The 100th term of the arithmetic sequence is 203.
Let the first term of the arithmetic sequence be a and the common difference be d.
The general term of the sequence is given by
[tex]T_{n} = a + (n-1)d[/tex]
It is given that the 6th term is 15, we have :
[tex]T_{6} = a +5d[/tex]
a + 5d = 15......equation(1)
It is given that the 9th term is three times the 2nd term, we have :
[tex]T_{9} = 3*T_{2} \\a + 8d = 3(a +d)\\a + 8d = 3a +3d\\a -3a = 3d -8d = -5d\\-2a = -5d\\2a = 5d\\a = \frac{5d}{2}[/tex]
Putting this value in equation(1)
[tex]\frac{5d}{2} + 5d = 15 \\\\5d + 10d = 30\\15d= 30\\d = \frac{30}{15} = 2[/tex]
a = 5*2/2 = 5
Hence, the first term is 5 and the common difference is 2.
Now, evaluating the 100th term of the sequence, we have :
[tex]T_{n} = a +(n-1)d\\T_{100} = a +99d\\T_{100} = 5 +99*2 = 5 +198 = 203[/tex]
Hence, the 100th term of the arithmetic sequence is 203.
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PreviousWhich of the following sampling methods would most likely have the largest margin of error?OA. Roll a die 100 times and estimate the proportion of 3's that result.OB. Sample 10 adults and ask them if they regularly smoke cigarettes and use this data to represent the proportion of adults who smoke in a community.OC. Sample 500 registered voters in a large city and ask them their political preference and use the results to estimate the breakdown by party of all registered voters in the citOD. Flip a coin 1000 times and estimate the proportion of "heads" that result.Reset SelectionNextacer
have the largest margin of error
The more trials or samples that occur, the greater the chance of making mistakes. or increasing the margin error,
then the sample with a largest margin of error is
flip a coin 1000 times
I need help with this practice problem solving. It asks to graph the function yourselfIf you can, use desmos.
Given the function:
[tex]f(x)=\cot (x+\frac{\pi}{6})[/tex]To graph the given function, first, we will graph the parent function [ cot x]
the function [cot x] has a period of π and has an x-intercept at x = π/2
then we will make a shift to the left side by (π/6)
the graph of the function will be as shown in the following picture:
As shown, the red dot graph is the function [cot x]
and the blue graph is the given function f(x)
Can someone help with these two pages if possible?
The rules of the transformations using the translation notation are;
11) [tex]T_{(2, \,-1)}[/tex]
12) [tex]T_{(-5, \,2)}[/tex]
13) [tex]T_{(-1, \,3)}[/tex]
14) [tex]T_{(0, \,-1)}[/tex]
15) [tex]T_{(3, \,4)}[/tex]
16) [tex]T_{(-3, \,1)}[/tex]
17) [tex]T_{(1, \,0)}[/tex]
18) [tex]T_{(6, \,-5)}[/tex]
19) [tex]T_{(4, \,0)}[/tex]
20) [tex]T_{(2, \,4)}[/tex]
21) [tex]T_{(1, \,-5)}[/tex]
22) [tex]T_{(5, \,-1)}[/tex]
23) [tex]T_{(0, \,-1)}[/tex]
24) [tex]T_{(-2, \,-1)}[/tex]
25) [tex]T_{(-3, \,-2)}[/tex]
What is a translation transformation?A translation transformation is a rigid transformation in which the location of the image obtained from the pre-image is different, but the dimensions are the same.
11) The transformation is similar to a rigid transformation
The change in coordinate is from (2, 2), to (4, 1), which is a translation 2 units to the right and -1 unit down
12) The shape is preserved and the length of the sides are also preserved, therefore, the transformation is a rigid transformation, with a change from (5, 3) to (0, 5), which is a translation 5 units to the left and 2 units up.
