The expression that represents the area of the new room is (c) 3.5s^2 + 5.25s
How to determine the area of the new room?The given parameters are:
Wall =Square
Length = s
When the wall of the square room is torn down and rebuilt, the area of the new room is represented by 1.75s(2s + 3).
This means that
Area= 1.75s(2s + 3)
Expand the expression
Area= 1.75s * 2s + 1.75s * 3
Evaluate the products
Area= 3.5s^2 + 5.25s
This means that the expression that represents the area of the new room is (c) 3.5s^2 + 5.25s
Hence, the expression that represents the area of the new room is (c) 3.5s^2 + 5.25s
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CAN SOMEONE HELP PLEASE!
Answer:
None of these
Step-by-step explanation:
[tex]\frac{360}{n}=24 \implies n=15[/tex]
This is called a pentadecagon.
2. What is the value of x? Show your work.
can someone explain this to me? how would I find X? Thank you in advance!
Answer:
7
Step-by-step explanation:
→ Find the scale factor
30 ÷ 25 = 1.2
→ Multiply answer by 20
20 × 1.2 = 24
→ Equate equation to 24
4x - 4 = 24
→ Add 4 to both sides
4x = 28
→ Divide both sides by 4
x = 7
please help me! in need of help due tomorrow!
Answer:
Step-by-step explanation:
(1). A = π r²
A = 4 π
Area of shaded region is [tex]\frac{4\pi *260}{360}[/tex] = [tex]\frac{26}{9} \pi[/tex] or [tex]\frac{26\pi }{9}[/tex]
(2). C = 4 π
In this case, the length of the bigger arc and the area of shaded region happen to be the same.
The length of the arc ADB is [tex]\frac{26}{9} \pi[/tex] or [tex]\frac{26\pi }{9}[/tex]
What is the measure of
Answer:
C
Step-by-step explanation:
[tex]\cos E=\frac{11}{18} \\ \\ E=\cos^{-1} \left(\frac{11}{18} \right) \\ \\ E \approx 52.33^{\circ}[/tex]
Help me with this please asap?!
Answer:
None of these answers are correct.
Step-by-step explanation:
[tex]QR=\frac{25+45}{2}=35[/tex]
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
By Trapezoid mid - segment theorem :
[tex] \qquad❖ \: \sf \:QR = \cfrac{MN+ OP}{2} [/tex]
[tex] \qquad❖ \: \sf \:QR= \cfrac{25+ 45}{2} [/tex]
[tex] \qquad❖ \: \sf \:QR = \cfrac{70}{2} [/tex]
[tex] \qquad❖ \: \sf \:QR= 35 \: \: units[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
length of segment QR = 35F(v) =2x if g(x)=5x then f(g(x)
Answer:
10x
Step-by-step explanation:
g(x)=5x
f(x)=2x
f(g(x))=f(5x)
f(g(x))=2*5x=10x
How would you prove that Angle2 ≈ Angle4?
Angles 2 and 4 are corresponding angles. They are congruent, not supplementary because they have the same measure and do not add up to 180 degrees. Therefore, the answer is the third option. Corresponding angles are congruent.
if u=–s^2rt then what does r equal?
The required rewritten equation in terms of variable 'r' is r = -u/s²t. By applying simple arithmetic operations, the required equation is obtained.
How to rewrite an equation in terms of another variable?Consider an equation c = ax + by. Solving for variable 'a'.
Step1: Write the required variable terms on one side
Step2: Add/Subtract like terms if any or take common if any
Step3: Divide/Multiply the coefficient of the required variable
Step4: simplify the obtained terms for the required variable
As follows:
c = ax + by
⇒ ax = by - c
⇒ ax/x = (by - c)/x
∴ a = (by - c)/x
Calculation:The given equation is u = -s²rt
dividing by 't' on both sides:
⇒ u/t = -s²rt/t
⇒ u/t = -s²r
dividing by 's²' on both sides:
⇒ u/s²t = -s²r/s²
⇒ u/s²t = -r
∴ r = -u/s²t
Thus, the required equation for variable 'r' is r = -u/s²t.
