Answer
Step-by-step explanation:
What is the nth term rule of the linear sequence below?
7
,
9
,
11
,
13
,
15
,
.
.
.
Answer:
\(a_n=5+2n\)
Step-by-step explanation:
Each term is 2 more than the previous term, so the common difference is 2.
Let \(a_n\) be the nth term of the sequence. Then, the first term is \(a_1=7\).
The second term is \(a_2=7+2=9\), and the third term is \(a_3=7+2+2=11\).
Therefore, every term can be written as
\(a_n=7+\underbrace{2+2\cdots +2}_{n-1~\text{times}}\).
Since repeated addition is multiplication, this can be written as
\(a_n=7+2(n-1),\)
which is the nth term rule of the linear sequence.
This could also be expanded to \(\boxed{a_n=5+2n.}\)
A person invests $350 in an account that earns 3.65% annual interest compounded
semiannually. Find when the value of the investment reaches $5675.
M = C(1+r)^t
5675 = 350(1+0.0365/2)^t
5675=350×1.01825^t
t = 154.04
Answer:
Approximately 77 years
Step-by-step explanation:
V(t)=P(1+r/n)^nt
5675=350(1+.0365/2)^2t
16.214=1.01825^2t
log16.214=log1.01825^2t
log16.214=2t(log1.01825)
log16.214/2log1.01825=t
77=t
Please help me. I don’t know the answer.
Step-by-step explanation:
number 2)
3√2/3√4=
=3√2/3×2
=3√2/6
=3√2/6 ×3/3
=1√2/2
=√2/2
what is 52837848 X 18283943
The result is 965996074012064, or approximately 9.66 x \(10^{14\).
The product of 52837848 and 18283943 is a very large number, which is difficult to calculate by hand. However, it is possible to obtain an approximate value using a calculator or a computer program.
Assuming that you meant to multiply these two numbers together, the result is 965996074012064, or approximately 9.66 x \(10^{14.\)
To put this number into perspective, it is larger than the number of seconds that have elapsed since the dawn of human civilization, which is estimated to be around 6 x \(10^{11\) seconds. In fact, this number is so large that it is difficult to conceptualize its magnitude.
In practical terms, this product may represent the result of a complex calculation in fields such as finance, engineering, or science. It could also represent the outcome of a mathematical or statistical model that requires a high degree of precision.
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what is 2/4 + 6/8 + 2/4 + 15/24 + 7/8
Answer:
13/4
Step-by-step explanation:
(-1, 1) and (1, -1) is on the line.
The equation of the line in point slope form is:
Answer:
6
Step-by-step explanation:
Are these vectors orthogonal?:v = 6i - 3jw = i+2j
The vectors v = 6i - 3j and w = i + 2j are orthogonal.
To determine if the vectors v and w are orthogonal, we need to find their dot product. If the dot product is 0, the vectors are orthogonal.
Here are the steps to find the dot product of v = 6i - 3j and w = i + 2j,
1. Identify the components of the vectors: v = (6, -3) and w = (1, 2)
2. Multiply the corresponding components of the vectors:
\((6 \times 1) + (-3 \times 2) = 6 - 6 \)
3. Add the products: 6 - 6 = 0 Since the dot product is 0, the vectors v = 6i - 3j and w = i + 2j are orthogonal.
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Correct question is " Are these vectors orthogonal? v = 6i - 3j and w = i+2j"
Which is the equation of the line in slope-intercept form?
A) y = -3x - 2
B) y = 3x + 2
C) y=-1/3x+2
D) y= 1/3x-2
Answer:
A). y = -3x - 2
Step-by-step explanation:
Since the line is going downwards from left to right, we know that it is a negative line.
Slope equals rise/run. If you take any two points, it goes down 3 and 1 right. You don't put 1 so it's simply just -3x.
The line crosses the y axis at -2.
What is the length of diagonal AC?
Answer:
....... The answers is 7.8cm
Solve the following problem using the problem solving strategy.
Be sure to label your diagram, including your origin, sides of any triangles, etc.
List your knowns and unknowns.
Write equations in variable form before plugging numbers in.
An owl accidentally drops a mouse it was carrying while flying horizontally at 10 m/s. The mouse drops to the ground 10 m below. What is the mouse’s impact speed and its direction?
The mouse's impact speed is approximately 14 m/s, and its direction is downward.
- Initial horizontal velocity of the owl: 10 m/s
- Vertical displacement of the mouse: 10 m
- Acceleration due to gravity (g): 9.8 m/s²
```
|
| 10 m
|
O--------M
```
Here, O represents the initial position of the mouse (where it was dropped) and M represents the position where the mouse lands.
