Answers
The number of terms in the sequence is given as follows:
135 terms.
How to obtain the number of terms in the sequence?The general notation of a sequence is given as follows:
[tex]\sum_{m = a}^{k} f(m)[/tex]
The parameters are given as follows:
a is the initial index.k is the final index.Hence the number of terms in the sequence is obtained as follows:
n = k - a + 1.
The parameter values for this problem are given as follows:
a = 1, k = 135.
Considering the parameter values above, the number of terms of the sequence is given as follows:
n = 135 - 1 + 1
n = 135.
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Related Questions
which equation does the graph of the systems of equations solve
Answers
Answer:
(a) -1/2x +3 = 3x -4
Step-by-step explanation:
Given a graph of two lines, you want to know which equation it is showing the solution for.
LinesThe blue line has a slope of -3/6 = -1/2, and a y-intercept of +3, so its slope-intercept equation is ...
y = -1/2x +3
This expression is seen on the left side of the equal sign for the first choice, and is not seen anywhere else.
By way of confirmation, the red line has slope 3/1 = 3 and a y-intercept that is a negative value less than -2. It is reasonable to say its slope-intercept equation is ...
y = 3x -4
This expression matches the right side of the equal sign for the first choice.
SolutionThe solution to the system of these two equations might reasonably be found by equating the expressions for y:
-1/2x +3 = 3x -4
a regular hexagon is shown below O is the centre of the hexagon
Answers
AO in terms of P and/or Q is OA = Q = Q
OB in terms of P and/or Q is OB = P =Q
EB in terms of P and/or Q is EB = 2P =2Q
What is a Hexagon?A hexagon, also known as a sexagon, is a six-sided polygon that forms the shape of a cube in geometry. Any basic hexagon has a total internal angle of 720°.
In a regular hexagon, all sides are equal
Which means:
AB= BC
5p + q -5p = 6p-5p
q = p
So, every side of the hexagon is p = q
Which means that AB = BC = CD = DE = EF = FA = p =q
Recall that at the center, each side forms an angle
There are six sides in a hexagon.
Total angle = 360°
6x= 360°
x= 60°.
By the symmetry of regular hexagon, OA = OB
<OAB = <OBA
<AOB = x = 60°
Sum of all angles in a triangle is 180°
We add the values
<OAB = 60°.
<OAB is an equilateral triangle, thus every side is equal
Hence,
a. OA = Q = Q
b. OB = P =Q
c. EB = 2P =2Q.
From the figure, <BOE= 180° which makes it a straight line.
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The average major league baseball team has around 2.5 million people in attendance each year. We-Seat-U sells 60% of the tickets for three of the teams at a charge of $1.50 per ticket. How much does We-Seat-U make per year just from ticket sales of these three teams?
Answers
We-Seat-U sells 60% of the tickets, so they sell 7.5 million * 60% = 4.5 million tickets
At a charge of $1.50 per ticket, We-Seat-U makes 4.5 million * $1.50 = $6.75 million per year.
A farmer takes 250 chickens to be sold at a market. In the first hour he sells 8% of his chickens. In the second hour he sells 10% of those that were left. How many chickens has he sold in total?
Answers
Answer:
43 chickens
Step-by-step explanation:
1) 250*8%=20
2) 250-20=230
3) 230*10%=23
4) 20+23=43
Over spring break, you are going to volunteer and paint 30
houses. You will need 8 gallons of paint for each home. You
receive two donations of paint, each with 15 containers, and
will purchase the required remaining paint.
If each container holds 5 gallons of paint, how many
containers do you need to buy?
Answers
Answer:
33 containers
Step-by-step explanation:
total gallons needed=8×30=240
gallons in 15 containers=15×5=75
gallons needed=240-75=165
no. of containers needed to buy=165÷5=33
What is the image of point (4,5) after a rotation of 90 counterclockwise about the origin
Answers
Answer: ez ahh question, the answer is (4,-5)
Step-by-step explanation:
Calculate 12% of 14=______
Answers
Calculate 12% of 14= 1,68
Answer
1,68 is the answer of your question
we are interested in testing to see if the variance of a population is less than 7. the correct null hypothesis is
Answers
The test is determined whether the population variance is less than 7.
