Answer:
Limit = 2
Step-by-step explanation:
\(\sum _{n=1}^{\infty }\frac{2^n}{3^n}\\= \sum _{n=1}^{\infty \:}\left(\frac{2}{3}\right)^n\\\\= \sum _{n=0}^{\infty \:}\left(\frac{2}{3}\right)^n-\left(\frac{2}{3}\right)^0\)
\(\sum _{n=0}^{\infty \:}\left(\frac{2}{3}\right)^n=3,\\\\= 3-\left(\frac{2}{3}\right)^0\\= 2\)
In this case it does converge, as 2/3 is between 1 and 0
Answer:
0
Step-by-step explanation:
2ⁿ / 3ⁿ = (⅔)ⁿ
⅔ is less than 1, so as n approaches infinity, the sequence approaches 0.
the quotient of x divided by 5 is greater than or equal to 6. Write an inequality and graph its solution
Justin makes 8 dollars for each hour of work. Write an equation to represent his total pay p after working h hours
Which is JK = C solved for K?
Answer:
k=c/j
Step-by-step explanation:
When you calculate (In) 7, you would be finding the
value of which of the following expressions?
O log10 7
O log, 10
O log, e
O log 7
Option (O log 7) refers to the base-10 logarithm of 7, represented as log10(7), which is not the same as ln (7). Optional (O log, 10) and (O log, e) mathematical expressions are not acceptable.
what is logarithm?In mathematics, the logarithm is the reciprocal of a power. As a result, the exponent by which b must be raised to achieve a number x matches its logarithm in base b. For example, because 1000 = 103, the base-10 logarithm is 3, or log10 = 3. For example, the base 10 logarithm of 10 is 2, but the square of 10 is 100. Log 100 = 2. A logarithm (or log) is the mathematical word used to answer questions such as how many times a base of 10 must be multiplied by itself to get 1,000. The answer is 3 (1,000 = 10 10 10).
When you compute (In), you are calculating the natural logarithm of 7, which is indicated as ln(7) or loge (7).
As a result, the expression you'd be looking up the value of is: ln(7) or loge (7).
Option (O log 7) refers to the base-10 logarithm of 7, represented as log10(7), which is not the same as ln (7). Optional (O log, 10) and (O log, e) mathematical expressions are not acceptable.
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AREA OF THESE TWO POLYGONS?
Answer:
Step-by-step explanation:
I need help please! I’ll give brainliest, thank you!
A bookstore has 45 copies of a bestseller available on Saturday morning. Twenty-one customers purchase the book that day. On Monday, a shipment of 25 books arrives and 14 copies are sold. Which statements are correct?
Answer:
Need to see the statements
Step-by-step explanation:
A study was conducted showing the relationship between the average maintenance cost and the age of a car in years.
Number of observations: 13
Least Squares | Standard | T
Parameter | Estimate | Error | Statistic| P-Value
Intercept | 54.7757 | 54.87 | 0.998282 | 0.3396
Slope | 120.689 | 11.8442 | 10.1898 | 0.0000
a) What is the formula for the regression function based on the output above (Write your equation in the context of question)?
b) Interpret the slope of the regression equation (In the context of question)?
c) Construct an 95% interval to predict the maintenance cost for a car that is 7 years old?
d) Based on this analysis, can we conclude that a relationship exists between the maintenance cost and the age of the car in years? What is the null and alternative hypothesis? Justify your answer using three steps process.
Answer:
Step-by-step explanation:
a) The formula for the regression function is:
Maintenance Cost = 54.7757 + 120.689 x Age of Car
b) The slope of the regression equation is 120.689. This means that on average, for every one year increase in the age of a car, the maintenance cost is expected to increase by $120.689.
c) To construct a 95% interval to predict the maintenance cost for a car that is 7 years old, we can use the formula:
Y = a + bX ± tα/2 * SE
where Y is the predicted maintenance cost, a is the intercept, b is the slope, X is the age of the car, tα/2 is the t-value for the 95% confidence level with n-2 degrees of freedom (11 in this case), and SE is the standard error of the estimate.
