The common difference is 7/4 and the required terms are 16a,28a,49a
What is a geometric progression?Any progression in which the ratio of adjacent terms is fixed is a Geometric Progression. The general form of representation of a geometric sequence is a, ar, ar2, ar3, ar4,...
Given here: The fifth, ninth, sixteenth terms of a linear sequence (a.p.) are consecutive terms of an expodencial sequence (g.p.)
5th term of the ap: a+4d
9th term: a+8d
16th term: a+15d
In a gp, the square of any term is equal to the product of the terms before and after it:
(a+8d)²=(a+4d).(a+15d)
[tex](a^2+16ad+64d^2)=a^2+19ad+60d^2\\4d^2-3ad=0\\d(4d-3a)=0[/tex]
(i) ANSWER: d = (3/4)a
(ii) 21st term: a+20d = a+15a = 16a
37th term: a+36d = a+27a = 28a
65th term: a+64d = a+48a = 49a
28a/16a = 7/4; 49a/28a = 7/4; this sequence is geometric with common ratio 7/4
Hence, The common difference is 7/4 and the required terms are 16a,28a,49a
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If QR=28 and SV=45 what is TU?
Answer:
QR could be diagonal of a parallelogram.
(if i got it wrong sorry i tried my best)
Please help me you guys
Answer:
Step-by-step explanation:
Kahn acadamy ahe A and D
Which is better, an ACT score of 28 or a combined SAT score of 2100 when
ACT: μ = 21 and σ = 5;
SAT: μ = 1500 and σ = 325
and assume ACT and SAT scores have approximately bell-shaped distributions?
- ACT score of 28
- SAT score of 2100
- I don't know
A better score is the SAT score of 2100 which has an average of 1500 with an SD of 325.
- SAT score of 2100
Now, According to the question:
"Information available from the question"
An ACT score of 28 or a combined SAT score of 2100 when
ACT: μ = 21 and σ = 5;
SAT: μ = 1500 and σ = 325
In order to determine which is a better score, we compare the scores in standard deviation units.
We can convert the score to standard deviation units by subtracting the mean and dividing by the standard deviation.
ACT: (28-21)/5 = 1.2
SAT: (2100-1500)/325 = 1.38
As we see SAT score is better than ACT score as it is 1.38 standard deviation units above the mean, while the ACT score is only 1.2 standard deviation units above the mean.
Hence, SAT score of 2100
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2.¿qué operación es la que debes realizar para convertir un valor en pivote? a)suma de renglón más escalar. por ejemplo: r1 2 b)suma o resta de dos renglones. por ejemplo: r1-r2
The final equation in the system, and it can be used to solve for either x or y is x + 1.5y = 3
The pivot operation is used to solve linear equations. The operation starts by selecting a pivot element from a matrix. This pivot element is usually the first non-zero element in the first column of the matrix. The pivot element is then multiplied by a scalar to create a new equation. This new equation is then added to or subtracted from the other equations in the system to eliminate the coefficient of the pivot element. This process is repeated until the system of equations is solved.
For example, consider the following system of equations:
2x + 3y = 6
4x + 6y = 12
The first non-zero element in the first column is 2, so this will be our pivot element. To use the pivot operation, we multiply 2 by a scalar and add this new equation to the other equation. Let's use the scalar 4. This gives us:
8x + 12y = 24
Now we subtract this equation from the other equation to eliminate the coefficient of the pivot element:
2x + 3y = 6 - 8x - 12y = 24
This leaves us with:
-6x - 9y = 18
We now have an equation with only one variable. To solve for this variable, we can divide both sides by -6, giving us:
x + 1.5y = 3
This is the final equation in the system, and it can be used to solve for either x or y.
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By inspecting the equations, what can you determine about the solution(s) of this system?
X+4=Y
X+4Y=1
the value of x=-3 and y=1 by a solving equation system.
What is a System of Equations?
A system of equations in algebra is made up of two or more equations that are solved together. "A group of equations satisfied by the same set of variables are called a system of linear equations. Finding the values of the variables employed in the system of equations is the first step toward solving it. While maintaining the balance of the equations on both sides, we compute the values of the unknown variables. Finding a variable whose value makes the condition of all the given equations true is the primary goal of solving an equation system.
X+4=Y ...1
X+4Y=1 .....2
x-y=-4
x+4y=1
-5y = -5
y=1
x =-3
Hence the value of x=-3 and y=1 by a solving equation system.
