Answer:
a) Arithmetic,b) t(n) = 16 - 3n.-------------------------------
We observe that the sequence is decreasing with common difference of - 3.
16, 13, 10, 7, 4, 1Therefore, this is an AP, with the first term of t(1) = 13 and common difference of d = -3.
Use the nth term formula for AP:
t(n) = t(1) + (n - 1)dt(n) = 13 + (n - 1)(- 3) = 13 - 3n + 3 = 16 - 3nAnswer:
a) Arithmetic sequence
b) t(n) = 16 - 3n
Step-by-step explanation:
An Arithmetic Sequence has a constant difference between each consecutive term.
A Geometric Sequence has a constant ratio (multiplier) between each consecutive term.
Part (a)From inspection of the given table, t(n) decreases by 3 each time n increases by 1. Therefore, the sequence is arithmetic with a common difference of -3.
Part (b)[tex]\boxed{\begin{minipage}{8 cm}\underline{General form of an arithmetic sequence}\\\\$a_n=a+(n-1)d$\\\\where:\\\phantom{ww}$\bullet$ $a_n$ is the nth term. \\ \phantom{ww}$\bullet$ $a$ is the first term.\\\phantom{ww}$\bullet$ $d$ is the common difference between terms.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
Given:
a = 13d = -3aₙ = t(n)Substitute the initial value (when n = 1) and the common difference into the formula to create an equation for the nth term:
[tex]\implies t(n)=13+(n-1)(-3)[/tex]
[tex]\implies t(n)=13-3n+3[/tex]
[tex]\implies t(n)=16-3n[/tex]
(x+3)(x+7)=0
Problem answered, solution and why!
[tex](x+3)(x+7)=0\\x=-3 \vee x=-7\\\\x\in\{-7,-3\}[/tex]
At a conference of educators, there ore 189 people total, and 128 are teachers. If the rest are principals, then how many principals are present?
Answer:
61 principals
Step-by-step explanation:
189 total - 128 teachers = 61 principals
Find the exact values of the six trigonometric functions of the angle O shown in the figure.
sin(0) -
X
cos(0) -
tan(0) -
csc(0) -
sec(0)-
cot(0) -
0
3
3
The values of
1. cosθ = √3/2
2. sinθ = √3/2
3. tanθ = 1
4. sec θ = 2/√3
5. cosec θ = 2/√3
6. cot θ = 1
What is trigonometric ratio?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
cosθ = adj/hyp
sinθ = opp/hyp
tanθ = opp/adj
sec θ = 1/cosθ
cosec θ = 1/sinθ
cot θ = 1/tanθ
We need to find the hypotenuse of the triangle
x² = 3² +3²
x = √9+9
x = √18
x = 2√3
cosθ = 3/2√3 = 6√3/12
= √3/2
2. sinθ = 3/2√3 = √3/2
3. tanθ = 3/3 = 1
4. sec θ = 2/√3
5. cosec θ = 2/√3
6. cot θ = 1
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Use the given data to make a box-and-whisker plot.
5, 4, 16, 21, 10, 6, 15
Answer:
To make a box-and-whisker plot, we first need to order the data from smallest to largest:
4, 5, 6, 10, 15, 16, 21
Next, we can find the median, which is the middle value of the ordered data set. In this case, the median is 10.
Then, we can find the lower quartile (Q1) and the upper quartile (Q3). The lower quartile is the median of the lower half of the data set, and the upper quartile is the median of the upper half of the data set. To find Q1 and Q3, we can split the data set into two halves:
4, 5, 6, 10 and 15, 16, 21
The median of the lower half is (5+6)/2 = 5.5, and the median of the upper half is (16+21)/2 = 18.5. Therefore, Q1 = 5.5 and Q3 = 18.5.
Now we can draw the box-and-whisker plot. The box represents the middle 50% of the data, with the bottom of the box at Q1 (5.5), the top of the box at Q3 (18.5), and the line inside the box at the median (10). The whiskers extend from the box to the smallest and largest values inthe data set that are not outliers. To determine whether there are outliers, we can use the following formula:
Outlier = Q1 - 1.5 * (Q3 - Q1) or Q3 + 1.5 * (Q3 - Q1)
Plugging in the values, we get:
Outlier = 5.5 - 1.5 * (18.5 - 5.5) = -13.25 or Outlier = 18.5 + 1.5 * (18.5 - 5.5) = 37.25
Since there are no values in the data set that are less than -13.25 or greater than 37.25, there are no outliers.