13) The change in the coordinates from the pre-image to the image are from V(-3, 2) to V(-4, 5), which is a transformation of 1 unit to the left and 3 units up
14) The coordinates of a point on the pre-image is T(-5, 2), and the coordinates of the corresponding point on the image is T'(-5, 1), which is a translation of one unit downwards, [tex]T_{(0, \,-1)}[/tex]
15) A point on the pre-image is T(-3, -1), the corresponding point on the image is T'(0, 3), which indicates that the rule for the transformation is a translation of 3 units to the right and a vertical translation of 4 units upwards
16) The difference between the x and y values are;
Δx = 0 - 3 = -3
Δy = -3 - (-4) = 1
The transformation is therefore of the form [tex]T_{(-3, \,1)}[/tex], which is a translation of 3 units to the left and 1 unit upwards
17) The change in the x and y values are;
Δx = -2 - (-3) = 1
Δy = -3 - (-3) = 0
The rule of the transformation is therefore of the form [tex]T_{(1, \,0)}[/tex], which is a translation one unit to the right.
18) The change in the x and y values of the transformation are;
Δx = 1 - (-5) = 6
Δy = -4 - 1 = -5
The rule of the transformation is therefore, [tex]T_{(6, \,-5)}[/tex], which is a translation of 6 units to the right and 5 units down
19) The transformation of J(-5, 3), K(-3, 5), L(0, 1) to J'(-1, 3), K'(1, 5), L'($, 1) is a transformation of the form [tex]T_{(4, \,0)}[/tex] which is a horizontal translation 4 units to the right
20) H(-4, -3), I(-5, 0), J(-3, 0), K(-2, 1) to H'(-2, 1), 'I(-3, 4), J'(-1, 4), K'(0, 5) The transformation rule is [tex]T_{(2, \,4)}[/tex], which is a translation 2 units to the right and 3 units up
21) E(0, 1), F(-1, 5), G(0, 5), H(3, 2), to E'(1, -4), F'(0, 0), G'(1, 0), H'(4, -3), which is a transformation with the rule, [tex]T_{(1, \,-5)}[/tex], which is a translation one unit to the right and five units down
22) B(-4, -2), C(-3, 3), D(-2, 1) to B'(1, -3), C'(2, 2), D'(3, 0), which is a transformation of the form [tex]T_{(5, \,-1)}[/tex], which is a translation of 5 units to the right and 1 units down
23) I(2, 1), H(4, 4), G(5, 0) to I'(2, 0), H'(4, 3), G'(5, -1), which is a transformation with the rule [tex]T_{(0, \,-1)}[/tex], which is a translation of one unit down
24) X(1, -4) W(3, 0), V(3, -4) to X(3, -5) W(5, -1), V(5, -5), which is a transformation with the rule, [tex]T_{(-2, \,-1)}[/tex], which is a translation of 2 units to the left and 1 units down
25) G(1, -1), F(2, 3), E(4, 2), D(4, -3) to G'(-2, -3), F'(-1, 1), E'(1, 0), D'(1, -5) which is a transformation with the rule, [tex]T_{(-3, \,-2)}[/tex], which is a translation of 3 units to the left and 2 units down
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explain the error a problem states that Ursula earns $9 per hour to write an expression that tells you how much money that Ursula earns for H hours. Joshua 9 / h and Sarah wrote 9h who's expression is correct and why
We will have that Sarah's function is the correct one, since each hour she will get $9, then when we multiply will give us the amount of money she makes in the number of hours.
H = 9h
a population of amoebas in a petri dish will triple in size every hour .at the start of an experiment the population is =800x^3 where x is the number of hours models the population growth how amoebas are in the perri dish after 9 hours
From the given information, we know that the expression that models the population of amoebas with respect to time is:
[tex]P=8x^3[/tex]Where x is the number of hours. by replacing 9 for x, we can find the population after 9 hours, like this:
[tex]\begin{gathered} P=8\times9^3 \\ P=8\times729 \\ P=5832 \end{gathered}[/tex]Then, the population of amoebas after 9 hours is 5832.