For the horizontal motion:
- Initial horizontal velocity (u) = 10 m/s
- Final horizontal velocity (v) = ? (this will remain constant)
- Horizontal displacement (s) = ? (we are not given this information, but it's not necessary to solve for the impact speed)
For the vertical motion:
- Initial vertical velocity (u) = 0 m/s (since the mouse was dropped vertically)
- Final vertical velocity (v) = ? (this will be the impact speed we're looking for)
- Vertical displacement (s) = -10 m (negative because it's downward)
We can use the equation s = ut + (1/2)at² to solve for time (t), as the horizontal and vertical motions are independent.
For the vertical motion:
s = ut + (1/2)at²
-10 = 0 + (1/2)(-9.8)t²
-10 = -4.9t²
Simplifying the equation, we get:
t² = 2.04
t ≈ 1.43 s (taking the positive square root since time cannot be negative)
Now, we can find the impact speed using the equation v = u + at:
v = 0 + (-9.8)(1.43)
v ≈ -14 m/s (negative sign indicates downward direction)
The mouse's impact speed is approximately 14 m/s, and its direction is downward.
So, the mouse's impact speed is 14 m/s in the downward direction.
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Emilio is designing the packaging for a new MP3 player. The box for the MP3 player is 5cm by 3cm by 2cm. Emilio needs to find the surface area of the box
Answer:
Step-by-step explanation:
It is correct, it doesn't need a correction.
Emilio is designing the packaging for a new MP3 player, and the dimensions of the box are given as 5cm by 3cm by 2cm. The task is to find the surface area of the box.
To find the surface area of the box, we need to calculate the sum of the areas of all its sides. The box has six sides, and each side has a rectangular shape. The formula for calculating the area of a rectangle is length multiplied by width. Let's calculate the surface area step by step: The front and back sides have dimensions 5cm by 3cm, so their combined area is 5cm * 3cm = 15cm². The top and bottom sides have dimensions 5cm by 2cm, so their combined area is 5cm * 2cm = 10cm². The two remaining sides (left and right) have dimensions 3cm by 2cm, so their combined area is 3cm * 2cm = 6cm² each. To find the total surface area, we add up the areas of all sides: 15cm² + 15cm² + 10cm² + 10cm² + 6cm² + 6cm² = 62cm². Therefore, the surface area of the box is 62cm².
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There are 6 new books and 7 used books on a shelf.
Part A
The ratio of all books to new books is 13 : 6
Part B
The ratio of used books to all books is 7 : 13
The number of new books = 6
The number of used books = 7
Total number of books on the shelf = The number of new books + The number of used books
Substitute the values in the equation
Total number of books on the shelf = 6 +7
Add the numbers
= 13 books
Part A
The ratio of all books to new books is
The total number of books : Number of new books = 13 : 6
Part B
The ratio of used books to all books is
Number of used books : Total number of books = 7 : 13
Hence,
Part A
The ratio of all books to new books is 13 : 6
Part B
The ratio of used books to all books is 7 : 13
The complete question is
There are 5 new books and 6 used books on a shelf.
(a) What is the ratio of all books to new books?
(b) What is the ratio of used books to all books?
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hey please help this is really important (first to answer i will give brainlyiest) after some else answers
Answer:
can u type out the question i cant see the photo i will help thou
Step-by-step explanation:
Answer:
29
-26
Step-by-step explanation:
the equation of f(x) is given. to find f(8) just apply 8 in the place of x in the equation
same method for f(-3) just apply -3 in place of x
is (-3,0) (-1,3) (1,0) (3,3) a relation and function
The set of ordered pairs (-3,0), (-1,3), (1,0), (3,3) forms a relation and is also a function.
To determine if the set of ordered pairs (-3,0), (-1,3), (1,0), (3,3) forms a relation and a function, we need to check two conditions: the set must be a relation, and for it to be a function, each input (x-value) must have a unique output (y-value).
Relation: A relation is a set of ordered pairs that relate inputs (x-values) to outputs (y-values). In this case, we have a set of four ordered pairs (-3,0), (-1,3), (1,0), (3,3). This set satisfies the condition of a relation because it provides a mapping between x-values and y-values.
Function: For the set of ordered pairs to be a function, each input (x-value) must have a unique output (y-value). In other words, no two ordered pairs should have the same x-value with different y-values. Let's check if this condition is met:
The x-value -3 is associated with the y-value 0.
The x-value -1 is associated with the y-value 3.
The x-value 1 is associated with the y-value 0.
The x-value 3 is associated with the y-value 3.
Since each input (x-value) corresponds to a unique output (y-value) in the given set, we can conclude that the set of ordered pairs (-3,0), (-1,3), (1,0), (3,3) is indeed a function.
