Money received in tenth month: $104.
A formula that describes this arithmetic sequence: [tex]a_n=a_{n-1}+n[/tex], n > 1., where n = number of month.
What is arithmetic progression?A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.
Given:
Money received in first four months: $50, $52, $55, %59.
To find: Money received in tenth month.
Finding:
As we can see, the pattern followed here is: increment in each amount received each month by $1. Thus it is an arithmetic progression.
That is: 50, 52 (0+2), 55 (2+3), 59 (2 + 3 + 4) and so on.
Thus, for the tenth month, we can use the formula of recursion, given by: [tex]a_n=a_{n-1}+n[/tex], n ≥ 1.
For a₁ = 50, a₂ = a₁ + 2
=> a₂ = 50 + 2
This way, a₅ = a₄ + 5
=> a₅ = 59 + 5 = 64
a₆ = a₅ + 6
=> a₆ = 64 + 6 = 70
a₇ = a₆ + 7
=> a₇ = 70 + 7 = 77
a₈ = a₇ + 8
=> a₈ = 77 + 8 = 85
a₉ = a₈ + 9
=> a₉ = 85 + 9 = 94
a₁₀ = a₉ + 10
=> a₁₀ = 94 + 10 = 104
Thus, the payment received in tenth month will be $104.
A formula that describes this arithmetic sequence: [tex]a_n=a_{n-1}+n[/tex], n > 1., where n = number of month.
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Can please help me with this question
The possible coordinates of point G on the number line is -15 and 7.
How to find the coordinates on a number line?On the number line, point E has the coordinates of - 4, and EG = 11 .
The possible coordinates of point G are as follows:
A number line is a horizontal straight line with numbers placed at equal distances from each other along that line.
Negative numbers are on the left side while the positive numbers are on the right side.
Therefore, the possible coordinates of G is when we go left or right side of E on the number line.
Hence,
Let's go left E to G on the number line
-4 - 11 = -15Let's go right E to G on the number line
-4 + 11 = 7Therefore, the possible coordinates of point G on the number line is -15 and 7.
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h(x)
=
x² + 3x
4x + 27
Find h(-8)
Step-by-step explanation:
it is -8 because negative times negative is positive
(-8)Match each expression to the correct point
Answer:
Step-by-step explanation:
f = -3/2
d = -[tex]\pi[/tex]
e = - [tex]\sqrt{8}[/tex]
Answer:
56892 that's it hope it helps
Which number is divisible by both 2, 5, and 10?
Answer: A number that ends in 0 is divisible by 2, 5, and 10. 6730 is divisible by 2, 5, and 10, which means that it is in the 2, 5, and 10 times tables.
Step-by-step explanation:
Answer: 6,730
Step-by-step explanation: A number is divisible by 10 if it ends in a 0. The number ends in a 0 and so it is divisible by 10. A number that ends in 0 is divisible by 2, 5 and 10. 6730 is divisible by 2, 5 and 10, which means that it is in the 2, 5 and 10 times table.
logarithmic differentiation Y=2^X
By logarithmic differentiation, the first derivative of y = 2ˣ is y' = 2ˣ · ㏑ 2.
How to use logarithmic differentiation
Logarithmic differentiation is a combination of derivative rules and logarithm properties which is useful to derive power, exponential and power-exponential functions:
y = 2ˣ
㏑ y = ㏑ 2ˣ
㏑ y = x ㏑ 2
y' / y = ㏑ 2
y' = y · ㏑ 2
y' = 2ˣ · ㏑ 2
By logarithmic differentiation, the first derivative of y = 2ˣ is y' = 2ˣ · ㏑ 2.
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Write a flow proof.
Given: ∠A and ∠C are right angles.
∠A B E ≅ ∠C B D, AE ≅ CD
Prove: BE ≅ BD
BE ≅ BD under corresponding parts of the congruent triangles.
What do we mean by a triangle's congruency?If all three corresponding sides and angles of two triangles are the same size, they are said to be congruent.These triangles can be moved, rotated, flipped, and turned to appear identical.If they are moved, they will coincide.When two triangles satisfy the five congruence conditions, congruence exists.They are the side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and right angle-hypotenuse-side (RHS).So,
Given:
∠A and ∠C are right angles.∠ABE ≅ ∠CBD, AE ≅ CDSo, we can say that △ABE ≅ △CBD is under AAS condition.