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Identify the vertex of the parabola ?
Step-by-step explanation:
second one
explanation: trust me bro
Which of the following statements is equivalent to 10x – 30? 10(x – 30) 10(x – 3) 10 + (x – 20) 10(x – 20)
Answer:
10(x-3) is equivalent to 10x – 30
Step-by-step explanation:
First you have to take everything of out the parentheses and then simplify if needed.
10(x – 30) is not equivalent to 10x – 30 because, 10 times x is 10x, but 10 times 30 is 300. So, 10(x – 30) is not equivalent to 10x – 30.10(x – 3) is equivalent to 10x – 30 because, 10 times x is 10x, and 10 times 3 is 30. So, 10(x – 3) is equivalent to 10x – 30.10 + (x – 20) is not equivalent to 10x – 30 because, 10 minis 20 plus x are -10 + x. So, 10+(x – 20) is not equivalent to 10x – 30.10(x – 20) is not equivalent to 10x – 30 because, 10 times x is 10x, but 10 times 20 is 200. So, 10(x – 20) is not equivalent to 10x – 30.Answer: 10(x-3) is equivalent to 10x – 30
An investment pays 10% interest compounded monthly. What percent, as a decimal, is the effective annual yield? Enter your answer as a decimal rounded to four decimal places.
[tex]~~~~~~ \textit{Annual Percent Yield Formula} \\\\ ~~~~~~~~~~~~ APY=\left(1+\frac{r}{n}\right)^{n}-1 ~\hfill \begin{cases} r=rate\to 10\%\to \frac{10}{100}\dotfill &0.1\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12 \end{cases} \\\\\\ APY=\left(1+\frac{0.1}{12}\right)^{12}-1\implies APY=\left( \frac{121}{120} \right)^{12}-1\implies APY\approx 0.1047[/tex]
I need help with this question:
Simplify
The simplified form of the given expression as a fraction is 7x/x-7
Simplification of fractionsFractions are written as a ratio of two integers. For instance a/b is a fraction where a and b are integers.
Given the expression below;
(1/7+1/x)/(1/49+1/x²)
Find the LCM to have:
(x+7/7x)/(x²-49)/49x²
Divide to have:
x+7/7x * 49x²/(x²-49)
(x+7) * 7x/(x+7)(x-7)
Cancel out the like terms to have:
1 * 7x/x-7
= 7x/x-7
Hence the simplified form of the given expression as a fraction is 7x/x-7
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1+r+r²+...........+r^n+1=1-r^n/1-r
mathematical induction mesthod
Answer + Step-by-step explanation:
the correct question:
For r ≠ 1 ,Prove using the mathematical induction method that :
[tex]1+\cdots+r^n =\frac{1-r^{n+1}}{1-r}[/tex]
………………………………………………………………………………………………………………
for n = 0 :
1⁰ = 1 and (1 - r⁰⁺¹)/(1 - r) = (1 - r)/(1 - r) = 1
Then the property is true for n = 0.
For n ≥ 0 :
Suppose
[tex]1+\cdots+r^n =\frac{1-r^{n+1}}{1-r}[/tex]
And prove that
[tex]1+\cdots+r^{n+1} =\frac{1-r^{n+2}}{1-r}[/tex]
Since :
[tex]1+\cdots+r^{n+1} =(1+\cdots+r^n)+r^{n+1}[/tex]
Then
[tex]1+\cdots+r^n+r^{n+1} =\frac{1-r^{n+1}}{1-r}+r^{n+1}[/tex]
[tex]= \frac{1-r^{n+1}+r^{n+1}(1-r)}{1-r}[/tex]
[tex]= \frac{1-r^{n+2}}{1-r}[/tex]
Then according to the mathematical induction method
[tex]1+\cdots+r^n =\frac{1-r^{n+1}}{1-r}[/tex]
Where n is a natural number and r ≠ 1.
Could you please help me solve this question?
Brandon enters bike races. He bikes 91 half miles every1 half hour. Complete the table to find how far Brandon bikes for each time interval.