The hypothesis formulation-
‘H0: σ² ≥ 7’
‘H1: σ² < 7’
Now let us solve this question options-wise:
Option a is incorrect because we should always contain the ‘=’ or ‘≥’ or ‘≤’ sign, and in the null hypothesis, and also this option denotes the standard deviation, not the variance.
Option b is correct because it contains a ‘≥’ sign and it is the right complement to the alternative hypothesis.
Option c is incorrect because it measures the standard deviation instead of the variance.
Option d is incorrect because it has the lower limit of the variance as 49 instead of 7
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full question:
We are interested in testing to see if the variance of a population is less than 7. The correct null hypothesis is
a. σ< 7.
b.σ^2≥7.
c. σ< 49.
d.σ^2≥ 49
You are tiling a floor with parallelogram shaped tiles. If one angle of the
parallelogram is 48 degrees, what are all the other angles?
Answers
The provided parallelogram has angles of 45 degrees and 45 degrees, as well as 48 degrees and 48 degrees.
What is parallelogram?A parallelogram is a basic quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposing or facing sides are of equal length, and its opposite angles are of equal measure. A parallelogram is a quadrilateral with opposing sides that are parallel and equal. It has equal interior opposite angles. In addition, the angles on the same side of the transversal add up to 180 degrees or are additive to each other.
Here,
A parallelogram has two pairs of opposite angles that are equal.
Since one angle of the parallelogram is 48 degrees, its opposite angle must also be 48 degrees.
The other two angles must add up to 90 degrees (since they form a right angle), so they must each be equal to 180 - 90 = 90 degrees / 2 = 45 degrees.
So, the other angles of the parallelogram are 45 degrees and 45 degrees.
The angles of given parallelogram are 45 degrees and 45 degrees as well as 48 degrees and 48 degrees.
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At the Piedmont Middle School baseball game last Friday, the Piedmont Ravens hit 3 times as many foul balls as the other team, the Rossville Crows.
Answers
Step-by-step explanation:
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5- A rectangle that has a perimeter of 16 cm has been dilated with a scale factor of 3. What is the perimeter of the new shape?
6- A triangle that has an area of 36 squared cm has been dilated with a scale factor of 0. 5.
Find the area of the new triangle.
CAN I PLEASE GET SOME HELP ON THIS. THANK YOU
Answers
5- Perimeter of the new rectangle is 48 cm.
6- Area of the new triangle is 9 cm².
5- A rectangle that has a perimeter of 16 cm has been dilated with a scale factor of 3. To find the perimeter of the new shape, we need to multiply the original perimeter by the scale factor:
16 cm * 3 = 48 cm
So the perimeter of the new shape is 48 cm.
6- A triangle that has an area of 36 squared cm has been dilated with a scale factor of 0.5. To find the area of the new triangle, we need to multiply the original area by the square of the scale factor:
36 cm² * (0.5)²
= 36 cm² * 0.25
= 9 cm²
So the area of the new triangle is 9 cm².
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of six letters (a, b, c, d, e, and f), two letters are to be selected at random. how many outcomes are possible?
Answers
Answer:
Below
Step-by-step explanation:
6 C 2 = 6! /(4! 2!) = 15 outcomes
A slow 24-hour clock loses 25 minutes a day. At noon on the first of October, it is set to show the correct time. When will this clock next show the correct time?
