Answer:
9
Step-by-step explanation:
The [tex]n[/tex]term is [tex]2n+1[/tex].
[tex]S_n=\frac{3+2n+1}{2}(n)=99 \\ \\ \frac{n(2n+4)}{2}=99 \\ \\ n(n+2)=99 \\ \\ n^2+2n-99=0 \\ \\ (n+11)(n-9)=0 \\ \\ n=9 \text{ } (n>0)[/tex]
The number of terms that needed to make the sum to 99 is 9
The first term of the arithmetic progression = 3
The common difference = 2
The sum of n term is = (n/2) [2a+(n-1)d]
Where a is the initial term
d is the common difference
Substitute the values in the equation
(n/2) [2(3)+(n-1)2] = 99
(n/2) [6 + 2n - 2] = 99
(n/2)[4+2n] = 99
n(2 + n) = 99
2n + [tex]n^2[/tex] = 99
[tex]n^2[/tex] + 2n - 99 = 0
Split the terms
[tex]n^2[/tex] - 9n +11n - 99 =0
n(n -9) + 11(n - 9) = 0
(n + 11)(n - 9) = 0
n = -11 or 9
Since n cannot be a negative number, therefore n = 9
Hence, the number of terms that needed to make the sum to 99 is 9
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Darrien is building a model of the Globe Theatre stage using a scale of 1in:3 feet. On the model, the width of the stage is 15 inches. What is the actual width, in feet, of the stage?
a. 2.5 feet
b. 45 feet
c. 180 feet
d. 540 feet
Answer:
b. 45 ft
Step-by-step explanation:
The scale is 1 in : 3 ft.
1 inch in the model equals 3 feet real.
To go from the model size to the real size, multiply the model inch measurement by 3 and change to feet.
15 inch model size = 15 × 3 ft real size
Answer: 45 ft
if a is an m × n matrix and b is in r m, the general least-squares problem is to find an x that makes ax as close as possible to b. true or false?
The statement that if a is an m × n matrix and b is in r m, the general least-squares problem is is; TRUE
How to Interpret Least squares problem for augmented matrix?The way that we compute a least-squares solution of Ax = b is;
Compute the matrix A T A as well as the vector A T b .Form the needed augmented matrix for the given matrix equation A T Ax = A T b , and then row reduce.This equation is always consistent, and as such any solution K x will be a least-squares solution.By definition, the least squares problem is to find xˆ such that |Axˆ − b| ≤ |Ax − b| for all x in IRⁿ
This means that we are to find a vector x that makes Ax (which is in
the Col(A)) as close to b as possible.
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My-Lien has enough room in her truck to move 3.385 tons of gravel. Her father has asked her to move 3 5/16 tons. My-Lien will have enough room to move the amount of gravel her father has asked her to.
I need this by tonight :) pls my little brother made me make this account for his homework help
Answer:
True
Step-by-step explanation:
You want to know if My-Lien has enough room in a truck with a capacity of 3.385 tons to move 3 5/16 tons of gravel.
Space availableThe empty space can be found by subtracting the load from the capacity of the truck. The attached calculator output shows there is room for an addition 0.0725 tons.
My-Lien will have enough room to move the gravel.
__
Alternate solution
You can convert 3 5/16 to a decimal: 3.3125. Clearly, this amount is less than 3.3850.
Sarah negotiated a price of $25,290.00 for a new Toyota Camry Hybrid Sedan. She is prepared to give a down payment of 13%. Her credit union offered her a 4-year amortized loan for the remaining amount at a rate of 1.75%.
How much money will be paid in interest?
How much will the car cost, in total?
Answer: D
Step-by-step explanation:
The nth term of a series is represented by an=4n/5^n+1 ⋅n.
Otto correctly applies the ratio test to determine whether the series converges or diverges.
Which statement reflects Otto's conclusion?
The nth term of the series is 0.8 < 1 so, the series converges. Therefore, option C is the correct answer.
Given that, the nth term of a series represented by [tex]a_n=\frac{4^n}{5^{n+1}.n}[/tex].
What is the series converges or diverges?A convergent series is a series whose partial sums tend to a specific number, also called a limit. A divergent series is a series whose partial sums, by contrast, don't approach a limit. Divergent series typically go to ∞, go to −∞, or don't approach one specific number.