The set of ordered pairs (-3,0), (-1,3), (1,0), (3,3) forms a relation and is also a function.
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Triangle ABC is shown below. Using a compass and straightedge, construct the dilation of ABC centered at B with a scale factor of 2.
Triangle ABC would remain the same because a dilation generally preserves the measure of an angle.
What is scale factor?A scale factor simply refers to a ratio of two (2) corresponding side lengths or diameter in two (2) similar geometric figures such as triangles.
In this exercise, you're required to construct a dilation of triangle ABC that is centered at B with a scale factor of 2 by using a compass and straightedge.
In conclusion, triangle ABC would remain the same because a dilation generally preserves the measure of an angle.
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Can someone answer this question please please help me I really need it if it’s correct I will mark you brainliest .
Answer:
what i know for sure is 10/19 is rational
Answer:
=> All of the options are correct.
Step-by-step explanation:
a rational number is a number that can be shown as the quotient of two integers a and b(the denominator b must not be equal to zero).
10/19 => a = 10, b = 19 (correct)
85/74 => a = 85, b = 74 (correct)
-48 => a = -48, b = 1 (correct)
-57 =>a = -57, b = 1 (correct)
=> All of the options are correct.
Hope this helps!
Se han gastado 5/9 de la capacidad de un depósito u aun quedan 108L. Cuál es la capacidad del depósito?
Answer: 5/9 of the capacity of a tank has been used and there are still 108L left. What is the capacity of the deposit?
Step-by-step explanation:
Amia went to a flower farm and picked
�
ff flowers. When she got home, she put the flowers in
4
44 vases, with
22
2222 flowers in each vase.
Write an equation to describe this situation.
How many flowers did Amia pick at the farm?
Answer:
88 flowers
Step-by-step explanation:
(F)=4×22= 88 flowers
during a sale, every item in the store is 45% of its regular price. if the regular price of a shirt is $30, what is its sale price?
The sale price of the shirt is $162.5
What is a percentage?A percentage is a number or ratio that can be expressed in the form of a fraction by 100. The percentage of a number is defined as the value of the number out of 100. Percentage does not have any unit of measurement.
If the regular price is $30 and the sale is 45%,it means the $30 represents the other 55% of the sale price. So it can be written as
sale price= 55%×regular price
Here sale price is taken as s
s= 55%×$30
Solving this for s, we get
s= (55/100)×$30
s=0.55×$30
s=$16.5
So, the sale price is $16.5
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At an archery competition, Aylin hits the target 14 out of 20 tries in round one. If Aylin gets 24 tries in round two, approximately how many times are they most likely to hit the target
Answer:
16.8
Step-by-step explanation:
14/20 = 0.7
24 x 0.7 = 16.8
(Feel free to round up or down, or keep it the same depending on the criteria of the question!)
Determine whether the set, together with the indicated operations, is a vector space. Explain a) The set {(x,x): x is a real number} with the standard operations b) The set {(x,x): x is a real number} with the standard operations. The set of all 2 x 2 matrices of the form with the standard operations The set {(x, y): x ≥ 0, y is a real number} with the standard operations in R² e) The set of all 2 x 2 singular matrices with the standard operations
Sets a) and b) form vector spaces, while sets c), d), and e) do not form vector spaces.
The axioms include properties such as closure, associativity, commutativity, additive and multiplicative identities, additive and multiplicative inverses, and distributive properties. Let's analyze each set:
a) The set {(x, x): x is a real number} with the standard operations:
This set forms a vector space because it satisfies all ten axioms of a vector space. The operations of addition and scalar multiplication are defined elementwise, which ensures closure, and the required properties hold true.
b) The set {(x, x): x is a real number} with the standard operations:
Similar to the previous set, this set also forms a vector space.
c) The set of all 2 x 2 matrices of the form [[a, b], [0, a]] with the standard operations: This set does not form a vector space. The zero matrix, which has the form [[0, 0], [0, 0]], is not included in this set.
d) The set {(x, y): x ≥ 0, y is a real number} with the standard operations in R²: This set does not form a vector space. It fails the closure axiom for scalar multiplication since multiplying a negative scalar with an element from the set may result in a point that does not satisfy the condition x ≥ 0.
e) The set of all 2 x 2 singular matrices with the standard operations:
This set does not form a vector space. It fails the closure axiom for both addition and scalar multiplication.
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Please help me on #5 Please show work so I can follow
#5
Since the elevation of the picture is
\(-8\frac{5}{12}\)We need to change it in decimal, then divide the numerator of the fraction by the denominator of the fraction
\(\frac{5}{12}=0.41666666=0.416^-\)Then the elevation in decimal is
\(-8.416^-\)Find x correctly pleaseeee !!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!