1. A roll of ribbon contains 5 yards of ribbon, Janet cuts 1 yards of ribbon from the roll. How much ribbon is left on the roll? 4įyards 3ş yards 6 yards 4ş yards
Given that the total length of the ribbon on the roll is 5 yards.
Janet cuts 1 (1/3) yards of ribbon from the roll, then the remaining length of ribbon on the roll is calculated as,
[tex]\begin{gathered} \text{Remaining Ribbon length=Total Length-Length cut out} \\ \text{Remaining Ribbon length=}5\text{ yards-1}\frac{1}{3}\text{ yards} \\ \text{Remaining Ribbon length=}(5-\frac{4}{3})\text{ yards} \\ \text{Remaining Ribbon length=(}\frac{15-4}{3})\text{ yards} \\ \text{Remaining Ribbon length=(}\frac{11}{3})\text{ yards} \\ \text{Remaining Ribbon length=3}\frac{2}{3}\text{ yards} \end{gathered}[/tex]Thus, the length of the ribbon left on the roll is 3 (2/3) yards.
So the second option is the correct choice.
how do i solve each system for these equations
x-y=4 2x+y=5
Answer:
x = 3
y = -1
Step-by-step explanation:
x-y=4 [1]
2x+y=5 [2]
rearrange [1] and label it [3]
x = 4 + y [3]
substitute [3] into [2]
2(4 + y) + y = 5
8 + 3y = 5
3y = -3
y = -1
substitute y = -1 into [1]
x - (-1) = 4
x = 3
3. the mean lifetime for cardiac stents is 8.7 years. a medical device company has implemented some improvements in the manufacturing process and hypothesizes that the lifetime is now longer. a study of 100 new devices reveals a mean lifetime of 9.3 years with a standard deviation of 3.8 years. is there statistical evidence of a prolonged lifetime of the stents?
There is no statistical evidence of a prolonged lifetime of the stents.
Given data,
n (sample size) = 100
X (sample mean) = 9.3
s (sample standard deviation) = 3.8
Next, we need to define the null hypothesis and alternative hypothesis
Null hypothesis
[tex]H_{o}[/tex] : u (mu) = 8.7
Alternative hyptohesis
[tex]H_{o}[/tex] : u (mu) > 8.7
Next, we need to do hypothesis testing to get the claim about a population mean is tested under the null and the alternative hypotheses by using t-test and p-value.
t-test is a sampling test statistic and used when the population standard deviation is unknown.
the t-test can be calculated as follows:
= [tex]\frac{X-u}{s/\sqrt{n} }[/tex]
= [tex]\frac{9.3-8.7}{3.8/\sqrt{100} }[/tex]
= 1.578
Next, we need to calculate the p-value using Microsoft excel function. The p-value helps decide whether to reject the null hypothesis.
Enter the function below in excel to calculate p-value:
=TDIST(1.578,40-1,1)
= 0.061322.
The p-values is greater than the common threshold ( p<0.05), which means We can conclude that there is no statistical evidence of a prolonged lifetime of the stents.
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Hello I got this wrong will you help me solve
Solve for y
[tex]4x+3y=-21[/tex]Subtract 4x both sides
[tex]\begin{gathered} 4x+3y-4x=-21-4x \\ 3y=-21-4x \\ \end{gathered}[/tex]Divide by 3 into both sides
[tex]\begin{gathered} \frac{3y}{3}=-\frac{21}{3}-\frac{4x}{3} \\ y=-7-\frac{4}{3}x \\ by\text{ reordering} \\ y=-\frac{4}{3}x-7 \end{gathered}[/tex]Answer:
[tex]y=-\frac{4}{3}x-7[/tex]What is the equation of a line that passes through (1,4) and (3, -6)?l
The equation of the line is that passes through (1,4) and (3, -6) is
y = -5x + 9
First, write the equation in slope-intercept form:
y = mx + b
(the m is the slope, and b is the y-intercept)
Now, Lets find the slope(m) of the line by using the formula:
y2-y1/x2-x1
(-6 - 4)/ (3 - 1) = -10/2 = -5
Next, find the y-intercept (b) by using the slope-intercept form equation and substituting -5 in for m and one of the ordered pairs in for x and y:
4 = (-5)(1) + b
b = 9
-OR-
-6 = (-5)(3) + b
b = -6 + 15 = 9
b = 9
Now, we can write the full equation of the line:
y = -5x + 9 is the answer
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Landyn's brother is five years older than Landyn. Their combined ages add up to 23. How old is Landyn?