Plugging in the values, we get:
Y = 54.7757 + 120.689 * 7 ± 2.201 * 11.8442
Y = 923.167 ± 26.010
Therefore, we can be 95% confident that the maintenance cost for a car that is 7 years old will be between $897.16 and $949.17.
d) The null hypothesis is that there is no significant linear relationship between the average maintenance cost and the age of a car in years. The alternative hypothesis is that there is a significant linear relationship between the average maintenance cost and the age of a car in years.
To test the hypothesis, we can perform a t-test on the slope coefficient using the t-statistic and the p-value provided in the output. The t-statistic is 10.1898, which is much greater than the critical t-value at the 0.05 level of significance for a two-tailed test with 11 degrees of freedom (2.201). The p-value is 0.0000, which is less than the significance level of 0.05. Therefore, we can reject the null hypothesis and conclude that there is a significant linear relationship between the maintenance cost and the age of the car in years.
Both of the correct answers equal 2,400 points. Why do they have the same value?
Answer:
because 200 + 200 12 times is equal to 200 x 12Step-by-step explanation:
Answer:
Multiplication is a short way to write repeated addition. So 200 •12 means the same as 200 + 200 + . . . + 200.
Step-by-step explanation:
Use the relationship represented in this Venn diagram to identify the true statement.
A. All trapezoids are rhombuses
B. All rhombuses are trapezoids
C. No trapezoids are rhombuses
D. No rhombuses are trapezoids
The true statement based on the relationship depicted in the Venn diagram is that no rhombuses are trapezoids (option D).
To identify the true statement using the relationship represented in the Venn diagram, we need to analyze the overlapping regions and the properties of the shapes involved.
A trapezoid is a quadrilateral with at least one pair of parallel sides, while a rhombus is a quadrilateral with all sides of equal length. Let's evaluate the options:
A. All trapezoids are rhombuses: This statement is not true based on the diagram. The overlapping region between the trapezoids and rhombuses shows that there are trapezoids that are not rhombuses. Therefore, option A is incorrect.
B. All rhombuses are trapezoids: This statement is true based on the diagram. The entire region representing rhombuses is also included within the region representing trapezoids. Every rhombus can be considered a trapezoid because it has at least one pair of parallel sides. Thus, option B is correct.
C. No trapezoids are rhombuses: This statement is not true based on the diagram. The overlapping region indicates that there are trapezoids that are indeed rhombuses. Therefore, option C is incorrect.
D. No rhombuses are trapezoids: This statement is true based on the diagram. There is no overlap between the regions representing rhombuses and trapezoids, implying that no rhombus can be considered a trapezoid. Hence, option D is correct.
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find the value of each variable in the parallelogram
Answer:
1. x = 15°
2. y = 12
Step-by-step explanation:
1. Determination of the value of x.
(5x – 5) + 110 = 180 (Adjacent angles add up to 180)
5x – 5 + 110 = 180
5x + 105 = 180
Collect like terms
5x = 180 – 105
5x = 75
Divide both side by 5
x = 75/5
x = 15°
2. Determination of the value of y.
3y – 4 = 2y + 8 (opposite sides are equal)
3y – 4 = 2y + 8
Collect like terms
3y – 2y = 8 + 4
y = 12
what is 3/31 + 17/93 as a simple fraction in lowest terms please help fast !!
Answer:
26/93
Step-by-step explanation:
3/31=9/93
9/93 +17/93=26/93
Solve for x. The polygons in each pair are similar.
Answer:
higigj jo Dickenson g three-dimensional
Select the correct answer.
It costs $480.00 to rent an apartment on the Gold Coast for a weekend. Last year it cost $400.00.
What method below shows how you would calculate the % increase?
The method is: Find the increase and find the ratio of the increase and the old price.
The percentage increase is 20%
What method below shows how you would calculate the percentage increase?A percentage is defined as the ratio that can be expressed as a fraction of 100.
The method below shows how you would calculate the % increase.