Next term in the series is [tex]a_{n+1}=\frac{4^{n+1}}{5^{n+2}.(n+1)}[/tex]
Now, the ratio is [tex]|\frac{a_{n+1}}{a_n}| =|\frac{\frac{4^{n+1}}{5^{n+2}.(n+1)}}{\frac{4^n}{5^{n+1}.n}}}|[/tex]
⇒ [tex]\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \lim_{n \to \infty} | \frac{\frac{4^{n+1}}{5^{n+2}.(n+1)}}{\frac{4^n}{5^{n+1}.n}}}|[/tex]
⇒ [tex]\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \lim_{n \to \infty} |\frac{4^{n+1}}{4^n}.\frac{5^{n+2}}{5^{n+1}} .\frac{(n+1)}{n} |[/tex]
⇒ [tex]\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \lim_{n \to \infty} |4.\frac{1}{5}} .\frac{(n+1)}{n} |[/tex]
⇒ [tex]\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \frac{4}{5} \lim_{n \to \infty} |\frac{(n+1)}{n} |[/tex]
⇒ [tex]\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \frac{4}{5} \lim_{n \to \infty} |1+\frac{1}{n} |[/tex]
⇒ [tex]\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= \frac{4}{5} \lim_{n \to \infty} |1+0|[/tex]
⇒ [tex]\lim_{n \to \infty}| \frac{a_{n+1}}{a_n} |= 0.8[/tex]
Since 0.8 < 1 so the series converges.
The nth term of the series is 0.8 < 1 so, the series converges. Therefore, option C is the correct answer.
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Answer:
From the ratio test, r = 0.8. The series converges.
Step-by-step explanation:
TTT
Sam Long anticipates he will need approximately $225,300 in 12 years to cover his 3-year-old daughter's college bills for a 4-year
degree.
How much would he have to invest today at an interest rate of 8% compounded semiannually?
The amount of principal for the given situation is $87,894.37
What is compound interest?
The interest that is paid on both the initial principal and the accumulated past interest is known as compound interest.
The principal, interest rate, and time period are used to calculate compound interest.
Given, compound amount (A) = $225,300
time period (t) = 12 years
interest rate (r) = 8% = 0.08
compounded semiannually (n) = 2
principal amount (P) =?
Then. the compound amount is given by
[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]
or, [tex]225300 = P(1 + \frac{0.08}{2} )^{2*12}[/tex]
or, [tex]P= 225300/(1+0.04)^{24}[/tex]
or, P = 87,894.37
Hence, the amount of investment today is $87,894.37
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Over the interval [0,2π ), what are the solutions tosin (2 x)=sin (x)? Check all that apply. 0 π/3 2π/3 π 4π/3 5π/3
The solutions to the trigonometric equation sin(2x) = sin(x) on the first quadrant is given as follows:
0.π/3.π.5π/3.How to obtain the solutions to the trigonometric equation?
The trigonometric equation in this problem is defined as follows:
sin(2x) = sin(x).
To verify the solutions, we replace each possible solution into each side of the equation, and verify if they are equal, as follows:
sin(2(0)) = sin(0) -> sin(0) = sin(0) -> 0 is a solution.sin(2π/3) = sin(π/3) = sqrt(3)/2, as they are equivalent angles, hence it is a solution.sin(4π/3) = -sqrt(3)/2 = -sin(2π/3), hence it is not a solution.sin(2π) = sin(π) = 0, hence it is a solution.sin(8π/3) = sqrt(3)/2 = -sin(4π/3), hence it is not a solution.sin(10π/3) = -sqrt(3)/2 = sin(5π/3), hence it is a solution.More can be learned about trigonometric equations at https://brainly.com/question/24349828
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the mean systolic blood pressure of all healthy adults is less than 122 mm Hg. Simple data for 281 healthy adults, the mean systolic blood pressure level is 119.87 mm Hg and the standard deviation is 15.21 mm Hg. Complete part a and b. express the original claim in symbolic form. Let the parameter represent a value with respect to systolic blood pressure for a healthy adult
a) The claim is given as follows:
[tex]\mu < 122[/tex]
b) The null and the alternative hypothesis are given as follows:
Null hypothesis: [tex]H_0: \mu \geq 122[/tex].Alternative hypothesis: [tex]H_0: \mu < 122[/tex].What are the null and the alternative hypothesis?The claim in this problem is given as follows:
The mean systolic blood pressure of all healthy adults is less than 122 mm Hg.
Symbolically, the claim is given as follows:
[tex]\mu < 122[/tex].