Then, we can conclude that BE and BD are identical. (Corresponding parts of the congruent triangles)So, BE ≅ BD.Therefore, BE ≅ BD under corresponding parts of the congruent triangles.
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ax+ 5x = 10b; solve for x
Answer:
[tex](a + 5) \times = 10b \\ \times = \frac{10b}{a + 5} [/tex]
12. A 500 N force is applied to a 25 m/s² object. The mass of the object is
A. 12,500 kg
B. 12,500 m/s
C. 20 kg
D. 20 m/s
Answer:
C is right 20kg
Step-by-step explanation:
bec
ause the formula of force=mass ×acceleration
to find mass= force/acceleration.
need help solving please
Answer: the answer is D
Both sides are equal to 5 radical 2
Step-by-step explanation:
Please help i'm stuck
Answer:
Decreases two times
Step-by-step explanation:
[tex].[/tex]
nancy wants to vacation in austin texas. Hotel A charges $179 per night with a 14% nightly room tax and free parking. Hotel B charges $169 per night with 18% nightly room tax plus a one time $40 parking fee. After how many nights will Hotel B be less expesnsive?
The number of nights will be 8.62 when the Hotel B charge is less than A.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that hotel, A charges $179 per night with a 14% nightly room tax and free parking. Hotel B charges $169 per night with 18% nightly room tax plus a one-time $40 parking fee. The number of the nights will be calculated as below:-
From the given data from the equations:-
A = 179 + ( 0.14 x 179 ) x
A = 204.06x
B = ( 169 + ( 0.18 x 169 )x + 40
B = 199.42x + 40
Equate the two equations:-
204.06x = 199.42x + 40
4.64x = 40
x = 40 / 4.64
x = 8.62 nights
Therefore, the number of nights will be 8.62 when the Hotel B charge is less than A.
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Identify the number as prime, composite or neither. If the number is composite, write it as the product of prime factors. 1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The number is composite. Its prime factors written as a product are ( )
B. The number is prime.
C. The number is neither prime nor composite.
The correct option regarding number 1 is given by:
C. The number is neither prime nor composite.
What are prime numbers?Prime numbers are numbers that have only two factors, that are 1 and itself. Examples of prime numbers are 2, 3, 5, 7, and so on...
Number 1 has only one factor, itself, hence for this reason it is neither prime(two factors are needed) nor composite, as it cannot be written as a product of two numbers both different than 1, hence option c is correct.
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Find the equation for the line parallel to 3x+5y-4=0, with the same x-intercept as 2x-3y-6=0
Equation of line is 5y = -3x + 9 .
What is equation of line?
A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.
3x+5y-4=0
5y = -3x + 4
y = -3/5 x + 4/5
since it is parallel, its slope, m is -3/5
2x-3y-6=0
3y = 2x - 6
y = 2/3x - 2
at x-intercept, y is zero
2 = 2/3x
x = 3
therefore
y = mx + c
0 = (-3/5 * 3 ) + c
c = 9/5
equation is
y = -3/5x + 9/5
5y = -3x + 9
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Use the given information to write an equation of the circle.
center (6,4) , through (2,1)
Using the given information, the equation of the circle with center located at point (6 , 4) and passes through the point (2 , 1) is (x - 6)^2 + (y - 4)^2 = 25.
Using the distance formula, get the radius of the circle by solving for the distance between the center (6 , 4) and the point (2 , 1).
radius = distance = √(x2 - x1)^2 + (y2 - y1)^2
radius = √(2 - 6)^2 + (1 - 4)^2
radius= √16 + 9
radius = √25
radius = 5
The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (6 , 4)
r = 5
(x - 6)^2 + (y - 4)^2 = 5^2
(x - 6)^2 + (y - 4)^2 = 25
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Pls pls help whoever gets it right gets a crown
Answer:
last one is right
Step-by-step explanation:
multiply 8 by X is 8x and 8 multiplied by 8 is 64
Hope it helps
Answer: 8x+64=8x(x+8)
Step-by-step explanation:
8 is a common of 8 so 8x8=64
Sketch the solid that results when the region enclosed by the given equations is revolved about the y -axis.
y = x²
y = 2 x
y = x² , y = 2 x are the region enclosed by the given equations is revolved about the y -axis.