Help,
Using proportions, it is found that he bikes:
19 miles in one hour.28.5 miles in one and a hour.38 miles in two hours.47.5 miles in two and a hours.What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
In this problem, the proportion is that he bikes 9.5 miles each half hour, hence:
In one hour, he bikes 2 x 9.5 = 19 miles.In one and a half hour, he bikes 3 x 9.5 = 28.5 miles.In two hours, 4 x 9.5 = 38 miles.In two and a half hours, he bikes 5 x 9.5 = 47.5 miles.More can be learned about proportions at https://brainly.com/question/24372153
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Write an expression involving exponents to represent the shaded area in square inches of the diagram than use that expression to calculate the shaded area in squares inches of the diagram
The expression involving exponents to represent the shaded area in square inches of the diagram is: 6²- (3² + 2²). The shaded area in squares inches of the diagram is: 23 square inches.
Expression involving exponents and shaded areaThe expression is:
6²- (3² + 2²)
The shaded area:
Shaded area=6²- (3² + 2²)
Shaded area=36-(9+4)
Shaded area=36-13
Shaded area=23 square inches
Therefore the expression involving exponents to represent the shaded area in square inches of the diagram is: 6²- (3² + 2²). The shaded area in squares inches of the diagram is: 23 square inches.
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3. What is f(2) if f(x) = 2x³ - 19x² +28x + 47?
O 45
O 40
O 43
O 37
Answer: C: 43
Step-by-step explanation:
As we are calling the function with 2 for x, we can substitute 2 for every x we see in the function and solve.
[tex]f(2)=2(2)^3-19(2)^2+28(2)+47\\=2(8)-19(4)+28(2)+47\\=16-76+56+47\\=43[/tex]
Hence, f(2) is 43.
Find the upper quartile summary for the data. {51, 49, 52, 46, 50, 38, 38, 45, 34, 52, 46}
The upper quartile for the given data is 51 .
Given data: {51,49,52,46,50,38,38,45,34,52,46}
Data in arranged form: {34,38,38,45,46,46,49,50,51,52,52}
Find the median first, then the upper quartile. There are eleven data points, thus look at term six to determine the median as there are five data points on any side. The median is 46 because the sixth term is 46.
The upper extreme, 52, and the median are then used to determine the upper quartile; make sure not to include the median data point when dividing the groups. The upper quartile is the third term (between the median and upper extreme) because there would be two data points on each side if there were only five data points from the median to the upper extreme. The third term, which is 51, falls into the upper quartile.
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What is the smallest odd number of using 9,3,6,8,1,9
Answer: well one is
Bc its the smallest besides zero, but zero is neither odd or even
Step-by-step explanation:
pleaseeeee help me with this algebra question! select the solutions for the quadratic equation!
Answer:
I dont know if this is right but i got -7/3.
Sorry if its wrong
The length and width of a rectangle must have a sum of 60. Find the dimensions of the rectangle that will have the maximum area. [Hint: Let x and 60-x be the length
and width. The area can be described by the function f(x)=x(60-x).]
The length is… and the width is…
If the sum of the length and width of rectangle is 60 and rectangle is having maximum area then the dimensions are 30 units each.
Given that the sum of length and breadth of rectangle is 60.
We are required to find the dimensions of the rectangle that will have the maximum area. Area is basically how much part of surface is being covered by that particular shape or substance.
Let the length of rectangle be x.
According to question the breadth will be (60-x).----2
Area of rectangle=Length *Breadth
A=x(60-x)
A=60x-[tex]x^{2}[/tex]
Differentiate A with respect to x.
dA/dx=60-2x
Again differentiate with respect to x.
[tex]d^{2} A/dA^{2}[/tex]=-2x
-2x<0
So the area is maximum because x cannot be less than or equal to 0.
Put dA/dx=0
60-2x=0
60=2x
x=30
Put the value of x in 2 to get the breadth.
Breadth=60-x
=60-30
=30
Hence if the sum of the length and width of rectangle is 60 and rectangle is having maximum area then the dimensions are 30 units each.