As:
The symbol [tex]\mu[/tex] represents the mean.The symbol < represents less than.At the null hypothesis, it is tested if there is not enough evidence to conclude that the claim is true, that is, not enough evidence to conclude that the mean systolic blood pressure of all healthy adults is less than 122 mm Hg, hence:
[tex]H_0: \mu \geq 122[/tex].
At the alternative hypothesis, it is tested if there is enough evidence to conclude that the claim is true, that is, enough evidence to conclude that the mean systolic blood pressure of all healthy adults is less than 122 mm Hg, hence:
[tex]H_1: \mu < 122[/tex].
Missing InformationThe questions are given by the image at the end of the answer.
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Karen needs to buy plastic forks. Brand A has a box of 42 forks for $2.17. Brand B has a box of 48 forks for $3.97.
Find the unit price for each brand. Then state which brand is the better buy based on the unit price.
Round your answers to the nearest cent.
The unit price for brand A is $0.0517 and the unit price for brand B is $0.0828. Based on the unit price Brand A is better to buy.
Given that, Brand A has a box of 42 forks for $2.17. Brand B has a box of 48 forks for $3.97.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Here,
The cost of each fork of brand A
= 2.17/42
= $0.0517
The cost of each fork of brand B
= 3.97/48
= $0.0828
Therefore, the unit price for brand A is $0.0517 and the unit price for brand B is $0.0828. Based on the unit price Brand A is better to buy.
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WILL ASSIGN BRAINLIEST
determine the quadratic function of the form f(x)=a(x-h)^2+k
Whose graph is given below
Graph shows -3,8 and 0,-19
The quadratic function of the given graph is y = (x + 3)² + 8.
Quadratic function:
Basically, the standard form of the quadratic function is written as,
f(x) = a(x - h)² + k,
And a not equal to zero.
Here if a is positive, the graph opens upward, and if a is negative, then it opens downward. And the line of symmetry is the vertical line x = h, and the vertex is the point (h,k).
Given,
Here we have the graph and we have to find the quadratic function of the graph.
While we looking in to the given graph,
We have identified then the graph is opening the upward direction, So, the value of a is positive.
Now, we have to find the value of a which is 1.
And the vertex of the graph is (-3, 8).
So, the standard form of the quadratic function of the graph is written as,
=> y = (x + 3)² + 8.
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Please help will mark Brainly
The graph of g(x) = f(x - 5) has a slope of 1 and the y-intercept is -5
How to interpreted the graphA graph is a pictorial representation of data and the graph presented represents g(x) = f(x - 5) is attached
The graph shows a linear function written in the slope intercept form form as
y = mx + c
where
m = slope
c = intercept
x = input variables
y = output variables
Comparing the equation with the above we can see that
m = 1
y intercept, c
this is a point where the graph cuts the y axis
c = -5
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Championship T-shirts sell for $22 each.
What point(s) MUST be on the graph for the quantities to be proportional to each other?
The points that must be on the graph for the quantities to be proportional to each other are (2, 44), (3, 66) and (4, 88)
How to determine the points that must be on the graph?From the question, we have the following parameters that can be used in our computation:
Championship T-shirts sell for $22 each.
The above parameter means that
The unit rate of a T-shirt = $22
This can be represented as
Unit rate = 22
The interpretation of the above rate is that:
The number of n T-shirts is the unit rate multiplied by n
So, we have the following equation
Cost of n shirts = Unit Rate * n
When the number of shirts is 2, we have
Cost of 2 shirts = 22 * 2
Cost of 2 shirts = 44
When the number of shirts is 3, we have
Cost of 3 shirts = 22 * 3
Cost of 3 shirts = 66
When the number of shirts is 4, we have
Cost of 8 shirts = 22 * 4
Cost of 4 shirts = 88
So, the points are (2, 44), (3, 66) and (4, 88)
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For a hypothesis test where H0: μ=μ0, Ha: μ≠μ0, α=0.10 , and n=50, which of the following test statistics reject H0?
The test statistics that reject the null hypothesis are given as follows:
t such that |t| > 1.6766.
When is the null hypothesis rejected?The null hypothesis is rejected when the test statistic is out of the accept done, defined by the critical value.
The critical value is obtained considering these three features are follows:
The significance level.The number of degrees of freedom.The tail.These parameters in this problem are given as follows:
Significance level of 0.10.50 - 1 = 49 degrees of freedom.Two-tailed test, as we are testing if the mean is less than a value.Using a t-distribution calculator, the critical value is given as follows:
t = 1.6766.
Hence, as we have a two-tailed test, test statistics with absolute value greater than the critical value reject the null hypothesis.