What exactly is a closed area?
All space between a floor and ceiling that is enclosed on all sides by solid walls or windows, except doors that stretch from the floor to the ceiling, is referred to as an enclosed area.
What do you mean by the region that a closed curve encloses?
The sum of all infinitely thin rectangles with height f(x), enclosed by the curve y=f(x), and the x-axis between x=a and x=b, is what we mean when we write baf(x)dx.
Whether contained or not?
Use enclosed at all times. No longer regarded as a regular variety, enclosed would even be mistaken for another word by many readers. Use enclose, encloses, and enclosing rather than inclose for other words that are similar to enclosed.The graph is attached in equation y = x² , y = 2 x
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Solve for W
5 = 7w + 8w + 2
w = 5
Step-by-step explanation:
2+(7w)+(8w)=5
(7÷5)+(8÷5)+2
(1.4) (1.6) +2
+1.5
=3+2=5
Use the spinner to find following probability. The spinner is spun again if it stops on a line.
P (pointer landing on yellow)
The probability of the spinner's point landing on yellow is 30.56%.
What exactly would be a pie chart?A pie graph is a type of chart which displays data in the form of a circular graph.
We understand that the total value of the pie is always 100%. It is also understood that a circle will have a circumference of 360°. As a consequence, the total of all data points equals 360°. There appear to be two main pie chart formulas based on these:
To evaluate a proportion of the data set, we just use following formula: (Frequency ÷ Total Frequency) × 100To transform the information to degrees, we should use following formula: (Mentioned Data ÷ Total value of Data) × 360°When a circle is completely rotated, it forms a 360-degree angle in the center.
The overall percentage of all colors is 100%.
Because 360 degrees / 100 percent = 3.6, divide the valuation of yellow by 3.6.
The total percentage of yellow displayed by the spinner's pointer is 110%.
P (probability of landing on yellow) = 110/3.6
P (probability of landing on yellow) = 30.555... = 30.56 (approx.)
As a result, the probability of the pointer landing on the yellow is 30.56%
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Alec's car payment is $316 each month.
How much do his car payments
year?
Answer:
$3,792
Step-by-step explanation:
$316 x 12
Find the tenth term of each arithmetic sequence. 2,8,14,20, ...........
The 10th term of the given arithmetic sequence 2,8,14,20, ........... is ( a₁₀ = 56.)
Describe the AP arithmetic progression series?The difference between two mathematical orders is a fixed value in Arithmetic Progression (AP). Arithmetic Sequence is another term for it.
We'd come across a few key words in AP which have been classified as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)The AP can also be viewed in terms of common differences, as illustrated below.
The following is the process for evaluating an AP's n-th term: an = a + (n − 1) × dThe so these is the arithmetic progression sum: Sn = n/2[2a + (n − 1) × d].Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, the sequence given in the question is; 2,8,14,20, ...........
Define the first term as 'a₁' = 2.
Define 'a₂' = 8 is the second term.
Define the third term as 'a₃' = 14.
Evaluate the common difference;
d = a₂ - a₁
Put the values in the obtained equation;
d = 8 - 2 = 6
Now, to evaluate the value of the 10th term imply the formula of nth term.
an = a + (n − 1) × d , n = total number of terms = 10.
Substitute all the values;
a₁₀ = 2 + (10 - 1) × 6
a₁₀ = 2 + 9 × 6
a₁₀ = 2 + 54
a₁₀ = 56.
Therefore, the value of the 10th term is found as a₁₀ = 56.
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3 squared by 6 squared?
Answer: 1/4
Step-by-step explanation:
3^2 / 6^2 =
(3/6)^2=
(1/2) ^ 2=
1^2 / 2^2 = 1/4
What is the measure of n?