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Find the solution of the system of equations
shown on the graph.
Answer: (0,6)
Step-by-step explanation:
The solution is where the graphs intersect.
Suppose a stock qualifies as having moderate risk if the standard deviation of its monthly rate of return is less
than 10%. A stock rating agency randomly selects 36 months and decides the rate of return for a specific fund.
The standard deviation of the rate of return is computed to be 4.95%. Is there sufficient evidence to conclude
that the fund has moderate risk at the α=0.05 level of significance? A standard probability plot shows that the
monthly rates of return are typically distributed.
Test the claim using a hypothesis test.
What are the null and alternative hypotheses for the hypothesis test?
What is the conclusion based on the hypothesis test?
The conclusion of the Hypothesis Conclusion is; that there is sufficient evidence to support the claim that the fund has moderate risk.
How to test hypothesis claim?
We are given;
Sample size; n = 36
Population standard deviation; σ₀ = 10
Sample standard deviation; s = 4.95
Significance level; α = 0.05
Claim: Standard deviation less than 10
The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis needs to contain an equality and the value mentioned in the claim. If the claim is the null hypothesis, then the alternative hypothesis states the opposite of each other. Thus;
Null Hypothesis; H₀: σ = 10
Alternative Hypothesis; H₁: σ < 10
Compute the value of the test statistic:
χ2 = [(n - 1)/(σ²)] * s²
χ2 = [(36 - 1)/(10²)] * 4.95²
χ2 = 8.576
The critical value of the left-tailed test is given in the row with df = n - 1 = 36 - 1 = 35 and in the column with 1 − α = 0.95 of the chi-square distribution table online, we have;
χ2_{1 - α} = 21.77
The rejection region then contains all values smaller than 21.77
If the test statistic is in the rejection region, then reject the null hypothesis:
8.576 < 13.848
Thus, we will reject H₀ and conclude that there is sufficient evidence to support the claim that the fund has moderate risk.
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If 4 out of 7 students at
Johnson High play sports,
about how many of the 504
students at the school play
sports?
[tex]\frac{4}{7}(504)=\boxed{288}[/tex]
Line l has a slope of -3. The line through which of the points is perpendicular to l
Geometry: Explaining Volume Formulas
Step-by-step explanation:
volume = area of circle × hight of cylinder ....
V = πr² × h
so V = πr²h
Answer:
10831 mm³
Step-by-step explanation:
The volume of any solid figure with a uniform cross section parallel to the base can be found using the volume formula ...
V = Bh
where B is the area of the base, and h is the height perpendicular to the base.
Base areaThe base of this cylindrical stack of pennies is a circle of diameter 19.05 mm. The area formula for a circle in terms of diameter is ...
A = (π/4)d²
The stack of pennies has a base area of ...
A = (π/4)(19.05 mm)² ≈ 285.023 mm²
VolumeThe volume formula tells us the stack of pennies has a volume of ...
V = Bh
V = (285.023 mm²)(38 mm) ≈ 10830.9 mm³
The volume of the stack of pennies is approximately 10831 mm³.
8 ft
10 ft
20 ft
A trapezoid has a height of 10 feet,
and base measurements of 20 feet and
8 feet. What is the area?
[?] square feet
Hint: The formula for the area of a trapezoid is: (b₁b2). h
Enter
ग
15
The area of the trapezoid is 140 square feet
What are areas?The area of a shape is the amount of space on that shape
How to determine the area of the trapezoid?The dimensions of the trapezoid are given as:
Height = 10 feet
Parallel bases = 8 feet and 20 feet
The area of a trapezoid is calculated using
Area = 0.5 * (Sum of parallel bases) * Height
Substitute the known values in the above equation
Area = 0.5 * (8 + 20) * 10
Evaluate the equation
Area = 140
Hence, the area of the trapezoid is 140 square feet
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Determine if the series converges or diverges. If the series converges, find its sum.
9
Σ n(n+3)
n=1
OA. The series diverges.