The variable y represents: []
Equation: [] (Make sure to simplify this!)
Landyn is 9 years old.
Answer:
X = 9
Landyn is 9 and his brother is 14
Step-by-step explanation:
X + Y = 23
Y = X + 5
X + X + 5 = 23
2x + 5 + 23
- 5 - 5
2x / 2 = 18 / 2
Simplified = 9 / 1
Y = 9 + 5
Y = 14
through -4,-5 parrelel to y=1/2x-4
The equation of the line that passes through the point (-4, -5) and is parallel to y = 1/2x -4 is y = 1/2x - 3
Equation of a straight line passing through a given pointFrom the question, we are to determine the equation of the line that passes through the given point and is parallel to the given equation.
The given point is (-4, -5)
The given equation is y = 1/2x - 4
NOTE: If two lines are parallel, then their slopes are equal
Now, we will determine the slope of the given line '
y = 1/2x - 4
Compare to the general form of an equation of a straight line
y = mx + b
Where m is the slope
and b is the y-intercept
Therefore, m = 1/2
That is, the slope of the line is 1/2
Now, we will determine the equation of the line that has a slope of 1/2 and that passes through the point (-4, -5)
Using the point-slope form of the equation of a straight line
y - y₁ = m(x - x₁)
Then,
y - (-5) = 1/2(x - (-4))
y + 5 = 1/2(x + 4)
y + 5 = 1/2x + 2
y = 1/2x + 2 - 5
y = 1/2x -3
Hence, the equation of the line is y = 1/2x - 3
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If ED is the midsegment of ABC, which of the following statements are necessarily true?
If ED is the midsegment of triangle ABC, then that means that the points E and D are the midpoints of segments AC and AB since the midsegment is found by joining the midpoints of a triangle. Since E and D are midpoints then:
[tex]AE\cong EC[/tex]Also, by the midsegments theorem we have:
[tex]ED=2BC[/tex]Also, since segments ED and BC are parallel, that means that:
[tex]\angle ADE\cong\angle ABC[/tex]On a road map, the distance from City A to City B is 4 inches. The map scale is 1 inch = 20 miles. What is the actual distance, in miles, between City A and City B? A. 5 miles B. 24 miles C. 48 miles D. 80 miles
Answer: D. 80 miles
Step-by-step explanation:
if 1 inch is 20 miles, then 4 inches is 4 x 20 = 80 miles what is real distance between City A and City B
1 inch = 20 miles4 inch = 4 x 1 inch = 4 x 20 miles = 80 milesAnswer:
D. 80 miles
Step-by-step explanation:
If the map distance between Cities A and B is 4 in, and the map scale is 1 in = 20 mi, then the actual distance between Cities A and B is:
[tex]\frac{4\text{ in}}{1}\times\frac{20\text{ mi}}{1\text{ in}}=\frac{80\text{ mi}}{1}=80\text{ mi}[/tex]
In other words, every one inch on the map equates to 20 miles in actual distance. Therefore, 4 inches equates to 80 miles.
If a graph includes the points (2,5) and (8,5) which of the following must be true ? 1.it is the graph of a linear function 2.it is not the graph of a function 3.it is the graph of an increasing function 4.none of the above
Answer
Option 1 is correct.