6
3
n
18
n = [?]√
In the triangle, The measure of side n is √ 108
What is a Triangle ?It belongs to the basic geometric forms. A triangle having vertices A, B, and C is known as triangle ABC. Any three locations in Euclidean geometry that are not collinear result in a separate triangle and a distinct plane.
Identical sides have the same ratio since all of the triangles in the example are comparable.
Short side/long side:
n/6 = 18/n
n² = 6*18
n² = 108
n = √ 108
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Write a slope-intercept equation for a line passing through the given point that is parallel to the given line. Then write a second
equation for a line passing through the given point that is perpendicular to the given line.
(-7, 0), y=-0.9x + 4.4
The equation of the line parallel and perpendicular are y = -0.9(x+7) and y = 10/9(x+7) respectively
Equation of a lineThe equation of a line in point slope form is expressed as;
y - y₁ =m(x-x₁) (Parallel)
y - y₁ =-1/m(x-x₁) (Perpendicular)
Given the following
Point = (-7, 0)
Slope = -0.9
Substitute
y -0 = -0.9(x-(-7))
y = -0.9(x+7)
Similarly for the perpendicular line
y -0 = -1/-0.9(x-(-7))
y = 10/9(x+7)
Hence the equation of the line parallel and perpendicular are y = -0.9(x+7) and y = 10/9(x+7) respectively
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For each equation, find the center and radius of the circle.
(x-1)²+(y-1)²=1
The equation of the circle (x - 1)^2 + (y - 1)^2 = 1 has a radius of 1 and a center located at (1 , 1).
The standard form of the equation of circle is given by
(x - h)^2 + (y - k)^2 = r^2
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle, (x - 1)^2 + (y - 1)^2 = 1, is in standard form, then
h = 1
k = 1
r = 1
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Find the arithmetic mean a n of the given terms. a n₋₁ = 0.3, a n₊₁ = 1.9
The arithmetic mean a n of the given terms a n₋₁ = 0.3, a n₊₁ = 1.9 is
a n = 1.6.
What is direct variation?
a n₋₁ = 0.3, a n₊₁ = 1.9
a n = a [tex]n_{+1}[/tex] - a[tex]n_{-1}[/tex]
a n = 1.9 - 0.3
a n = 1.6
Direct variation is the change in one quantity as a result of the change in another. This suggests that if one quantity rises or falls, the other must rise or fall correspondingly as well.
The formula y = kx is used to answer direct variation questions. If finding the proportionality constant is necessary, the answer is obtained by dividing y by x.
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Y=44 when x=a^3
Y is inversely proportional to the cube of x
Show us that y=5.5 when x=2a
Answer:
0.283258167471352[tex]\sqrt[3]{k}[/tex]
Step-by-step explanation:
Based on the given conditions, formulate:
Write the equation of the function:
Substitute and calculate:
I really don't get this can someone help meh please :d
Answer:
this is a vertical problem what is on one side is on the other
Step-by-step explanation:
so r is the same as 95
Evaluate 4-0.25g + 0.5h when g=10 and h=5
Write –0.67 as a fraction.
Answer:
- [tex]\frac{67}{100}[/tex]
Step-by-step explanation:
there's a negative sign so the our fraction will also have a negative sign
notice each number and its position. 0 is at the ones position. 6 is at the tenths position. 7 is at the hundredths position. 1, 10, 100, 100, etc.
The denominator of a fraction will be 100, because that is the last position of this decimal.
the numerator is just the number value itself.
in total it is
- [tex]\frac{67}{100}[/tex]
Answer:
[tex] - \frac{67}{100} [/tex]
is this what you asked for?
How can you determine whether two variables x and y for a real-life situation are, correlated?
To determine if two variables, X and Y, are correlated, we can use the two simple ways. One is to create a scatter plot simply—a scatter plot plots X and Y pair values. A scatter plot shows a diagram of correlations. We can also identify if the correlation formed is positive, negative, or non-existent. Calculating the correlation coefficient R and determining its p-value associated with R is also possible.
Correlation coefficient values are always between -1 and 1.
Where
-1 indicates a perfect negative linear correlation between the two variables
0 shows a perfect positive linear correlation between the two variables
1 shows a perfect linear correlation between the two variables, indicates
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