OB. The series converges to
11
2
7
OC. The series converges to
2
D. The series converges
15
-
2
The true statement about the series [tex]\sum\limits^{\infty}_{n=1} \frac{9}{n(n +3)}[/tex] is that (a) the series diverges
How to determine if the series diverges or converges?The series is given as:
[tex]\sum\limits^{\infty}_{n=1} \frac{9}{n(n +3)}[/tex]
Take the limit of the function to infinity
[tex]\lim_{n \to \infty} \frac{9}{n(n +3)}[/tex]
This gives
[tex]\lim_{n \to \infty} \frac{9}{n(n +3)} = \frac{9}{\infty * (\infty +3)}[/tex]
Evaluate the sum
[tex]\lim_{n \to \infty} \frac{9}{n(n +3)} = \frac{9}{\infty * \infty}[/tex]
Evaluate the product
[tex]\lim_{n \to \infty} \frac{9}{n(n +3)} = \frac{9}{\infty}[/tex]
Evaluate the quotient
[tex]\lim_{n \to \infty} \frac{9}{n(n +3)} = 0[/tex]
Since the limit is 0, then it means that the series diverges
Hence, the true statement about the series [tex]\sum\limits^{\infty}_{n=1} \frac{9}{n(n +3)}[/tex] is that (a) the series diverges
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Answer:
B. The series converges to [tex]\displaystyle{\frac{11}{2}}[/tex].
Step-by-step explanation:
Before evaluating the infinite series, the expression can be decomposed as the sum of two fractions (partial fraction decomposition) as follows.
Let [tex]\textit{A}[/tex] and [tex]\textit{B}[/tex] be constants such that
[tex]{\displaystyle{\frac{9}{n\left(n+3\right)}}}} \ \ = \ \ \displaystyle{\frac{A}{n} \ \ \ + \ \ \frac{B}{n+3}}[/tex]
Multiply both sides of the equation by the denominator of the left fraction,
[tex]n\left(n+3\right)[/tex], yielding
[tex]9 \ \ = \ \ A\left(n+3\right) \ \ + \ \ B \-\hspace{0.045cm} n[/tex]
Now, let [tex]n \ = \ 0[/tex], thus
[tex]\-\hspace{0.2cm} 9 \ \ = \ \ A\left(0 + 3\right) \ + \ B\left(0\right) \\ \\ 3 \-\hspace{0.035cm} A \ = \ \ 9 \\ \\ \-\hspace{0.11cm} A \ \ = \ \ 3[/tex].
Likewise, let [tex]n \ = \ -3[/tex], then
[tex]\-\hspace{0.5cm} 9 \ \ = \ \ A\left(-3 + 3\right) \ + \ B\left(-3\right) \\ \\ -3 \-\hspace{0.035cm} B \ = \ \ 9 \\ \\ \-\hspace{0.44cm} B \ \ = \ \ -3[/tex]
Hence,
[tex]\displaystyle{\sum_{n=1}^{\infty} {\frac{9}{n\left(n+3\right)}}} \ = \ \displaystyle\sum_{n=1}^{\infty} \left(\frac{3}{n} \ - \ \frac{3}{n+3}\right)[/tex].
First and foremost, write the nth partial sum (first nth terms) of the series,
[tex]\displaystyle\sum_{n=1}^{n} \left(\frac{3}{n} \ - \ \frac{3}{n+3}\right) \ \ = \ \-\hspace{0.33cm} \displaytstyle{\frac{3}{1} \ - \frac{3}{4} + \ \frac{3}{2} \ - \frac{3}{5} \ + \frac{3}{3} \ - \frac{3}{6} \ + \frac{3}{4} \ - \frac{3}{7}} \\ \\ \\ \-\hspace{3.58cm} + \ \displaystyle{\frac{3}{5} \ - \ \frac{3}{8} \ + \ \frac{3}{6} \ - \ \frac{3}{9} \ + \ \frac{3}{7} \ - \ \frac{3}{10}} \\ \\ \\ \-\hspace{3.58cm} + \ \ \dots[/tex]
[tex]+ \ \ \displaystyle{\frac{3}{n-3} \ - \ \frac{3}{n} \ + \ \frac{3}{n-2} \ - \ \frac{3}{n+1}} \\ \\ \\ \ + \ \frac{3}{n-1} \ - \ \frac{3}{n+2} \ + \ \frac{3}{n} - \ \frac{3}{n+3}}[/tex].
