answer:
9/2 or 4.5
Step-by-step explanation:
3/4 divided by 1/6 changes into multiplication and you switch one of the denominators
it becomes 3/4 times 6/1 which is 18/4 when simplified, it's 9/2
Answer:
9/2
Step-by-step explanation:
Using Ratios to Solve Problems - Item 1457 Question 4 of 7 Evan's family drove to a theme park for vacation. They drove the same speed throughout the trip. The first day, they drove 300 300 miles in 6 6 hours. The second day, they drove 250 250 miles in 5 5 hours. The third day, they arrived at the park after driving for 3 3 hours. How many miles did they drive on the third day?
Answer:
150 miles
distance travelled on the third day = 150 miles
Step-by-step explanation:
Note: it was given that they drove the same speed throughout the trip. That means their speed is constant for all days;
For the first day
distance = 300 miles
time = 6 hours
Speed = distance/time
Speed = 300/6 = 50 mph
on the third day;
time = 3 hours
Speed = speed on first day = 50 mph
distance = speed × time
distance = 50 mph × 3 hours
distance = 150 miles
distance travelled on the third day = 150 miles