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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=7000(1.97)
The given exponential function is increasing so it will be growth and the percentage increase is 97%.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.
As per the given function,
y = 7000(1.97)^x
As x increase the 1.97^x will be increased thus, y will be increased so it will be growth.
Suppose x = 0
y = 7000
Suppose x = 1
y = 1.97 x 7000
% increase = (1.97 x 7000 - 7000)/7000
% increase = 97 %
Hence "The given exponential function is increasing so it will be growth and the percentage increase is 97%".
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How would y-x2=5 be written in function notation
What is the area of 300 meters by 200 meters in sq kilometers
Answer: 0.06 sq km
Step-by-step explanation:
We first convert each dimension from meters to kilometers. 300 meters is equal to 0.3 kilometers. 200 meters is 0.2 kilometers. We now compute the area: 0.3 km * 0.2 km = 0.06 sq km.
can someone help me with, expand 4(3x-5)?
Answer:
Step-by-step explanation:
12x-20
Answer:
Answer: 4 ∙ 3x - 4 ∙ 5
Step-by-step explanation:
10. (03.04 LC)
-
When the function f(x) = 6(9)* is changed to f(x) = 6(9)X + 1, what is the effect? (4 points)
O There is no change to the graph because the exponential portion of the function remains the same.
O All input values are moved one space to the right.
O The x-intercept is one space higher.
The y-intercept is one space higher.
Answer:
It is "The y-intercept is one space higher."
Step-by-step explanation:
Assuming your original equation is 6(9)^X, the + 1 at the end is moving the entire function up since all y values that are the output are 1 higher. This means the point on the y-axis will be one higher, leading us to the answer.
A credit union client deposits $2,500 in an account earning 7% interest, compounded annually. What will the balance of the account be at the end of 21 years?
Enter the answer in dollars and cents, and round to the nearest cent, if needed. Do not include the dollar sign. For example, if the answer is $0.61, only the number 0.61 should be entered.
Balance ≈ $______________ after 21 years.
The balance of the account at the end of 21 years, given the deposit amount and the interest rate is $10, 351. 41
How to find the balance on the account?The balance on the account at the end of 21 years is the future value of the amount in the account today. This means that this balance can be found by the formula:
= Amount deposited x ( 1 + rate) ^ number of years
The balance on the Credit union client's account after 21 years is therefore:
= 2, 500 x ( 1 + 7%) ²¹
= $10, 351. 41
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please refer to picture and answer all parts for brainliest
The value of the given limits [tex]\lim_{x \to \infty} 1/x^2[/tex] is 0,[tex]\lim_{x \to \22} \frac{(x^2-4)}_(x-2)}[/tex] is 4 ,[tex]\lim_{x \to \pi} sinx\\[/tex] is 0 and [tex]\lim_{x \to \55} e[/tex] is e.
What is the limit?Limit, a nearness in mathematical notion, is largely used to give values to some functions at locations that were usually not given or defined, in a manner consistent with neighboring values.
Because the value of that function at that point doesn't define.
a)
[tex]\lim_{x \to \infty} 1/x^2[/tex] by substitute limit 1/∞² = 0
b)
[tex]\lim_{x \to \22} \frac{(x^2-4)}_(x-2)}[/tex] here (x² - 4)/(x - 2) = (x - 2)(x + 2)/(x - 2) = (x + 2)
Putting x = 2 will give the limit as 2 + 2 = 4.
c)
[tex]\lim_{x \to \pi} sinx\\[/tex] herer put x to π so sinπ = 0.
c)
[tex]\lim_{x \to \55} e[/tex] here no variable thus e will be the answer.
Hence "The value of [tex]\lim_{x \to \infty} 1/x^2[/tex] is 0,[tex]\lim_{x \to \22} \frac{(x^2-4)}_(x-2)}[/tex] is 4 ,[tex]\lim_{x \to \pi} sinx\\[/tex] is 0 and [tex]\lim_{x \to \55} e[/tex] is e".