First step: Find the increase:
increase = 480 - 400 = $80
Second step: Find the ratio of the increase and the old price and multiply by 100 to express in percentage:
80/400 * 100 = 20%
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PLEASE I NEED HELP
Use composition to prove that f(x) and g(x) are inverses. Check your work
F and G are inverse if both of them satisfy the condition h(x)=x. f(g(x))=g(f(x))=x, as we discovered. The argument f(x) and g(x) are inverse functions is thus established.
How do you verify that f x and G x are inverses?If f (x) and g (x) are inverse functions, it can be determined using one of two ways. For more information, see the explanation.
Explanation:
Instance 1
Inverse functions of both functions can be found using the first method.
Example.
Inverse of f (x) = x + 7 is what we're looking for.
We attempt to determine x using the equation y = x + 7.
y = x + 7
Inferring that g (x) is the inverse of f (x) from the fact that x = y 7
Finding g (x inverse )'s is now necessary.
g( x ) = x − 7
y = x − 7
x = y + 7
As a result, we discovered that f (x) is the inverse function of g (x).
f and g are equal if g is inverse of f and vice versa.
The second approach entails locating the compound functions f ( g ( x ) ) and g ( f ( x ) ). In this case, f and g are inverse if they are both h (x ) = x.
Example:
f ( g ( x ) = [ x − 7 ] + 7
G ( x ) placed as x is the expression in brackets.
f ( g ( x ) ) = x − 7 + 7 = x
g (f ( x ) = [ x + 7 ] − 7
f ( x ) inserted as x is the expression in brackets.
g ( f ( x ) ) = x + 7 − 7 = x
The equation f ( g ( x ) ) = g ( f ( x ) ) = x was what we discovered. The argument f (x) and g (x) are inverse functions is thus established.
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Write the equation of a line that goes through (1.-7) and has a slope of -5.
Shen bought a desk on sale for $218.40. This price was 72% less than the original price. What was the original price?
Answer:
780
Step-by-step explanation:
In this example we will call Original Price = y
72%=0.72
218.40=0.72*y
1-0.72=0.28
218.4÷0.28=780
6 ÷ 4 - 2 × 3 PEMDAS
First, do 6 divided by 4
Then, do 2 x 3
Finally, subtract the two numbers you got from the equations before and that the answer.
What is the measure of arc Q R?
26°
52°
104°
128°
Answer:
128
Step-by-step explanation:
i just took the test
Answer: D) 128
Step-by-step explanation:
2. 7th-grade easy math PLEASE Answer this is for a grade
SHOW YOUR WORK AND TAKE A PICTURE
PLS
PLEASE Answer correctly this is for a grade
SHOW YOUR WORK AND TAKE A PICTURE
The expression on the table shows that the shelf pace that the books take is 1 inch per book.
How to calculate the value?Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
It should be noted that from the table, the relationship between the books and the inches is illustrated on the table.
Relationships between two variables that are proportional occur when their ratios are equal. Therefore, this is a proportional relationship and is illustrated as:
= 2/2
= 1
Therefore, there's 1 inch per book.
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Find the value of the sphare
Answer:
\(2304\)\(\pi\)
Step-by-step explanation:
V = \(\frac{4}{3} \pi r^{3}\)
V = \(\frac{4}{3} *\pi * 12*12*12\)
Use 3 to divide one of the 12 which will be equal to 4
V = \(4 *\pi *4*12*12\)
V = \(2304\pi\)
Help help help help help help help help
Answer:
D 4+0.25m
Step-by-step explanation:
Answer:
the answer Is d
Step-by-step explanation:
because you don't know how many miles there will be
In 2021 a 30-second commercial during the Super Bowl cost $5.6 million and the CPI was approximately 271.4. Assuming that price changes are simply due to inflation, what would the same 30 second commercial have cost during the first Super Bowl in 1967, when the CPI was 33.4? Round your answer to the nearest hundred dollars.
In 2021 a 30-second commercial during the Super Bowl cost $5.6 million and the CPI was approximately 271.4. Assuming that price changes are simply due to inflation, when the CPI was 33.4 the estimated cost of a 30-second commercial during the first Super Bowl in 1967 would be approximately $68,900.