Answer:
No one gets math also saying you will mark Brainliest doesn't make me want to answer more...
Step-by-step explanation:
Try watching videos trust me you will learn a lot more.
a college professor conducted a survey in order to assess how much money nursing majors spend on course material compared to all other majors. to do so, she selected a random sample of 34 students. each student was classified as a nursing major or as a non-nursing major. they were then asked how much they spent on books and other materials required for their courses this semester. here are parallel boxplots summarizing the responses.
Option D. The median cost of course materials for nursing majors is over $300 more than the median cost of course materials for non-nursing majors.
The given boxplots show the circulation of the expense obviously materials for nursing majors and non-nursing majors. From the plots, we can reason that the scope of the circulation of the expense obviously materials for nursing majors is like that of non-nursing majors, as the most extreme and least qualities are around at a similar level. We can likewise infer that the most extreme expense for non-nursing majors is more prominent than the middle expense for nursing majors.
Also, the inconstancy of the expense obviously materials for the center half of nursing majors is more noteworthy than the fluctuation of the center half for non-nursing majors, as the cases for nursing majors are more extensive. In any case, we can't reason that the middle expense obviously materials for nursing majors is more than $300 more than the middle expense obviously materials for non-nursing majors, as the medians are not straightforwardly named and their division isn't plainly shown. At last, we can see that the study included 17 nursing majors and 17 non-nursing majors.
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The complete question is:
A college professor conducted a survey in order to assess how much money nursing majors spend on course material compared to all other majors. To do so, she selected a random sample of 34 students. Each student was classified as a nursing major or as a non-nursing major. They were then asked how much they spent on books and other materials required for their courses this semester. Shown above are parallel boxplots summarizing the responses. Based upon the boxplots, which of the following statements cannot be concluded?
A. The range of the distribution of the cost of course materials for nursing majors is about the same as that of non-nursing majors.
B. The maximum cost for non-nursing majors is greater than the median cost for nursing majors.
C. The variability of the cost of course materials for the middle 50% of nursing majors is greater than the variability of the middle 50% for non-nursing majors.
D. The median cost of course materials for nursing majors is over $300 more than the median cost of course materials for non-nursing majors.
E. The boxplots reveal that 17 students are nursing majors and 17 students are non-nursing majors
What is the measure of angle X?_
Answer:
Hey this isn’t the answer, sorry
Step-by-step explanation:
I just need this answer to so let me know if you get the answer Thank you
Find the perimeter of the polygon with the given vertices. Round your answer to the nearest hundredth.
L14
N(2.0)
P(-1, -2)
M(4,0)
*
The perimeter is about 6.31 x
units.
Answer:
the perimeter is 10.99 units.
Step-by-step explanation:
We have a triangle with points in:
X // Y
N 2 // 0
P -1 // -2
M 4 // 0
We can solve for the side of the triangle by subtracting the points to calculate the distance between them, AKA the side of the triangle.
M - N = NM = 4 - 2 = 2 units of X
M - N = NM = 0 - 0 = 0 units of Y
This has a length of 2 units of X and 0 units of Y thus, we already have a line of size 2.
Next side:
N - P = 2 -(-1) = 3 units of x
N - P = 0 - (-2) = 2 units of Y
We have a length of 3 units of X and 2 of Y we use Pythagoras to get the length of NP:
\(\sqrt{3^2+2^2} =NP\\\sqrt{9 + 4} = \sqrt{13}\)
Now, we do the same with MP:
M - P = 4 - (-1) = 5 units of X
M - P = 0 - (-2) = 2 units of Y
we solve for MP
\(\sqrt{5^2+2^2} = \sqrt{25 + 4} = \sqrt{29}\)
We now add up:
\(NM + NP + MP\\2 +\sqrt{13} + \sqrt{29} =\\10.99071608\)
please help with this
Answer:
x=3
Step-by-step explanation:
y= -2
4x-3y=18
4x-3(-2)=18
4x-(-6)=18
4x+6=18
4x+6-6=18-6
4x=12
\( \frac{4x}{4} = \frac{12}{4} \)
x=3
If its helpful ❤❤❤
THANK YOU
Area of a circle 12 mm diameter
Answer:
Area of a circle= 1/4*π d^2
A=1/4*π*12^2=
A=1/4*π*144=113.1
Step-by-step explanation:
Hope this helps!! :)). Mark me brainliest! :))
please answer this for me
Andrew runs around a circular track each morning. The diameter of the track is
approximately - mile. Approximately how far does Andrew run if he
completes 11 laps around the track?
Answer:
approximately 1/4 mile
Andrew runs around a circular track each morning. The diameter of the track is approximately 1/4 mil
Answer: 1/4
Step-by-step explanation: