The given situation shows an arithmetic sequence and the number of sales in the week 50 can be determined by using the nth term formula of arithmetic sequence. The sales in all 50 weeks can be determined by using the formula for sum of finite arithmetic sequence.
An arithmetic sequence is an ordered set of numbers that have a constant difference called a common difference between consecutive terms. Each term is obtained by adding the common difference to the previous term.
In the given situation, the first term (a) is the number of sales to be made in the first week. Hence, a = 10
The common difference (d) is the number added to get the number of sales in the next week. Hence,
d = 1
Hence, in the 2nd week the number of sales should be 11 and in 3rd week it should be 12.
Using the formula for nth term and n = 50,
an=a+(n-1)d
a50=10+(50-1)1
a50=10+(49)1
a50=10+49=59
The formula of finding the sum of the finite arithmetic sequence:
Sn=(n/2)(a1+an)
S50=(50/2)(10+59)
S50=25(69)=1725
Hence, the number of sales in the 50th week is 59 and the total number of sales made in the 50 weeks is 1725.
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A certain species of fish costs $3.49 each. You can spend at most $45: How many of this type of fish can you buy for your aquarium?
Find the coordinates of the midpoint of a segment with the given endpoints. A(2,14), C(0,5)
The coordinates of the midpoint of a segment with the given endpoints will be (1, 9.5).
What is the mid-point of the line segment?Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).
Then the coordinate of the mid-point of the line segment is given as,
(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]
The endpoints are A(2, 14) and C(0, 5).
Then the coordinates of the midpoint of a segment with the given endpoints will be
(x, y) = [(2 + 0) / 2, (14 + 5) / 2]
(x, y) = (2/2, 19/2)
(x, y) = (1, 9.5)
The coordinates of the midpoint of a segment with the given endpoints will be (1, 9.5).
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Workers in an office of 90 staff were asked their favourite type of take-away.
The results are summarised in the table.
Take-away Frequency Angle
Pizza 29
a
Curry 9
b
Fish & chips 24
c
Kebab 16
d
Other 12
e
How many degrees represent 1 person?
Each angle to draw a pie chart a, b, c, d, and e will be 116°, 36°, 96°, 64°, and 48°, respectively.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
Workers in an office of 90 staff were asked their favorite type of takeaway. The results are summarised in the table.
Take-away Frequency Angle
Pizza 29 a
Curry 9 b
Fish & chips 24 c
Kebab 16 d
Other 12 e
The angles on the pie chart are calculated by multiplying the table by 4. Then the angles will be
∠a = 4 x 29 = 116°
∠b = 4 x 9 = 36°
∠c = 4 x 24 = 96°
∠d = 4 x 16 = 64°
∠e = 4 x 12 = 48°
Each angle to draw a pie chart a, b, c, d, and e will be 116°, 36°, 96°, 64°, and 48°, respectively.
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Find the distance between each pair of points. Round to the nearest tenth. X(5,4) and Y(2,1)
The distance between X(5,4) and Y(2,1) is 4.24 rounded to the nearest tenth.
How to find the distance between two points?Let's consider we have two points (x₁, y₁) and (x₂, y₂) the distance between these two points is given by the formula;
[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
The distance between two points (x₁, y₁) and (x₂, y₂) is given by ;
[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
So,
Distance between X(5,4) and Y(2,1)
[tex]d = \sqrt {\left( {5 - 2 } \right)^2 + \left( {4 - 1 } \right)^2 }[/tex]
d = √18 = 4.242640687
Roud to nearest tenth ⇒ 4.24 units.
Hence "The distance between X(5,4) and Y(2,1) is 4.24 rounded to the nearest tenth".
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This question has three parts.
Bruce deposited a certain amount of money in a simple interest bearing savings account.
He neither deposited nor withdrew any money from his account for 4 years.
He kept track of the money in his account by making a graph as shown.
Part A:
What was Bruce’s principle (initial amount deposited)
Part B:
How much interest did Bruce earn after 1 year?
Part C:
What was the interest rate that Bruce’s savings account was earning
Bruce's principle is $140.
The interest that Bruce earned is $9.80
The interest rate that Bruce savings account is 7%.
What is the simple interest?Simple interest is the interest that that is earned a certain amount over a period of time given a principal and the number of years.
Simple interest = amount deposited x time x interest rate.
A graph can be described as a pictorial representation of data. A graph has a y-axis and the x-axis. The y-intercept is a point where the graph touches the y-axis. The y-intercept represents the initial amount that is deposited. The principle is $140.
The slope of the graph represents the rate at which the amount invested increases in value.
Interest Bruce earned after 1 year : change in the slope
149.80 - 140 = $9.80
Interest rate = Interest / (principle x time)
9.80 / (140 x 1) = 0.07 = 7%
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If there are ten marbles in a bag (those marbles being two yellow, three pink, and five blue) and two are randomly drawn, what is the probability of drawing two yellow marbles if the first one isn't put back before the second draw? please help T^T
Answer:
the answer is 2 upon 10 ndnznnznznzjzjzj
Given the formula for an exponential function, is it possible to determine whether the function grows or decays exponentially just by looking at the formula?
yes, actually it is possible. The mathematical expression f(x)=exp or ex denotes the exponential function.
What is meant exponential function?The mathematical expression f(x)=exp or ex denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras. When the input variable x appears as an exponent in the formula f(x) = axe, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x.
One of the key mathematical operations is the exponential function (though it would have to admit that the linear function ranks even higher in importance). We allow the exponent to be the independent variable to create an exponential function. The formula f(x)=2x is a straightforward example.
Hence, yes, actually it is possible.
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Find the distance from the line to the given point.
x=4,(-2,5)
The distance from the line x=4 to the given point (-2,5) is 6 units .
Distance formula from line to point :
The distance from the line ax+by+c=0 to the point (u,v) is given by the formula
[tex]distance=\frac{|au+bv+c|}{\sqrt{a^{2} +b^{2} } }[/tex]
In the given question
the equation of the line is [tex]x=4[/tex]
taking all the terms to Left side we get
[tex]x-4=0[/tex]
[tex]1.x+0.y-4=0[/tex]
given the points (-2,5)
From above values we the values as a=1 , b=0 , c=-4 , u=-2 , v=5 .
Substituting the values in the distance formula we get
[tex]d=\frac{|1*(-2)+0*(5)-4|}{\sqrt{1^{2} +0^{2} } }[/tex]
[tex]=\frac{|-2+0-4|}{1} \\ \\ =|-6|\\ \\ =6[/tex]
Therefore , the distance from the line x=4 to the given point (-2,5) is 6 units.
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If A, B, and D are collinear and D bisects A and B. The Length of AD=2x-2 and the Length of DB=x+4.
Find the value of x.
The value of x if D bisects A and B is 6
How to determine the value of x?The given parameters are
D bisects A and B.
Length AD = 2x - 2
Length DB = x + 4
This means that
AD =DB
So, we have
2x - 2= x + 4
Evaluate the like terms
x = 6
Hence, the value of x if D bisects A and B is 6
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Write an explicit and a recursive formula for each sequence. -5,-3.5,-2,-0.5,1, . . . . . .
The formula for an arithmetic series -5,-3.5,-2,-0.5,1, is An = A1 + (n-1)d
What is arithmetic series ?
See the pattern
-5-(-3.5)= -1.5
-3.5-(-2)= -1.5
The formula for an arithmetic series -5,-3.5,-2,-0.5,1, is An = A1 + (n-1)d
An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.
Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.
An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.
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suppose that Angle Hik and Angle LIJ are verticle angles. find their measures if the following conditions apply. Question 2...
=========================================================
Explanation:
Vertical angles are always congruent.
Set the two expressions equal to one another and solve for x.
6x - 6 = 3(x+6)
6x - 6 = 3x + 18
6x - 3x = 18 + 6
3x = 24
x = 24/3
x = 8
Then use this x value to find each angle
angle HIK = 6x - 6 = 6*8 - 6 = 42angle LIJ = 3(x+6) = 3*(8+6) = 42Both angles are 42 degrees each to confirm the answer.
Set both given equations equal to zero, then combine them into one standard form equation. x + 6 = 0 and y - 3 = 4 x + 6 = 0 → y - 3 = 4 → Combined equation
The standard form of the given equation is; x + (-y) = -5
How to write a linear combined equation in standard form?
We are given the equations;
x + 6 = 0 -----(1)
y - 3 = 4 -----(2)
Add 4 to both sides of equation 2 to get;
y - 3 + 4 = 0
y + 1 = 0 -----(3)
Put y + 1 for 0 in eq 1 to get;
x + 6 = y + 1
The standard form of an equation is expressed in the form;
Ax + By = C
Thus;
x + 6 = y + 1 can be rewritten as;
x + (-y) = 1 - 6
x + (-y) = -5
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The sum of two numbers is thirty one. The first is five less than the second. Find the numbers
Answer:
Step-by-step explanation:
First Number : x - 5
Second Number : x
x + ( x - 5) = 31
2x - 5 = 31
2x = 31 + 5
2x/2 = 36/2
x = 18
Then plugin x= 18 into First numer X - 5
x - 5
18 - 5 = 13
18 + 13 = 31
so .....