Answers
Answer:
Nov 27 at 14:24 hours
Step-by-step explanation:
First let's figure out exactly when the slow clock will synchronize with a correct clockAt the rate of loss of 25 minutes per day, let x be the number of days when the two clocks coincideThe total time lost in x days = 25x minutesThe clocks will synchronize when the total time lost is exactly 24 hours.24 hours = 24 x 60 minutes = 1440 minutesSetting this equal to 25x we get
25x = 1440
[tex]x = \rm{{\dfrac{1440 \textrm{ minutes}}{25 \textrm{ min/day}} = 57.6 \;days}[/tex]
57.6 days equates to 57 days, 14 hours, 24 minutes (using a calculator)
Adding to Oct 1 at 12:00:00 we get this as Nov 27 at 14:24 hours
Could someone please answer for this section I will give 20 points for all of it
Answers
Answer:
1) 2/5
2) 4/13
3) 1/8
4) 25/4 or 6 + 1/4
Step-by-step explanation:
1) 5/2 * x = 1
x = 1 / (5/2)
x = 2/5
2) (3 + 1/4) * x = 1
13/4 * x = 1
x = 1 / (13/4)
x = 4/13
3) 8 * x = 1
x = 1/8
4) (2/5)^2 * x = 1
2^2 / 5^2 * x = 1
4/25 * x = 1
x = 1 / (4/25)
x = 25/4
x = 6 + 1/4
1. Write the following expression without negative
exponents
and without parentheses.
(-6x)-¹
Answers
Answer:
[tex]\frac{1}{-6x}[/tex]
Step-by-step explanation:
[tex]\frac{1}{-6x}[/tex] To get a positive exponent, put the expression over 1.
Malia was cutting out shapes from a rectangular piece of construction paper in art class.
The first shape Malia cut out was a circle from a piece of construction paper that
measured 8 inches by 10 inches, as shown in the diagram above. After Malia finished
cutting out the circle, what was the area of the piece of paper that was left after she
cut out the circle? Use 3.14 form.
Answers
The area of the piece of paper left after cutting out the circle is 29.76 in².
Area of a figure:
The amount of unit squares that completely encircle the surface of a closed figure is its area. Area is measured in square units like cm² and m². A shape's area is a two-dimensional measurement. The term “area” refers to the space inside the boundary or perimeter of a closed shape.
You need to first determine the rectangle's area.
8x10=80 in²
determine the circle's overall area.
The diameter is 8 in so you would use 4 as the radius
A=πr²
A=3.14x4²
A=3.14x16
A=50.24 in²
The area of the circle must then be subtracted from the area of the rectangle.
80-50.24=29.76
The area of the piece of paper is 29.76 in ².
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what is the highest number obtainable if you multiple the numbers 1-9? however you can only use each number once.
Answers
The highest number obtainable by multiplying the numbers 1-9 is 40,320. To obtain this result, you need to arrange the numbers in a specific order.
The problem is to find the highest number that can be obtained by multiplying the numbers 1-9, where each number can only be used once. To obtain the highest possible number, it's important to arrange the numbers in a specific order. One possible arrangement is 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1. This arrangement results in the highest product of 40,320. It's worth mentioning that different arrangements of the numbers may result in different products, but the arrangement mentioned above gives the highest possible product. Understanding the order of operations and how to manipulate the numbers is key to solving this problem and finding the highest number.
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Find each exact value if 0
Sin (x - y) if cos x = 8/17 and cos y = 3/5
Answers
Work Shown:
If cos(x) = 8/17, then sin(x) = 15/17. Use the identity [tex]\sin^2(\text{x}) + \cos^2(\text{x}) = 1[/tex] to determine this.
If cos(y) = 3/5, then sin(y) = 4/5 using that same identity.
So,
sin(x-y) = sin(x)cos(y) - cos(x)sin(y)
sin(x-y) = (15/17)*(3/5) - (8/17)*(4/5)
sin(x-y) = 45/85 - 32/85
sin(x-y) = (45 - 32)/85
sin(x-y) = 13/85
1.) The ( ) means that all of the points on the line will satisfy the inequality.
2.) The solution set for the inequality is the entire ( ) shown in the graph
Answers
1.) The "(≠)" means that all of the points on the line will satisfy the inequality.
2.) The solution set for the inequality is the entire region (shaded or unshaded portion) shown in the graph. The shaded region represents the set of all points that satisfy the inequality, while the unshaded region represents the set of all points that do not satisfy the inequality.
What is linear inequality?
A linear inequality is an equation that represents a linear relationship between two variables and is used to describe a region of the coordinate plane that satisfies a given set of conditions.