The graph could easily be the graph of a linear function.
Explanation
The points (2, 5) and (8, 5) can be seen to lie on the same line of y = 5
So, we can conclude that the graph could be a simple linear function, or a curve that passes this point twice.
So, option A is the only correct option here.
Hope this Helps!!!
Which of the following does () simplify to, for any nonnegative real number?
Solution
[tex](\sqrt[]{r})^2[/tex]We have
square will cancel out the square root
[tex](\sqrt[]{r})^2=(r)=r[/tex]Option A
1. Which is an example of categorical data?A eye colorB ageC weight
Age and you can also use weight too
you can easily group people by their age and weight but not by eye color
example
age people
5 - 10 14
10 - 15 5
the table above shows that we have 14 people within the range of 5 to 10 years
and likewise the weight of the people can serve the same purpose
A travel agency charges $64 for each bus ticket and $82 for each train ticket. How much does it cost for 3 bus tickets and 4 train tickets?
Cost of 3 bus tickets is $ 192 and cost of 4 train tickets is $ 328.
Explain the use of multiplication?
The process of finding the sum of two or more numbers is known as multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. We can rapidly determine the total number of things by multiplying.
When multiplying, we'll consider the number of groups with similar sizes and the number of items in each group.
It is given ,
Cost of each bus ticket = $ 64
Cost of each train ticket = $ 82
Number of bus ticket = 3
Number of train ticket = 4
Total cost of bus ticket = 3 × 64 = $ 192
Total cost of train ticket = 4 × 82 = $ 328
Hence , cost of 3 bus tickets is $ 192 and cost of 4 train tickets is $ 328.
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A new streaming service sent out a survey to 250 households to see who would be interested in its service. The company found that it could charge $45 per month, with a margin of error of ±1.5. If 1,000 people signed up for the service, what is the least amount of monthly revenue the company should expect?
$43,500
$45,250
$46,500
$47,000
Answer:
$43,500
Step-by-step explanation:
Charge for the month - margin of error
= 45 - 1.5
= $43.50
= 43.50 x 1,000
= $43,500
kinda due now pls help
The function describes the motorboat's distance from the shore
y = -4x+50
Given,
In the question:
A motorboat moves across a lake as a constant speed. when it begins, it is 50 km from the shore
After 9 minutes, it is 14 km from the shore.
So, The rate of change =
= [tex]\frac{Final Distance - initial distance}{time} \\\\\frac{14-50}{9} = -4[/tex]
Negative sign shows that there is decrease in distance per minute
The rate of change of distance is 4 km / minutes
General equation : y = mx+ c
Where m is the slope and c is the constant
Substitute the values in the equation :
y= -4x +50
Where y is the final distance and x is the minutes
So, Option C is true
Hence, The function describes the motorboat's distance from the shore
y = -4x + 50.
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Stevenson’s Market is selling 3 packs of toothpicks for $0.87. How much will 10 packs of toothpicks cost at this price? Round your answer to the nearest cent.
Answer:
$2.90
Step-by-step explanation:
87 cents / 3 packs = 29 cents per pack
$0.29 × 10 = $2.90
Vector v has an initial point at (9, 3) and a terminal point at (16, 12). Which of the following represents the linear form of v?
Answer:
The coordinate of the initial point is given below as
[tex](x_1,y_1)\Rightarrow(9,3)[/tex]The coordinate of the terminal point is
[tex](x_2,y_2)\Rightarrow(16,12)[/tex]Concept:
The formula below will be used to calculate a linear form of v
[tex]\Rightarrow(x_2-x_1)i+(y_2-y_1)j_{}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \Rightarrow(x_2-x_1)i+(y_2-y_1)j_{} \\ \Rightarrow(16-9)i+(12-3)j \\ \Rightarrow7i+9j \end{gathered}[/tex]Hence,
The final answer is
[tex]v=7i+9j[/tex]The FIRST OPTION is the right answer
true or false? the solutions for y>x+3 are all in the points in the shaded half plane but does not include points on the line y=x+3
When we have an inequality with the symbols < or >, the boundary line of the solution area will not be included in the solution of the inequality, then in this case that we have y>x+3 the solution set are all the points in the shaded half-plane but does not include points on the line y=x+3, and the answer is true
Jacob is buying pizza dough at the store to make pizzas for his family.