First Number is 13
Second number is 18
which equation describes a line of symmetry for the figure shown? y=0 y=-x y =x x=0
Answer:
The last option: x = 0
Step-by-step explanation:
The line of symmetry for a figure is a straight line that divides the figure into two congruent figures
The vertical line passing along the y axis is the line of symmetry and since it passes through all y values where x = 0, the equation is x = 0
bonjour pouvez-vous m’aidez avec se devoir svp?
Lors des soldes, Rami, qui accompagne sa mère et s'ennuie un peu, compare trois étiquettes pour passer le temps:
n°1-valeurs: 120 €
soldé: 105 €
n°2-Robe rouge: 45 euros
soldé: -30%
n°3-soldes: 25 € - 12,50 €
1. Quel est le plus fort pourcentage de remise?
2. Est-ce que la plus forte remise en euros est la plus forte en pourcentage?
merci d’avance
Answer:
Step-by-step explanation:
HELP ASP WILL GET SHOW UR WORK!! BRAINILEsT AND 10 points
Answer:
x=4
Step-by-step explanation:
Answer:
x=4
Step-by-step explanation:
2x-2=6
Okay, first we need to create the inverse of this equation.
The inverse of subtraction is addition.
2(x)-2=6
2x = 6+2
Now, we solve the right-hand side.
2x = 8
Then, divide both sides by the greatest common factor.
We get x by itself.
2x = 8
/2 /2
x = 4
a line contains the (2,2) and is parallel to y=1/2x +1. Write the equation of the line in slope-intercept form
Answer:
y=-2x+6
Step-by-step explanation:
Please see attachment.
Hope this helps!
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You thought the balance in your checking account was $68. When your bank statement arrived, you realized that you forgot to record a check. The bank statement listed your balance as $26. What was the amount of the check that you forgot to record?
10-2 (2x+1) = 4 (x-2)
x=2
10-2(2x+1)=4(x-2)
10-4x-2=4x-8
10-2=8x-8
8=8x-8
16=8x
2=x
Answer:
X = 2
Step-by-step explanation:
[tex] \sf \: First, solve \: the \: brackets. [/tex]
[tex] \sf \: 10 - 2(2x + 1) = 4(x - 2) \\ \sf10 - 4x - 2 = 4x - 8 \: \: \: \: \: \: \: [/tex]
[tex] \sf \: Combine \: like \: terms .[/tex]
[tex] \sf8 - 4x = 4x - 8[/tex]
[tex] \sf \: Subtract \: 4x \: from \: both \: sides \: to \: remove \: 4x.[/tex]
[tex] \sf \: 8 - 4x - 4x = 4x - 8 - 4x \\ \sf8 - 8x = - 8[/tex]
[tex] \sf \: Subtract \: 8 \: from \: both \: sides \: to \: remove \: 8.[/tex]
[tex] \sf8 - 8 - 8x = - 8 - 8 \\ \sf - 8x = - 16[/tex]
[tex] \sf \: Divide \: both \: sides \: by \: -8.[/tex]
[tex] \sf \: x = 2[/tex]
PLs help me pls help
The missing values from area model will be 48, 240.
Describe Area Model.An area model is a rectangular diagram or model used in mathematics for problems involving multiplication and division, where the length and breadth of the rectangle are determined by the factors, quotient, and divisor.
Write the enlarged form of each component first. Next, sketch your model. To get the area of each smaller rectangle, multiply next. To determine the entire area, add those items last.
The area model will be -
60 6
8 480 48
40 2400 240
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Complete the proofs on a seperate sheet of paper!
The proof is completed and showed that < 2 ≅ < 3 as required.
How to show that < 2 ≅ < 3Given data
<1 and <2 are linear pair
<1 + <3 = 180 degrees
required to proof <2 ≅ <3
linear pair implies mathematically that the sum of the two angles are 180 degrees, hence we have:
< 1 + < 2 = 180 degrees equation 1
also given that,
< 1 + < 3 = 180 degrees equation 1
equating equation 1 and equation 2 gives
< 1 + < 2 = < 1 + < 3
< 2 = < 3
Hence the required proof
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What is the vertex of y=|x|-5 ?
a. (5,0)
b. (-5,0)
c. (0,5)
d. (0,-5)
Answer: The answer is D
Step-by-step explanation:
Write each logarithmic expression as a single logarithm. 7 log p + 2log q
The given lograthimic expression 7log p + 2logq can be written as log(p^7q^2).
According to the given question.
We have a lograthimic expression.
7log p + 2logq
As we know that, a logarithmic expression is an expression that involves the logarithm of an expression containing a variable.