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Write an essay about the real-life application of lines (BODY PART ONLY PLEASE)
An essay on the real - life application of lines would include different fields where lines are used in real life.
Which fields use lines in real life ?Line drawings are used in the design and construction of buildings and infrastructure to represent their structure and layout. Lines are a fundamental element in graphic design, used to create contrast, texture, and visual interest in illustrations, logos, and other design elements.
Line drawings are used in medical illustrations to represent anatomy and in graphs to represent medical data and trends. Line production and assembly lines are used in the production of goods in many industries such as automotive, electronics, and food processing.
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Which is bigger 0.55 or 2/5
Answer:
Is 0.55 greater than 2/5?
0.55 as a fraction is 11/20
11/20 is greater than 2/5
0.55 is is greater than 2/5
Answer:
0.55
Step-by-step explanation:
Because 2/5 converted to a decimal is 0.4
each cone has a height of 11cm and a base diameter of 8cm
LEMONADE STAND: You have 10 gallons of lemonade to sell. (1 gal ≈ 3785 cm)
A. How much lemonade can one cone hold
B. Each customer uses one paper cup. How many paper cups will you need?
C. The cups are sold in packages of 50. How many packages should you buy?
One cup can hold (A), you will need a total of 205.37 paper cups (B), and a total of 5 packages (C).
How much lemonade can one cone hold?Let's calculate the volume of the cone:
V=1/3πhr²
V= 1.04 x 11 x 4 ^2 (diameter / 2 radius)
V= 1.04 x 11 x 16 = 184.30 cubic centimeters
How many paper cups will you need?Total of lemonade: 37850 cubic centimeters (10 gallons x 3785 cubic centimeters per gallon)
37850 / 184.30 = 205.37 cups
How many packages should you buy?205.37 / 50 cups = 4.1 packages
However, as you need to buy complete packages, this can be rounded to 5 packages.
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Please help with my math question
Answer:
Below
Step-by-step explanation:
From hour 1 to 2 pay goes from 90 to 120 or 30 dollar increase per hour
slope = rise / run = (120-90) / (2-1) = 30 dollar/hr
What is -2/3 x (-4/8) in simplest form?
Answer: 2/3
Step-by-step explanation:
First you multiply both numerators which equals 8
Then, you multiply the denomerators which is 24
This gives you 8/24
Since both 8 and 24 are divisible by 8, you divide them by 8 and you get 1/3
Since two negative numbers equal a positive one, the answer is positive
Answer for points please by 7!!!!!!
Step-by-step explanation:
So what you should do is open up the brackets of the top row, and to open up brackets with addition inside simply multiply the outside number with the two inside numbers. This would result in:
First Column: 5(5+7) = 5*5 + 5*7 = 25 + 35
Second Column: 5(5+8) = 5*5 + 5*8 = 25 + 40
Third Column: 7(4+5) = 7*4 + 7*5 = 28 + 35
Fourth Column: 14(2+3) = 14*2 + 14*4 = 28 + 42
Fifth Column: 15(2+3) = 15*2 + 15*3 = 30 + 45
68 divided by 0.4
Show work please
Help, please !!!!!!!!!!!!!!!
The required longest hike executed by the family is 2 hours.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
From the table,
Hike 1 took 1 2/4 hours which is equivalent to 1.5 hours.
Similarly
Hike 2 = 1.75 hours
Hike 3 = 2 hours
Hike 4 = 1.75 hours
Hike 5 = 1.5 hours
Hike 6 = 1 hours
Thus, the required longest hike executed by the family is 2 hours.
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if a function n=f(y) gives the number of police officers, n, in a town in year y, then what does f(2020) = 200 tell us?
There were 200 police officers in year 2020.
There were 200 police officers on average each year.
There will be 2020 police officers in 200 years
Not enough information given
The function f(2020) = 200 tells us that there were 200 police officers in the year 2020.
Mathematically, an equation can be described as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.
The equation f(2020) = 200 tells us that in the year 2020, there were 200 police officers in the town. The function n = f(y) gives the relationship between the number of police officers, n, and the year, y.
So, when we put in the value of 2020 for y, we get the number of police officers in that year, which is 200.