For every 15 pizza doughs he buys, he pays $20.
What is the price per pizza dough?
Answer: $1.33
This can be worked out as a simple algebra problem: 15x=20, x being 1 pizza dough. In order to find the value of one pizza dough (x) you need to isolate it. To do that, divide 15 from both sides and you'll be left with x=1.33
15x=20
/15 /15
x=1.33
What is the equation for this please help
Answer:
the equation would be 1.67x+0
4. Find each amount:
3.8% of 25
0.2% of 50
180.5% of 99
how do I find and explain this??
The result of each part is
Part 1
3.8% of 25 is 0.95
Part 2
0.2% of 50 is 0.1
Part 3
180.5% of 99 is 178.695
Part 1
The given expression is
3.8% of 25
Here we have to find the 3.8 percentage of 25
Then the mathematical expression will be
25 × 3.8% = 25 × 3.8/100
= 25 × 0.038
= 0.95
Part 2
The given expression is
0.2% of 50
The mathematical expression will be
50 × 0.2% = 50 × 0.2/100
= 50 × 0.002
= 0.1
Part 3
The expression is
180.5% of 99
The mathematical expression will be
99 × 180.5% = 99 × 180.5/100
= 99 × 1.805
= 178.695
Hence, the result of each part is
Part 1
3.8% of 25 is 0.95
Part 2
0.2% of 50 is 0.1
Part 3
180.5% of 99 is 178.695
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
length = 12 miles
width = 6 miles
Step-by-step explanation:
Framing algebraic expression and solving:length = x miles
width = (x - 6) miles
Area of rectangle = 72 square miles
length * width = 72
x * (x - 6) = 72
x*x - 6*x = 72
x² - 6x - 72 = 0
Sum = -6
Product = -72
Factors = 6 , (-12) { 6 + (-12) = -6 and 6*(-12) =-72 }
Rewrite the middle term using the factors.
x² + 6x - 12x - 72 = 0
x(x + 6) -12(x + 6) =0
(x + 6)(x - 12) = 0
{x + 6 = 0 is rejected as length will not have negative value}
x - 12 = 0
[tex]\sf \boxed{\bf x = 12 \ miles}[/tex]
length = 12 miles
Width = 12 - 6 = 6 miles
what is the value of X? 16X = 156.8
the given expression is,
16x = 156.8
x = 156.8/16
x = 9.8
thus, the answer is 9.8
Answer:
x = 9.8
Step-by-step explanation:
16x=156.8
x = 156.8/16
x = 9.8
13. Suppose you live in a state that collects 18.2c excise tax on a gallonof gasoline. If you buy 18.5 gallons of gasoline, how much state excise taxis collected?a, $3.06b 83.37$2.99C
The excise tax on 1 gallon of gasoline = 18.2 cents
You will buy 18.5 gallons
We need to find the excise tax you should pay
At first let us change the cent to dollar
1 cent = 1/100 dollars
18.2 cents = 18.2 * 1/100 = 0.182 dollars
Now you will buy 18.5 gallons
You will pay = 18.5 * 0.182 = 3.367 Dollars
The state excise tax = $3.367
Round the number to the nearest cent, then it will be $3.37
What is the midpoint of the line segment with the endpoint (3.5,2.2) and (1.5,-4.8)?
Given
A = (3.5, 2.2)
B = (1.5, -4.8)
Procedure
A midpoint is a point on a line segment that divides the segment into two equal segments.