Also according to the product and power rule we know that
log(mn) = logm + logn
log(x^y) = ylogx
Therefore, the given lograthimic expression 7log p + 2logq can be written as
7log p + 2logq
= log p^7 + log q^2
= log(p^7q^2)
Hence, the given lograthimic expression 7log p + 2logq can be written as log(p^7q^2) as log(p^7q^2).
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A certain state uses the following progressive
tax rate for calculating individual income tax:
Income
Progressive
Range ($)
Tax Rate
0 - 10,000
3%
10,001 - 50,000
5%
50,001 - 100,000
5.5%
Calculate the state income tax owed on a $50,000
per year salary.
tax = $[?]
Round your answer to the nearest whole dollar amount.
Answer: 52
Step-by-step explanation: it might not be it. GOD BLESS.
Theresa purchased 10 rakes and 15 shovels for $595. brett purchased 8 rakes and 20 shovels for $676. assume the rakes are all priced the same, and all shovels are priced the same.
The price of a rake and a shovel is $22 and $25 respectively.
Let's assume the price of a rake is x and the cost of a shovel is y.
Now, Theresa purchased 10 rakes and 15 shovels for $595.
10x + 15y = $595 -------------------(1)
Taking 5 common out from each side of the equation,
5( 2x + 3y) = 5( 119)
2x + 3y = 119 ------------------(2)
Brett purchased 8 rakes and 20 shovels for $676.
8x + 20y = $676 ------------------(3)
Multiply equation (2) by 4 and subtract from equation (3),
8x + 20y - ( 8x + 12y ) = 676 - 476
8x + 20y - 8x - 12y = 200
8y = 200
y = $25
Therefore,
10x + 15y = 595
10x + 15(25) = 595
10x + 375 = 595
10x = 595 - 375
10x = 220
x = $22
Hence, the price of a rake and shovel is $22 and $25 respectively.
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Recycled CDs, Incorporated, offers a choice of 5 used CDs for $29, with each additional CD costing $. Write a cost function for purchasing 5 or more CDs. What will the cost of buying CDs be? Let x represent the number of CDs over 5.
The cost function will be of the form f(x) = x + 29.
What is a function ?A function have a set of dependent variable for the given or specified independent variable.
According to the given question Recycled CDs, Incorporated, offers a choice of 5 used CDs for 29 dollars with each additional CD costing a dollar.
We have to write a function for purchasing 5 or more CDs where x represents the no. of CDs over 5.
Let f(x) represents the cost of CDs.
∴ f(x) = x + 29.
Here the constant 29 dollars represents the cost of 5 CDs and x represents no. of CD's over 5.Put x = 0 and the cost for 5 CDs will be 29 and for any more value of x we will get our desire result.
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Use the following information to complete parts I, II, and III.
Part I: Use scientific notation to estimate the number of hours in one year.
Part II: Use scientific notation to calculate the exact number of hours in one year.
Part III: In two or more complete sentences, compare your answers to parts I and II. In your comparison, discuss similarities and differences in your answers.
I) There are 8.76* 10³ hours in 1 year.
II) The exact number of hours in one year is 8.76582*10³ hours.
What is scientific notation?Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.
Given:
1 hour=3600 seconds
1 year = 31556952 seconds.
Now,
I) Use scientific notation to estimate the number of hours in one year.
1 day = 24 hours
1 year = 365 days
So, number of hours in one year is given by,
=24*365
=8760
=8.76* 10³
So, there are 8.76* 10³ hours in 1 year.
II) 1 year = 31556952 seconds.
1 hour = 3600 seconds
In one year the number of hour is given by,
=31556952/3600
=8765.82
=8.76582*10³
So, the exact number of hours in one year is 8.76582*10³ hours.
III)
The exact numbers of hours using 365 days is 8760 which is written as in scientific notation but using the given data we get hours.
Comparing these answers the first one has only 3 significant figures and the second answer has six significant figures.
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Use the table below to find the cumulative frequency of the class "less then 30.5?"
What is the y -value of the focus of the parabola?
Answer:
8136366271773737i228882ywhw
g(t) = t^2 + 4t
h(t) = 2t
Find (g/t) (-6)
The value of h(g(t))(-6) is 24.
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences.
An example of this would be y=x².
If you put in anything for x, you get one output for y. We would say that y is a function of x since x is the input value.
Given:
g(t) = t² + 4t
h(t) = 2t
h(g(t))
=h( t² + 4t)
=2( t² + 4t)
And, h(g(t)) (-6)
=2( (-6)² + 4(-6))
=2(36-24)
=2*12
=24
Hence, the value of the function is 24.
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