Therefore, the box-and-whisker plot for the given data is:
| 4
___|___
| |
| |
| 5.5 |-----
| | |
| | |
|------------| 10 |
| | |
| 15.5 |------
| | |
___|___
| 21
The box spans from Q1 (5.5) to Q3 (18.5), with the median line inside the box at 10. The whiskers extend from the box to the minimum value of 4 and the maximum value of 21, since there are no outliers.
Hope this helps!
STRUCTURE Gustavo sets up tables for a caterer on weekends. Each round table can seat 8 people. Each rectangular table can seat 10 people. One weekend, his boss asked him to set up tables for 124 people. He uses 2 more round tables than rectangular tables. Write a system of equations to find the number of round tables and rectangular tables Gustavo used. Then graph the system on a separate sheet of paper to solve the system. Let x = the number of round tables and let y = the number of rectangular tables. y = x+ x+ y= WHAT DO I PUT IN THE BOXES
The system of equation of the tables used is 8x + 10y = 124 and x = y + 2
He used 8 round tables and 6 rectangular tables
How to determine the system of equation of the tables usedFrom the question, we have the following parameters that can be used in our computation:
Each round table = 8 peopleEach rectangular table = 10 peopleTotal number of table = 124Using the above as a guide, we have the following:
8x + 10y = 124
Where
x = round tables
y = rectangular tables
We understand that
He uses 2 more round tables than rectangular tables
This means that
x = y + 2
So, the system of equations is 8x + 10y = 124 and x = y + 2
The graph of the system is attached, where we have x = 8 and y = 6
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Stuck on this and cant move along until I get it correct. Please help.
Fill in the missing value.
The measure of angle F is ___°
The solution is: the measure of angles 2, 3, and 4 are:
m∠2 = 95°
m∠3 = 85°
m∠4 = 95°
Vertical Angle Theorem:
When two straight lines intersect, the opposite vertical angles formed are always equal (congruent) to each other.
Therefore,
m∠3 = 85°
m∠2 = m∠4
Linear pair:
Two adjacent angles which, when combined, form a line, so the sum of a linear pair is 180°.
Therefore,
85° + m∠2 = 180°
m∠3 + m∠4 = 180°
If 85° + m∠2 = 180°
⇒ m∠2 = 180° - 85°
⇒ m∠2 = 95°
As m∠2 = m∠4 then m∠4 = 95°
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complete question:
Find the measure of angles 2, 3, and 4. input the measures then click done. i-ready
please help i missed a day of class i cant figure this out
Which of the following circles have their centers on the x-axis?
Check all that apply.
A. (x-4)2 + (y-0)² = 22
B. (x-0)2 + (v-0)² = 25
C. (x + 1)² + (y-7)² = 16
D. (x-0)2 + (v-5)2 = 49
The equations of the circles that have centers on the x-axis are;
A. (x - 2)² + (y - 0)² = 22
B. (x - 0)² + (y - 0)² = 25
What is the general form of the equation of a circle?The equation of a circle is; (x - h)² + (y - k)² = r², where;
(h, k) = The coordinates of the center of the circle
r = The radial length of the circle
The center of the circle is on the x-axis when the y-coordinate of the center of the circle is; k = 0, therefore, the circle that have their centers on the x-axis are the circles with the term (y - 0)²
The option of the circle that has the term (y - 0)² are the first and second option, where the v is actually a y; option A and .