Notice that the expression forms a telescoping sum where subsequent terms cancel each other, leaving only
[tex]\displaystyle\sum_{n=1}^{n} \left(\frac{3}{n} \ - \ \frac{3}{n+3}\right) \ \ = \ \-\hspace{0.33cm} \displaytstyle{\frac{3}{1} \ + \ \frac{3}{2} \ + \frac{3}{3} \ - \ \frac{3}{n+1}} - \ \frac{3}{n+2} \ - \ \frac{3}{n+3}}}[/tex].
To determine if this infinite series converges or diverges, evaluate the limit of the nth partial sum as [tex]n \ \rightarrow \ \infty[/tex],
[tex]\displaystyle\sum_{n=1}^{\infty} \left(\frac{3}{n} \ - \ \frac{3}{n+3}\right) \ \ = \ \-\hspace{0.33cm} \lim_{n \to \infty} \left(\displaytstyle{\frac{11}{2} \ - \ \frac{3}{n+1} \ - \ \frac{3}{n+2} \ + \ - \ \frac{3}{n+3}\right) \\ \\ \\ \-\hspace{3.25cm} = \ \ \ \displaystyle{\frac{11}{2} \ - \ 0 \ - \ 0 \ - \ 0} \\ \\ \\ \-\hspace{3.25cm} = \ \ \ \displaystyle{\frac{11}{2}[/tex]
Consider the following figure:
The value of a is
Answer:
125
Step-by-step explanation:
The sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle.
We can write the following equation according to this information and that will help us find the value of x:
65 + 60 = x add like terms
125 = x is the answer we are looking for.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{equation:}[/tex]
[tex]\large\textsf{a = 60 + 65}[/tex]
[tex]\huge\textsf{solving:}[/tex]
[tex]\large\textsf{a = 60 + 65}[/tex]
[tex]\large\textsf{60 + 65 = a}[/tex]
[tex]\huge\textsf{simplify it:}[/tex]
[tex]\large\textsf{a = 125}[/tex]
[tex]\huge\textsf{therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{a =} \frak{125}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Will mark brainliest
Using the given definition and [tex]\Delta x=\frac{0-(-2)}n=\frac2n[/tex], we have
[tex]\displaystyle \int_{-2}^0 (7x^2+7x) \,dx = \lim_{n\to\infty} \sum_{i=1}^n \left(7\left(-2+\frac{2i}n\right)^2 + 7\left(-2+\frac{2i}n\right)\right) \frac2n \\\\ ~~~~~~~~ = \lim_{n\to\infty} \frac2n \sum_{i=1}^n \left(14 - \frac{42i}n + \frac{28i^2}{n^2}\right)[/tex]
Recall the well-known power sum formulas,
[tex]\displaystyle \sum_{i=1}^n 1 = \underbrace{1 + 1 + 1 + \cdots + 1}_{n\,\rm times} = n[/tex]
[tex]\displaystyle \sum_{i=1}^n i = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2[/tex]
[tex]\displaystyle \sum_{i=1}^n i^2 = 1 + 4 + 9 + \cdots + n^2 = \frac{n(n+1)(2n+1)}6[/tex]
Reducing our sum leads to
[tex]\displaystyle \int_{-2}^0 (7x^2+7x) \,dx = \lim_{n\to\infty} \frac2n \left(\frac{7n}3 - 7 + \frac{14}{3n}\right) = \lim_{n\to\infty} \left(\frac{14}3 - \frac{14}n + \frac{28}{3n^2}\right)[/tex]
As [tex]n[/tex] goes to ∞, the rational terms containing [tex]n[/tex] will converge to 0, and the definite integral converges to
[tex]\displaystyle \int_{-2}^0 (7x^2+7x) \,dx = \boxed{\frac{14}3}[/tex]