To calculate the cost of the 30-second commercial during the first Super Bowl in 1967, we can use the concept of inflation and the Consumer Price Index (CPI).
The CPI measures the average price change of a basket of goods and services over time. By comparing the CPI values of two different years, we can estimate the relative increase in prices due to inflation.
Given data:
Cost of a 30-second commercial in 2021 = $5.6 million
CPI in 2021 = 271.4
CPI in 1967 = 33.4
To calculate the cost in 1967, we need to adjust the 2021 cost for inflation using the CPI ratio:
Cost in 1967 = (Cost in 2021) * (CPI in 1967 / CPI in 2021)
Cost in 1967 = ($5.6 million) * (33.4 / 271.4)
Cost in 1967 ≈ $0.689 million
To round the cost to the nearest hundred dollars, we can multiply the cost by 100 and round it to the nearest whole number:
Cost in 1967 ≈ $68,900
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Multiply both equations by a constant
Answer:
(- \(\frac{1}{3}\), \(\frac{3}{4}\) )
Step-by-step explanation:
9x + 8y = 3 → (1)
6x - 12y = - 11 → (2)
Multiplying (1) by 12 and (2) by 8 and adding will eliminate the y- term
108x + 96y = 36 → (3)
48x - 96y = - 88 → (4)
Add (3) and (4) term by term to eliminate y
156x = - 52 ( divide both sides by 156 )
x = \(\frac{-52}{156}\) = - \(\frac{1}{3}\)
Substitute this value into either of the 2 equations and solve for y
Substituting into (1)
9(- \(\frac{1}{3}\) ) + 8y = 3
- 3 + 8y = 3 ( add 3 to both sides )
8y = 6 ( divide both sides by 8 )
y = \(\frac{6}{8}\) = \(\frac{3}{4}\)
solution is (- \(\frac{1}{3}\), \(\frac{3}{4}\) )
Which of the following is the explicit rule for a geometric sequence de
a recursive formula of a = 138,- for which the first term is 7?
O A. an = 13.70-1
O B. an = 761301-1
O c. an= 7.130+1
D. an = 13.70+1
3+ a equals 17 when a equals four is this given value a solution of the equation or an quality?
mnbvcxAnswer:
Step-by-step explanation:dfghjmjnhgf
Can someone PLEASE HELP ME WITH THIS QUESTION I REALLY NEED HELP
Integer includes all negative and positive whole numbers including zeros
A store is having a sale on trail mix and jelly beans. For 5 pounds of trail mix and 3 pounds of jelly beans, the total cost is $22. For 2 pounds of trail mix and 12 pounds of jelly beans, the total cost is $25. Find the cost for each pound of trail mix and each pound of jelly beans.
Solving a system of equations we can see that each pound of trail mix costs $3.50, and each pound of jelly beans costs $1.50
How to find the cost of each?Let's define the variables:
x = cost of a pound of trail mix.y = cost of a pound of jelly beans.Then we can write a system of equations so we will get:
5x + 3y = 22
2x + 12y = 25
To solve this, we can subtract 4 times the first equation fom the second one:
2x + 12y - 4(5x + 3y) = 25 - 4*22
2x + 12y - 20x - 12y = -63
-18x = -63
x = -63/-18
x = 3.5
That is the cost of each pound of trail mix, and replacing that in one of the equations:
2*3.5 + 12y = 25
y = (25 - 2*3.5)/12
y = 1.5
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what is 2y is y = -3
Answer:
-6
Step-by-step explanation:
2 x -3 = -6
1 positive and a negative integer multiplied will get a negative answer
18) Solve for side AC.
A) 1.10
B) 8.24
C) 9.50
70
C
3
B
Step-by-step explanation:
tan0=opp/adj
where opposite =3,adjacent =x,=70
tan 70=3/x
2.7474=3/x
2.7474x=3
divide both sides by 2.7474
x=3/2.7474
x=1.0919
x=1.10 to 1 d.p