The correct option is therefore;
A. (x - 4)² + (y - 0)² = 22
B. (x - 0)² + (y - 0)² = 25
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PLEASE HELP ON VOLUME! ASAP❗️ I BEG❗️❗️❗️
The volume of the cylinder A = 1006.76 m³
The volume of the cylinder B = 2893.82 ft³
The volume of the cylinder C = 2712.96 in³
The volume of the cylinder D = 111.78 in³
The Volume of the cylinder = πr²h
Where r = radius , h = height
A) r = 15/2 = 7.5
h = 5.7
Volume = 3.14 × (7.5)² × 5.7
Volume = 1006.76
B) r = 8
height = 14.4
Volume = 3.14 × (8)² × 14.4
Volume = 2893.82
C) r = 6
h = 24
Volume = 3.14 × (6)² × 24
Volume = 2712.96
D) r = 2
h = 8.9
Volume = 3.14 × (2)² × 8.9
Volume = 111.78
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imagine that a friend asks you for investment advice. he bas $10,000 to invest and he has about 35 years before he will be ready for his financial goal of early retirement. what types of investments would you recommend to your friend? why? what other investing advice would you give him to help him achieve his financial goals?
When it comes to long-term investment goals like early retirement, it is generally recommended to focus on investments that offer potential growth over an extended period of time. Here are some investment options and advice that could be beneficial for your friend:
Stock market investments: Investing in a diversified portfolio of stocks can provide the potential for long-term growth. Your friend can consider investing in individual stocks or exchange-traded funds (ETFs) that represent a basket of stocks.
Mutual funds: Mutual funds offer diversification by pooling money from multiple investors to invest in a variety of assets. They are managed by professionals who make investment decisions on behalf of the investors.
Index funds: Index funds are a type of mutual fund that aims to replicate the performance of a specific market index, such as the S&P 500. They offer broad market exposure and generally have lower expense ratios compared to actively managed funds.
Retirement accounts: Encourage your friend to take advantage of tax-advantaged retirement accounts like a 401(k) or an individual retirement account (IRA). These accounts provide tax benefits and can help grow savings faster.
Dollar-cost averaging: Advising your friend to invest regularly, regardless of market conditions, through a strategy called dollar-cost averaging can help mitigate the impact of market volatility. By investing a fixed amount at regular intervals, your friend will buy more shares when prices are low and fewer shares when prices are high.
Rebalancing: As time goes on, it's important to periodically review and rebalance the investment portfolio. This involves adjusting the asset allocation to maintain the desired level of risk and return. Regularly rebalancing ensures that the investments stay aligned with the financial goals and risk tolerance.
Emergency fund: Remind your friend about the importance of building an emergency fund with three to six months' worth of living expenses. This will provide a safety net and help prevent the need to tap into long-term investments during unforeseen circumstances.
Seek professional advice: Depending on your friend's knowledge and comfort level with investing, it may be helpful to recommend consulting with a financial advisor who can provide personalized advice based on their specific financial situation and goals.
Remember, investing involves risks, and it's crucial for your friend to carefully evaluate investment options, consider their risk tolerance, and have a long-term perspective. Regularly monitoring and adjusting the investment strategy over time will help ensure progress towards achieving their financial goals.
A shirt company has 3 designs each of which can be made with short or long sleeves. There are 6 color patterns available. How many different shirts are available from this company?
Answer:
36 different shirts-----------------
Given that there are 3 designs, 2 sleeve lengths, and 6 color patterns, we can multiply these values together:
3 designs × 2 sleeve lengths × 6 color patterns = 36So, there are 36 different shirts available from this company.
There are 36 different types of shirt available for this company.
Given that;
Number of design Company has = 3
Number of color pattern available = 6
Types of shirt (short or long sleeves) = 2
Now, We need to find the number of different types of shirts are available from this company.
Since, the number of different types of shirts can be calculated by multiplying Number of design Company has with Number of color pattern available also multiplying with Types of shirt (short or long sleeves).
Hence, By framing in equation form we get;
the number of different types of shirts is,
⇒ 3 × 6 × 2
⇒ 36
Therefore, We get;
There are 36 different types of shirt available for this company.
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I need help finding the Component form and Magnitude of the vector V.
To find the magnitude of the vector, we can use the Pythagorean theorem: ||V|| = sqrt((5 * √2 / 2)^2 + (5 * √2 / 2)^2) = 5.
To find the component form of a vector, you need to break it down into its x and y components. Let's say our vector V has a magnitude of 5 and is pointing in the direction of 45 degrees (measured from the positive x-axis).
To find its x component, we can use cosine: Vx = V cos(45) = 5 * √2 / 2. To find its y component, we can use sine: Vy = V sin(45) = 5 * √2 / 2. So the component form of vector V is (5 * √2 / 2, 5 * √2 / 2).