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For each of the following variables, determine whether the variable is categorical or numerical. If the variable is numerical, determine whether the variable is discrete or continuous. In addition, determine the measurement scale.a. Number of students in a classNumber of students in a classb. Satisfaction rating of a cable television provider left parenthesis from low to high right parenthesisSatisfaction rating of a cable television provider (from low to high)c. Time comma in hours comma spent working per monthTime, in hours, spent working per monthd. Where the individual uses social networks to find sought dash after informationWhere the individual uses social networks to find sought-after informatione. Volume of water comma in gallons comma used by an individual showering per month
As per the type of variable, the measurement scale is nominal scale and ratio scale.
The term type of variable is divides as Discrete variables are those that can be counted on the fingers whereas continuous variables are those that cannot be counted on the fingers and may be represented as decimals or fractions.
Here we know that the variable is categorical or numerical.
And here we need to find the variable is discrete or continuous.
a. Number of cellphones in the household is numerical, discrete, ratio scale
b. Length (in minutes) of the longest telephone call made in a month is measured by using the scale numerical, continuous, ratio scale
c. Weather someone in home owns a Wi Fi capable cell phone is measured using categorical, nominal scale
d. Whether there is a high speed Internet connection in household is measured as categorical, nominal scale.
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A quadratic function has x-intercepts at (-6,0) and the origin, and passes through (-5,-5). Write the equation of the quadratic function in standard form.
f(x)=blank
The equation of the quadratic function is:
f(x) = x^2 - 11x + 6
How can we explain it ?The standard form of a quadratic function is given by:
f(x) = ax^2 + bx + c
We can find the values of a, b and c using the three points given in the question:
The x-intercepts of (-6, 0) and (0, 0) give us two equations:
f(-6) = 0 = a(-6)^2 + b(-6) + c = 36a - 6b + c
f(0) = 0 = a(0)^2 + b(0) + c = c
The point (-5, -5) gives us a third equation:
f(-5) = -5 = a(-5)^2 + b(-5) + c = 25a - 5b + c
Solving the system of three equations, we get:
a = 1, b = -11 and c = 6
Thus, the equation of the quadratic function is:
f(x) = x^2 - 11x + 6
What is quadratic equation ?A quadratic equation is a polynomial equation of degree 2 that can be written in the form:
ax^2 + bx + c = 0
where x is an unknown variable and a, b, c are constants. The equation can be solved to find the values of x that satisfy the equation, which are referred to as the roots or solutions of the equation. The roots can be found using methods such as factoring, the quadratic formula, or completing the square.
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find the range of values that satisfy the inequality
[tex]2x - 3 < 7 [/tex]
Answer:
=2x-3<7
=2x=7+3
=2x<10/2
=x=5
therfore x=5
range=1,2,3,4 5
Step-by-step explanation:
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Which line has a slope of 3 over 2??? PLEASE HELP
The top right line has a slop of 3/2
It goes up 3 and goes to the left 2
Answer:
B
Step-by-step explanation:
Points on graph B (2,3) (4,6)
We see the y increase by 3 and the x increase by 2, which matches the slope of 3/2
So, the answer is B
Is it possible to have a triangle with angle 60°,70°,and 50°
Answer:
Yes, it is possible to have a triangle with angles 60°, 70°, and 50°. The sum of the angles must equal 180° in order for a triangle to be formed.
Step-by-step explanation:
Answer:
Yes.
Step-by-step explanation:
To create any possible triangle, all three angle measurements should add up to 180° and the exterior angle should also be equal to the sum of two interior opposite angles!
The Debate Club and Math Club are each having a pizza party to celebrate the results of their state competitions. The Debate Club would like to order their pizza from Antonio's
Pizzeria at a cost of $12.10 per pizza and a $5. 25 delivery fee. The Math Club would like to order their pizza from Mamma Mia's Pizzeria at a cost of $11. 75 per pizza and a
C
represents the total cost C, and the number of pizzas, p. Determine how many pizzas each club can order
if both clubs have the same amount of money to spend. Is the solution viable or not viable?
$7.50 delivery fee. The system of equations
12.10p+5.25
C=11.75p+7.50
Part A
Select the correct statement
O Each club can purchase 6.43 pizzas and the solution is viable.
O Each club can purchase 7 pizzas and the solution is viable.
O Each club can purchase 6 pizzas, as 6.43 pizzas is not viable.
Each club does not have enough money to purchase 6 pizzas, the solution is not viable.