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Imagine this:
The altitude of an airplane coming in for a landing is represented by the equation shown below, where y represents the altitude, in feet, of the airplane and x represents the number of minutes the plane has been descending.
y = -10x + 1500
This means y is the altitude with -10ft decent every x minutes when the initial altitude is 1500Ft
Part A: Create a table for the values when x = 0,5,8,10,10
Show your work with the equation used to identify the values you put in the table when X = 0,5,8,10 and 30.
Part B: identify the altitude after 5 minutes and after 30 minutes. use 1-2 sentences to explain the altitude at these two times and describe what is happening to the airplane at these time intervals. Starter: The plane's altitude after 5 minutes would be _________. After 30 minutes, the plane's altitude would be ________.
Then describe if the plane is in the air or on the ground at those times.
Answers
The table for the values when x = 0,5,8,10, will be:
x (minutes) y (altitude in feet)
0 1500
5 1450
8 1420
10 1400
30 1200
How to explain the equationAn equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
When x = 0, y will be:
-10x + 1500
= -10(0) + 1500
= 1500
When x = 5 y will be:
= -10(5) + 1500
= 1500 - 50
= 1450
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A team of dogs in Alaska can run 4.3 miles per hour. There is approx. 1.61 kilometers in a mile. How many kilometers per hour can they run each hour?
Answers
In the diagram shown below,
ABCE is a trapezium,
AD is parallel to BC,
DE=4cm,
Area of ABCE=60cm^2
Area of ABCD=40cm^2
Work out the values of f and g.
You must show all your working
Answers
The values for g and f for the length of sides of the trapezium are 8 and 6 respectively.
How to evaluate for the values of g and f for the trapeziumGiven the area of trapezium = 60 cm², then:
1/2 × (g + 4g) × f = 60 cm²
by simplification
f(g + 2) = 60 cm²...(1)
for the area of ABCD = 48 cm², then:
f × g = 48 cm²
f = 48/g...(2)
put 48/g for f in equation (1) to get g;
48/g(g + 2) = 60
60g = 48g + 96 {cross multiplication}
60g - 48g = 96 {collect like terms}
12g = 96
g = 96/11 {divide through by 11}
g = 8
put 8 for g in equation (2) to get f;
f = 48/8
f = 6.
Therefore, the values for g and f for the length of sides of the trapezium are 8 and 6 respectively.
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do you think this model satisfies assumptions for multiple regression? list 4 of the assumptions and next to each one tell why you do or do not think it is valid.
Answers
In multiple regression, we have 4 assumptions listed and explained below. They are valid.
Following are assumptions for multiple regression model:
1. Linear connection: Each predictor variable and the responder variable have a linear relationship.
Making a scatter plot of each predictor variable and the response variable is the simplest technique to check if this premise is true.
2. Lack of Multicollinearity: There is no significant correlation between any of the predictor variables.
Calculating the VIF value for each predictor variable is the quickest approach to see if this premise is true.
3. Independence: Each observation has its own validity.
The Durbin-Watson test, a formal statistical test that informs us whether or not the residuals (and consequently the observations) exhibit autocorrelation, is the easiest approach to find out if this assumption is true.
4. Homoscedasticity: At every point in the linear model, the residuals' variance is constant.
The simplest technique to check if this premise is true is to plot the standardized residuals against the expected values.
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Evaluate the expression.
5
−
3
=
Answers
Value of expression 5 - 3 is 2
What is subtraction?
Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
Given expression,
5 - 3 = ?
we need the difference of 5 and 3
5 - 3 = 2
Hence, 2 is value of expression 5 - 3
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The Smith family will drive 240 miles round-trip to visit a relative. Mr. Smith, Mrs. Smith, and their 20 -year old son, James, will share the driving. Determine whether each statement is correct by selecting True or False. A If Mrs. Smith and Mr. Smith drive 80 miles each, then James will drive for 13 of the round-trip distance. True False B If Mrs. Smith and Mr. Smith drive 90 miles each, then James will drive for 12 of the round-trip distance. True False C If Mrs. Smith drives 90 miles and Mr. Smith drives 50 miles, then James will drive for 512 of the round-trip distance. True False D If Mrs. Smith drives 60 miles and Mr. Smith drives 120 miles, then James will drive for 712 of the round-trip distance. True False
Answers
The correct answers is (a). False (b). False (c). False (d).True
(A). False
If Mrs. Smith and Mr. Smith drive 80 miles each, then the total miles they drive is 80 + 80 = 160 miles. That means James will have to drive 240 - 160 = 80 miles, which is 1/3 of the round-trip distance, not 13/3.