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The scatterplot above displays the relationship between the amount of food hippopotamuses eat per day and their age. Describe and explain any associations and data features on the scatterplot. Then, use the variables on the graph to interpret the relationship that is shown.
The scatter plot shows a [positive linear] association.
How to determine the association of the scatterplotFrom the question, we have the following parameters that can be used in our computation:
The image of the scatter plot
On the scatter plot, we can see that
The points appear to be on a straight line
Also, we can see that
As the x values increases the y values increases
This represents a positive linear association.
Hence, the association is a positive linear association.
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A rectangular prism measures 8 inches in width, 12 inches in length, and 4 inches in height. What is the surface area of the prism?
Step-by-step explanation:
It has
two sides 8x12
two sides 12x4
two sides 4x8 total 352 in^2
Sofia and ella are both writing expressions to calculate the surface area of a rectangular prism however they wrote different expressions.
a. examine the expressions below, and determine if they represent the same value. explain why or why not.
sofia's expression
(3 cm x 4 cm ) + (3 cm x 5 cm) + (4 cm x 5 cm) + (4 cm x 5 cm)
ella's expression:
2(3 cm x 4 cm) + 2(3 cm x 5 cm) + 2(4 cm x 5 cm)
b. what fact about the surface area of a rectangular prism does ella's expression show more clearly than sofia's?
a ) The given expression from Sofia and Ella represents two different values.
b.) The fact about the surface area of prism that Ella's expression shows that is not in Sofia's expression is that the expression is according to the formula.
How to determine the surface area of a rectangular prism?To determine the surface area of a rectangle prism, the formula that should be used would be given below:
That is;
Surface area of rectangular prism;
= 2(wl+hl+hw)
when the formula is multiplied out the following is gotten;
= 2wl + 2hl + 2hw
From Ella's expression,
2(3 cm x 4 cm) + 2(3 cm x 5 cm) + 2(4 cm x 5 cm). This follows the order of the formula. And it's final answer = 94cm²
From Sofia's expression,
(3 cm x 4 cm ) + (3 cm x 5 cm) + (4 cm x 5 cm) + (4 cm x 5 cm). This doesn't follow the order of the formula and therefore is not correct and not the same final value with Ella's expression.
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Graph
�
<
0
x<0x, is less than, 0.
The graph of the inequality is x < 0 and is plotted
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
A = x is less than 0
So , on simplifying , we get
x < 0
Hence , the inequality of x is all numbers less than 0 without including 0
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Help me with this problem please.
The product of matrices A and B are:
[tex]AB = \left[\begin{array}{ccc}-50&7\\44& -10\\\end{array}\right][/tex]
[tex]BA = \left[\begin{array}{ccc}-12&-30\\-16& -48\\\end{array}\right][/tex]
How to find the product of two matrices?A matrix (plural matrices) is a set of numbers arranged in rows and columns so as to form a rectangular array.
The number of rows of a matrix can be determined by counting from top to bottom and the number of columns can be determined by counting from left to right.
The product of matrices A and B are:
AB = A * B
[tex]AB = \left[\begin{array}{ccc}-3&-8\\2& 8\\\end{array}\right] * \left[\begin{array}{ccc}6&3\\4& -2\\\end{array}\right][/tex]
To get the product, multiply each row by the column. That is:
(-3 * 6) + (-8 * 4) = -50
(-3 * 3) + (-8 * (-2)) = 7
(2 * 6) + (8 * 4) = 44
(2 * 3) + (8 * (-2)) = -10
[tex]AB = \left[\begin{array}{ccc}-50&7\\44& -10\\\end{array}\right][/tex]
BA = B * A
[tex]BA = \left[\begin{array}{ccc}6&3\\4& -2\\\end{array}\right] * \left[\begin{array}{ccc}-3&-8\\2& 8\\\end{array}\right][/tex]
To get the product, multiply each row by the column. That is:
(6 * (-3)) + (3 * 2) = -12
(6 * (-8)) + (3 * 8) = -30
(4 * (-3)) + ((-2) * 2) = -16
(4 * (-8)) + ((-2) * 8) = -48
[tex]BA = \left[\begin{array}{ccc}-12&-30\\-16& -48\\\end{array}\right][/tex]
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Can someone help find the surface area, then round the answer to the nearest whole number please?