Each club can purchase 7 pizzas and the solution is viable.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given are the system of equations as -
{C} = 12.10p + 5.25
{C} = 11.75p + 7.50
We can write the system of equations as
{C} = 12.10p + 5.25
{C} = 11.75p + 7.50
For the same amount, we will equate both the equations as -
12.10p + 5.25 = 11.75p + 7.50
12.10p - 11.75p = 7.50 - 5.25
0.35p = 2.25
p = (2.25/0.35)
p = 6.4
Therefore, each club can purchase 7 pizzas and the solution is viable.
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Given right triangle ABCABC with altitude \overline{BD}
BD
drawn to hypotenuse \overline{AC}
AC
. If BD=2BD=2 and DC=1,DC=1, what is the length of \overline{AD}?
AD
?
The measure of the length AD will be 4cm.
What is are of triangle?
The area of a triangle is the region enclosed by its sides. The area of a triangle differs from one triangle to another depending on the length of the sides and the internal angles. Triangle areas are expressed using square measurements like m2, cm2, and in2. One right angle or two perpendicular sides are both acceptable for right triangles. They may also be known as orthogonal triangles, right-perpendicular triangles, or originally rectangular triangles. Trigonometry's foundation is formed by the relationship between the sides and other angles of a right triangle.
2 / 1= AD / 2
AD=4 cm
Hence The measure of the length AD will be 4cm.
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The speed of sound is 1236km/h
how many meters per second
Answer:
343 meters per second (3 sf)
Step-by-step explanation:
1236km/h is basically 1236km per hour.
1km = 1000 meters
1h = 60 minutes
1m = 60 seconds
Using these rules, we can convert the kilometers and hour to meters and minutes and then to seconds.
---
1236km = 1236*1000
= 1 236 000m
---
1h --> 1 236 000m
60m --> 1 236 000m
1m --> 1 236 000/60 = 20 600m
60s --> 20 600m
1s --> 20 600/60 = 343m (3 sf)
There are 343 (3 sf) meters per second.
what is the relationship between metrics and data
Metrics and data are intimately connected in the sense that metrics rely on data to function. Metrics are used to measure the performance of an organization Data is the source of information that is used to calculate metrics.
It is the raw numbers and facts that are collected, analyzed, and turned into metrics that can be used to measure performance. Data is the foundation of metrics because metrics are just a way of interpreting and organizing the data to gain insight into performance.
Without data, metrics would not exist. It is through data that metrics are able to provide an understanding of what is working and what is not. Metrics are the tool used to interpret data and make decisions that can help guide an organization or individual to success.
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if we assume a power-law relation , the linear regression between which two quantities do we need to analyze? (a) vs ; (b) vs ; (c) vs ; (d) vs .
If we assume a power-law relation T = b×aⁿ, the linear regression that needs to be analyzed is : (d) log(T) vs log(a) .
The Linear Regression between the two quantities do we need to analyzed is log(T) vs log(a) because when we take the logarithm of both sides of the power-law equation,
we obtain log(T) = n × log(a) + log(b), which is a linear equation in logarithmic form.
So , By performing linear regression on log(T) vs log(a), we can estimate the values of n and log(b), and then use these estimates to obtain estimates of b and n in the original power-law equation.
The given question is incomplete , the complete question is
If we assume a power-law relation T = b×aⁿ, the linear regression between which two quantities do we need to analyze?
(a) T vs a ;
(b) log(T) vs a ;
(c) T vs log(a) ;
(d) log(T) vs log(a) .
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Help Please it’s just Geometry
Specifically can you answer #14 but if you answer them all i would be more than grateful please help
Given P(-4,17), Q (1,-3), R(-9,3), S(-5,4), slope of line PQ m(PQ) = -4 and slope of line RS m(RS) = 1/4 and Both lines are perpendicular.
What are perpendicular lines?
If two non-vertical lines in the same plane intersect at a right angle then they are said to be perpendicular. Horizontal and vertical lines are perpendicular to each other i.e. the axes of the coordinate plane.
To calculate the slope of the two lines;
Mathematically;
Slope = y2-y1/x2-x1
For PQ; slope will be;
Slope of line PQ m(PQ) = (-3-17)/(1-(-4)
Slope of line PQ m(PQ) = -20/5
Slope of line PQ m(PQ) = -4
For RS; slope will be;
Slope of line RS m(RS) = (4-3)/(-5-(-9))
Slope of line RS m(RS) = 1/4
We want to determine the relationship between the two lines.