(B). False
If Mrs. Smith and Mr. Smith drive 90 miles each, then the total miles they drive is 90 + 90 = 180 miles. That means James will have to drive 240 - 180 = 60 miles, which is [tex](\frac{1}{4})[/tex] of the round-trip distance, not [tex]\frac{12}{4}[/tex].
(C). False
If Mrs. Smith drives 90 miles and Mr. Smith drives 50 miles, then the total miles they drive is 90 + 50 = 140 miles. That means James will have to drive 240 - 140 = 100 miles, which is [tex](\frac{1}{2} )[/tex] of the round-trip distance, not [tex](\frac{5}{12} )[/tex].
(D). True
If Mrs. Smith drives 60 miles and Mr. Smith drives 120 miles, then the total miles they drive is 60 + 120 = 180 miles. That means James will have to drive 240 - 180 = 60 miles, which is [tex](\frac{7}{12} )[/tex] of the round-trip distance.
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Answer:
Your answer should be: TRUE FALSE TRUE FALSE
А. B. Males Females Based on the information above, which statement is true? C. female students The number of male students in School A and School B are equal The number of male students in School B is less than the number of male students in School A The number of female students in School A is more than the number of male students
Answers
Based on the information below, a statement which is true include the following: C. the number of female students in School A is more than the number of male students in School B.
What is a pie chart?In Mathematics, a pie chart is sometimes referred to as a circle graph and it can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors or sections.
By critically observing the pie chart shown in the image attached below, we can reasonably infer and logically deduce that the total number of male students in School A is less than the total number of female students in School B.
In conclusion, School A has more female students than male students.
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help. need answer asap help.help.help.help.help.help.help.help.help.help.help.help.help.help.
Answers
The area of the triangle is calculated to be equal to 7.5 square inches.
How to evaluate for the area the triangleFor any triangle, the area is calculated as half the base multiplied by the height of the triangle, that is;
Area of triangle = 1/2 × base × height
we have the base of the triangle to be 6 inches and the height as 2.5 inches, so we solve for the area as follows:
1/2 × 6 inches × 2.5 inches
6 inches can be divided by 2 to give;
3 inches × 2.5 inches
7.5 square inches
Therefore, the area of the triangle is calculated to be equal to 7.5 square inches
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BROTHERS AND SISTERS, PLS HELP, REALLY NEED HELP!!!!!!!!
Answers
The functions that we have are;
1) y = 2.2x + 104
2) y =5.06e^-0.011t
3) The dependent variable is the number of organisms while the independent variable is the time in years.
4) This is an exponential decay
5) The decay rate is 1.1%
What is an equation?We know that an equation is often used to show a function. The equation is a mathematical rule that is used to express the particular situation that we have.
In the case of the problems that we have here, there is a mathematical function that can be used in the representation of each of the cases that have been shown as we can see above.
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Which expression represents the amount of money John has collected?
John collects $5 for club dues from each member. Use the variable
m
for the number of members in the club.
Answers
Answer: The expression that represents the amount of money John has collected is:
5 * m
This expression calculates the amount of money John collects by multiplying the number of members (m) by the amount of money collected per member ($5).
Step-by-step explanation:
If y varies directly with x and y= – 93 when x= – 3, find y when x=2.
Answers
Answer:
Below
Step-by-step explanation:
y varies directly with x means
y = k x
now with y = -93 and x = -3
-93 = k (-3) shows k = 30
so y = 30 x
now with x = -2
y = 30 (-2) = -60