The Surface Area of cylinders are: 100 yd² , 264 m², 226 mm²
The Surface Area of Can is 219 cm².
We know the formula for Surface Area of Cylinder
= 2πrh
1. Radius = 2 yd
Height = 8 yd
So, Surface Area of Cylinder
= 2πrh
= 2 x 3.14 x 2 x 8
= 100 yd²
2. Radius = 7 m
Height = 6 m
So, Surface Area of Cylinder
= 2πrh
= 2 x 3.14 x 6 x 7
= 264 m²
3. Radius = 3 mm
Height = 12 mm
So, Surface Area of Cylinder
= 2πrh
= 2 x 3.14 x 3 x 12
= 226 mm²
4. Radius = 3.5 cm
Height = 10 cm
So, Surface Area of Can
= 2πrh
= 2 x 3.14 x 3.5 x 10
= 219 cm²
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100 Points! Algebra question. Photo attached. Find the exact value of the expression. Please show as much work as possible. Thank you!
The exact value of the expression tan 15⁰ is determined as 2 - √3.
What is the exact value of the expression?The exact value of the expression is calculated by applying trigonometry identity as shown below;
The trig ratio is simplified as;
SOH CAH TOA;
SOH ----> sin θ = opposite side / hypothenuse side
CAH -----> cos θ = adjacent side / hypothenuse side
TOA ------> tan θ = opposite side / adjacent side
The given trigonometry expression;
tan 15⁰
The expanded trigonometry expression;
tan 15⁰ = tan (60 - 45)
Apply tan addition formula;
tan(A - B) = (tan A - tan B) / (1 + tan A×tan B).
Simplify as follows;
tan (60 - 45) = (tan 60 - tan 45) / ( 1 + tan60 x tan45)
tan 60 = √3
tan 45 = 1
Substitute this value back into the tan formula;
tan (60 - 45) = (√3 - 1 ) / ( 1 + √3)
Rationalize the surd expression as follows;
(√3 - 1 ) / (√3 + 1) x (√3 - 1 ) / (√3 - 1 )
= ( 4 - 2√3) / 2
= 2 - √3
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A TV station is going to air a movie marathon with 11 movies. It will consist of 6 science fiction movies and 5 horror movies. The horror movies will be aired later in the evening. So, all of the horror movies will be aired last (after all of the science fiction movies). In how many ways can the station air the movie marathon?
The solution is: In 86400 ways can the station air the movie marathon.
Given:
Number of total movies = 11
Number of science fiction movie = 6
Number of horror movie = 5
Computation:
Number of science fiction movies way air = 6!
so, we get,
Number of science fiction movies way air = 720
Number of horror movies way air = 5!
so, we have,
Number of horror movies way air = 120
The number of ways the station air the movie marathon is:
720 * 120
=86400
so, we get,
Final answer is 86400 ways.
Hence, The solution is: In 86400 ways can the station air the movie marathon.
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find the perimeter of a rectangle if: L= 12cm, W= 5cm.
(a) 34cm
(b) 21cm
(c) 14cm
(d) 17cm
Answer:
(a) 34 cm
Step-by-step explanation:
The formula for perimeter of a rectangle is
P = 2l + 2w, where
P is the perimeter,l is the length,and w is the width.Thus, we can plug in 12 for l and 5 for w in the perimeter formula and simplify to find the perimeter of the rectangle:
P = 2(12) + 2(5)
P = 24 + 10
P = 34
Thus, the perimeter of a rectangle with a length of 12 cm and a width of 5 cm is 34 cm.
1. Identify the variable that is contained in the expression.
7y+2y² +3
7
x
y
3
The variable that is contained in the given expression is y. Therefore, option C is the correct answer.
The given expression is 7y+2y² +3.
In the given expression there are 3 terms, so it is called trinomial.
In the term 7y, y is the coefficient of 7.
In the term 2y², y² is the coefficient of 2.
3 is the constant term.
Therefore, option C is the correct answer.