The product of both is 1/4 * -4 = -1
When two lines are perpendicular, the product of their slopes is -1
We can conclude that both lines are perpendicular to one another.
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A recent survey of 2500 college students revealed that during any weekend afternoon, 1480 receive a text message, 920 receive an e-mail and 547 receive both a text message and an e-mail. Suppose a college student is selected at random, what is the probability that he/she neither receives a text message nor an email during any weekend afternoon?
The probability that he/she neither receives a text message nor an email during any weekend afternoon be 0.3000.
What is meant by probability?The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
Using the method for the union of two sets, we can calculate the number of students who receive either a text message or an email (or both) based on the above data:
Number of students who receive either a text message or an e-mail = Number of students who receive a text message + Number of students who receive an e-mail - Number of students who receive both
= 1364 + 857 - 470
= 1751
The proportion of students who don't receive either a text message or an email divided by the total sample of students is the probability that a student will not receive either:
P(neither T nor E) = (2500 - 1751) / 2500
= 749 / 2500
= 0.2996
Rounding to four decimal places:
P(neither T nor E) = 0.2996 ≈ 0.3000
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. A marketing consultant produced the following graph to show a client how many lawn mowers she could expect to sell, based on how much she spent on advertising. Considering that the consultant wants the graph to show that spending $32,000 on advertising should result in sales of 2200 lawn mowers, choose appropriate units and scales for the two axes. A Horizontal axis: sales, in thousands; vertical axis: dollars, in hundreds B Horizontal axis: sales, in hundreds; vertical axis: dollars, in thousands C Horizontal axis: dollars, in thousands; vertical axis: sales, in hundreds D Horizontal axis: dollars, in hundreds; vertical axis: sales, in thousands
To create this graph, the best option for the information in two axes is "Horizontal axis: sales, in hundreds; vertical axis: dollars, in thousands " (option B)
What information should each axis include?To facilitate data analysis and observation it is recommended to have the sales on the horizontal axis (number of units sold), also known as the x-axis, and the money obtained or profit on the vertical axis or y-axis (dollars).
What units should be used?Considering the current data is $32,000 for 2200 lawnmowers, the best is to use thousands of dollars in the sales while using hundreds in the number of units (2200/ 100 = 22)
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Find the area of the composite figure below. (semicircle). Round to the nearest tenth. Use π = 3.14
Answer:
233.5
Step-by-step explanation:
1) Find the area of the rectangle
Area of rectangle = l × w12 × 11 = 1322) Find the area of the triangle
Area of triangle = (l × w) ÷ 2L = 20 - 11 = 99 × 12 = 108108 ÷ 2 = 543) Find the area of the semicircle
Area of semicircle = (πr²) ÷ 2Radius = diameter ÷ 2 = 11 ÷ 2 = 5.5πr² = 3.14 × 5.5² = 94.98594.985 ÷ 2 = 47.49254) Add the results together
132 + 54 + 47.4925 = 233.49255) Round the nearest tenth
233.4925 = 233.5Have a lovely day :)
A garage ha 2 mechanic. The Bob doe repair correctly on 105 car and
incorrectly on 35 car. Carl doe repair correctly on 51 car and incorrectly on 9 car. If an audit of repair i done, what i the probability that a repair done by the Bob i
done correctly and a repair from Carl wa done incorrectly?
The subject is about finding the joint probability of two independent events: a repair done by Bob being done correctly and a repair done by Carl being done incorrectly.
The answer was determined using the formula for joint probability: P(A and B) = P(A) * P(B), where P(A) is the probability of event A and P(B) is the probability of event B, and A and B are independent events. In this case, event A is a repair done by Bob being done correctly and event B is a repair done by Carl being done incorrectly. The probabilities of each event were calculated by using the number of correctly and incorrectly repaired cars done by each mechanic.
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Can the triangles below be proven similar by the sas similarity postulate?
Answer:
Yes it can!
Step-by-step explanation:
In the given triangles,
∠B = ∠F
Also, ratio of sides given are
2.3/13.8 ≈ 1.67 -> (i)
And 1.9/11.4 ≈ 1.67 -> (ii)
Thus, (i) = (ii)
∴ AB/BF = BC/DF
So we can prove both triangles are similar as the two sides are proportional and the angle between the corresponding sides are equal, so we can use the SAS similarity postulate as the two sets of corresponding sides are proportional and the included angles are congruent .