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Multiple Choice You are taking guitar •lessons. The cost of the first lesson is twice the cost of each additional lesson. You spend $360 for 8 lessons. How much did the first lesson cost'7 A $40 (C $50 (E $80 B) $45 (D $60
The first guitar lesson will cost (E $80
How to know the cost of the first lesson'The cost of the first lesson is solved by comparing the costs
Since the cost of the first lesson is twice the cost of each additional lessons, double counting the first lesson makes the total number of lesson to be 9
if 9 lessons costs $360 then 1 lesson will cost
9 = 360
1 = ?
cross multiplying
8 * ? = 360 * 1
? = 360 / 9
? = 40
The unit cost is 40 taking the double counts makes the first lesson to be 2 * 40 = $80 then other lessons are 40
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4x +5 what do I times and add
Answer:
to be real i don´t think you can do anything because they´re not like terms. you can´t combine them (add) because they don´t have anything in common
Step-by-step explanation:
Find the slopes of the lines that are (a) parallel to and (b) perpendicular to the line passing through the pair of points. (7, 3) and (6, −10)
13 is slope of parallel line and -1/13 is slope of perpendicular line.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The given points are (7, 3) and (6, −10)
m=-10-3/6-7
m=-13/-1=13
So slope of line is 13
The equation of line is y=13x+b
Now let us find b.
3=13(7)+b
3=91+b
-88=b
y=13x-88
Now we have to find slope of line parallel to y=13x-88.
The slope of parallel line is 13 because in parallel lines slopes will remain same.
-1/13 is the slope of perpendicular line.
Hence , 13 is slope of parallel line and -1/13 is slope of perpendicular line.
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need help with this math problem; think I have the answer but not quite sure
Answer:
0
-7+7 = 0 0/82=0 0x8-3=0
Which of the following fractions rounds most closely to 0? 7/12 10/11 5/10 1/5
Answer: 1/5
Step-by-step explanation:
Answer: 5/10
Step-by-step explanation:5/10 is the smallest answer here you et get to 0 concluding your answer to 5/10
more than 3.2% of homes have only a landline telephone and no wireless phone. sample data: A survey by the national center for health statistics showed that among 15800 homes 5.81% had landline phones without wireless phones. Complete parts a and b . Express the originall claim in symbolic form. Let the parameter represent a value with respect to homes that have only a landscape telephone and no wireless phone
a) The original claim expressed in symbolic form is; p > 0.032
b) The hypotheses are defined as;
Null hypothesis; H₀: p ≤ 0.032
Alternative hypothesis; Hₐ: p > 0.032
How to define the hypotheses?A hypothesis is defined as an educated guess while using reasonable thinking, about the answer to a scientific question.
a) We are told that the claim is that more than 3.2% (0.032) of homes have only a landline telephone and no wireless phone. Thus, the original claim in symbolic form is; p > 0.032
b) From the sample survey that we see, it is clear that among 15800 homes, 5.81% had landline phones without wireless phones. This would be the sample proportion.
This means that we can define the alternative hypothesis as;
Hₐ: p > 0.032
Null hypothesis is;
H₀: p ≤ 0.032
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How do you think you can find f(3) without using a graph?
Answer:
f(3)=13
Step-by-step explanation:
f(x)=5x-2
f(3)=5(3)-2
=15-2
=13
Find the length of AC and ED.
Answer:
A and C = 13 and D and E = 24
Step-by-step explanation:
GIVEN: g║ h < 1 ≅<2
PROVE: p ║r
Write a two-column proof to prove the given statement above.
The two column proof showing that p ║r is as shown below concluding that p ║r due to The Converse of the Alternate Exterior Angles Theorem
How to carry out a two column proof?The two column proof will be made up of statements and reasons to prove that p ║r. Thus;
Statement 1; g║ h
Reason 1; Given
Statement 2; ∠1 ≅ ∠2
Reason 2; Given
Statement 3; ∠1 ≅ ∠3
Reason 3; Corresponding angles theorem
Statement 4; ∠2 ≅ ∠3
Reason 4; Transitive property
Statement 5; p ║r
Reason 5; The Converse of the Alternate Exterior Angles Theorem
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Solve for x and graph the solution on the number line below. If possible, resolve your answer to a single inequality. In case of no solution (∅), leave the number line blank.
−3x+4≤−23 and−29≥−3x+4
The given inequalities have real or infinite solutions and the graph of the given inequalities is given below.
In the given question we have to solve for x and graph the solution on the number line below. If possible, resolve your answer to a single inequality. In case of no solution (∅), leave the number line blank.
The give inequalities are
−3x+4≤−23...............(1)
−29≥−3x+4
We can write it as
−3x+4≤−29.......................(2)
Subtract equation 1 and 2
−3x+4−(−3x+4)≤ −23−(−29)
Simplifying
−3x+4+3x−4≤ −23+29
0≤ 6
The statement is true. 6 is greater than the 0. So inequality have real or infinite solutions.
The graph of the given inequalities is given below;
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