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First to find correct answer will get brainly
The surface area of the dilated solid is 2,880 square units
What is the surface area of the dilated solid?Multiply each side of the shape by 4
Surface area of a rectangular prism = 2(LH + LW + WH)
Where,
Length, L = 8 × 4 = 32 units
Width, W = 6 × 4 = 24 units
Height, H = 3 × 4 = 12 units
Surface area of a rectangular prism = 2(LH + LW + WH)
= 2(32×12 + 32×24 + 24×12)
= 2(384 + 768 + 288)
= 2(1,440)
= 2,880 square units
Therefore, 2,880 square units is the surface area of the solid.
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Using the given scale 1:50, calculate the actual length of the wall if it is measured to be 15cm.
With a short time remaining in the day, a delivery driver has time to make deliveries at seven locations among the 8 locations remaining. How many different routes are possible? Question content area bottom Part 1 There are enter your response here possible different routes. (Simplify your answer.)
The number of different routes possible for the delivery driver, given the time to make deliveries at 7 out of the remaining 8 locations, is 8.
The number of different routes possible for the delivery driver can be calculated using combinatorics. Specifically, we need to determine the number of ways to choose 7 locations out of the remaining 8 locations. This can be found using the combination formula.
The combination formula, also known as "n choose k," is given by the expression C(n, k) = n! / (k! * (n-k)!), where n is the total number of items to choose from and k is the number of items to choose.
In this case, there are 8 locations remaining and the driver needs to choose 7 of them. Applying the combination formula, we have C(8, 7) = 8! / (7! * (8-7)!) = 8! / (7! * 1!) = 8.
Therefore, there are 8 possible different routes for the delivery driver to make deliveries at the remaining 8 locations, given that the driver has time to make deliveries at 7 of them.
To simplify the answer, we can state that there are 8 possible different routes for the driver.
In summary, the number of different routes possible for the delivery driver, given the time to make deliveries at 7 out of the remaining 8 locations, is 8.
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Help me solve this problem please
Answer:
450°
Step-by-step explanation:
if x+y+z=27 and x+y=17 then Z=
Answer:
Step-by-step explanation:
x+y+z=27
x+y=17
z=?
since x+y=17
then
17+z=27
z=27-17
z=10
A jewlary shop sells 240 necklaces in a month 180 of the necklaces were sold in a via the shops website the rest were sold in a high street shop .
Work out the ratio of online sales to shop sales
Give ur answers in its simplest form
Volume of Cone ___ mm3?
The volume of the cone is 301. 44mm³
How to determine the valueFirst, we need to know the formula
the formula that is used for calculating the volume of a cone is expressed as;
V = πr²h/3
Such that the parameters are;
V is the volume r is the radiush is the height of the coneSubstitute the values, we have;
Volume = 3.14 × 6² × 8/3
Multiply the values, we have;
Volume = 904.32/3
Divide the values
Volume = 301. 44mm³
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
The exact value of the cosine of θ is given as follows:
a) 3/5.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are obtained according to the rules presented as follows:
Sine of angle = opposite side/hypotenuse.Cosine of angle = adjacent side/hypotenuse.Tangent of angle = opposite side/adjacent side = sine/cosine.Applying the Pythagorean Theorem, the hypotenuse length is given as follows:
x² = 6² + (-8)²
x² = 100
x = 10.
As the x-coordinate is used for the cosine, the cosine is given as follows:
cos(θ) = 6/10
cos(θ) = 3/5.
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f(x) = x²/x² 2x+3 find Vertical asymptote find horizontal asymptote
The vertical asymptote of the equation does not exist, the horizontal asymptote of the equation is 1.
To calculate vertical asymptote,
Putting the denominator equal to zero,
x²+2x+3 = 0
Using Quadratic formulae,
b² - 4ac
where,
b = 2
a = 1
c = 3
putting value,
4-12 = -8<0
therefore, the solution is negative
Hence, no vertical asymptote of the given equation exists,
To calculate the horizontal asymptote,
the degrees of the numerator and denominator are the same. we can compare the coefficients of the highest power terms.
The coefficient of x² in the numerator is 1
Hence, the horizontal asymptote is y = 1.
To learn more about asymptotes, here:
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