Sum in the sigma notation of the given series is equal to
∑[1 /(2n +1)(2n + 3)] , n =0,1,2,3.
As given in the question,
Given series :
(1 /3) + ( 1/ 15) + ( 1/ 35) + ( 1/ 63)
Simplify the given series
= [1/ (1 ×3)] + [1/ (3 ×5)] + [1/ (5 ×7)] + [1/ (7×9)]
1, 3, 5, 7 can be expressed as ( 2n + 1) , where n = 0, 1, 2, 3
3, 5, 7, 9 can be expressed as ( 2n + 3) , where n = 0, 1, 2, 3
Express the given series as a sum in the sigma notation form
(1 /3) + ( 1/ 15) + ( 1/ 35) + ( 1/ 63)
=∑ [ 1/ (2n +1) (2n + 3) ] where n = 0,1,2,3
Therefore, sum in the sigma notation of the given series is equal to
∑[1 /(2n +1)(2n + 3)] , n =0,1,2,3.
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DERMarissa VasquezDATEArcs and ChordsLGEBRA Find the value of x in each circle.1.2.KN384x+10=384x=284x + 10X=7M70°LР4. OR = OS(5x - 1)°3..109°A
SOLUTION
Given the question in the image, the following steps can be used to get x
Step 1: Explain the concept of equal arcs in a circle
If a circle is divided into arcs, then each arc is a minor arc and they all sum up to be equal to the total angles in the circumfference of the circle which is 360 degrees.
Step 2: Explain the breakdown of the minor arcs in the circle
It can be seen that the minor arcs divided the circle into three parts which are two equal arcs and a 70 degrees arc. This implies that:
[tex]x+x+70=360^{\circ}_{}[/tex]Step 3: Find x
[tex]\begin{gathered} x+x+70=360 \\ 2x=360-70 \\ 2x=290 \\ x=\frac{290}{2} \\ x=145^{\circ} \end{gathered}[/tex]Hence, the value of x in the given circle is 145 degrees
Although there is a popular belief that herbal remedies such as Ginkgo biloba and Ginseng may improve learning and memory in healthy adults, these effects are usually not supported by well-controlled research (Persson, Bringlov, Nilsson, and Nyberg, 2004). In a typical study, a researcher
obtains a sample of n = 16 participants and has each person take the herbal supplements every day for 90 days. At the end of the 90 days, each person takes a standardized memory test. For the general popula-tion, scores from the test form a normal distribution with a mean of μ = 50 and a standard deviation of σ = 12. The sample of research participants had an average of M = 54. a. Assuming a two-tailed test, state the null hypoth-esis in a sentence that includes the two variables being examined.
b. Using the standard 4-step procedure, conduct a two-tailed hypothesis test with α = .05 to evaluate the effect of the supplements
Using the z-distribution to test the hypothesis, we have that:
a) The null hypothesis is [tex]H_0: \mu = 50[/tex].
b) The p-value of the test is greater than 0.05, hence we do not reject the null hypothesis, meaning that the supplements did not have the intended effect.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence that the mean was different, hence:
[tex]H_0: \mu = 50[/tex]
At the alternative hypothesis, it is tested if there is enough evidence that the mean was different, hence:
[tex]H_1: \mu \neq 50[/tex]
What is the test statistic?The test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.In the context of this test, the parameters are given as follows:
[tex]\overline{x} = 54, \mu = 50, \sigma = 12, n = 16[/tex]
Hence the test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{54 - 50}{\frac{12}{\sqrt{16}}}[/tex]
z = 1.33.
What is the p-value and what is the conclusion?Considering a two-tailed test, as we are testing if the mean is different of a value, with z = 1.33, the p-value of the test is of 0.1835, which is greater than 0.05, meaning that we do not reject the null hypothesis and the supplement did not change the mean.
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A scientist is working with two different concentrations of hydrochloric acid (HCI). One bottle is
80% HCI, and the other is 50% HCI. For their experiment they need 1 liter of 70% HCI.
How many liters of the 80% solution do they need?
How many liters of the 50% solution?
The liters of 80% material is 2/3 liters.
The liters of the 50% solution is 1/3 liters.
How to illustrate the information?Based on the information, the scientist is working with two different concentrations of hydrochloric acid (HCI).
Let x = volume of 80%
Let 1 -x =volume of 50%
Therefore, the expression to illustrate the information will be:
80x + 50 × (1 - x) = 70
80x + 50 - 50x = 70
30x = 70 - 50
30x = 20
Divide
x = 20/30
x = 2/3
Therefore there are 2/3 liters of 80% material
The liters for the 50% solution will be 2/3 subtracted from 1. The 2/3 implies that for the 80% material. This will be:
= 1 - 2/3
= 1/3
There are also 1/3 liters of 50% material.
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Given the following Information, find the length of the missing side. Leave your answer as a simplified radical.
Hypotenuse = 10
Long = ?
A. 5
B. 5/3
C. 10
D. 10/3
Answer: B. (5√3)
Step-by-step explanation: In a 60-30-90 triangle, the hypotenuse is 2x, and the long is x√3. Solve for x by setting 2x=10, which you would get 5. Then, you can plug 5 for x in x√3 to get 5√3.
Kara categorized her spending for this month into four categories: Rent, Food, Fun, and Other. The amountsshe spent in each category are pictured here.Food$289Rent$361Other$433Fun$217What percent of her total spending did she spend on Rent? Answer to the nearest whole percent.
Total expenses = $289 + $361 + $433 + $217 = $1300
Percentage of money spent on rent:
(Money spent on rent)/(Total expenses) = $361/$1300 = 0.2777 ≈ 28%
Therefore 28% of total expenses are for rent
Is it right?????????
Check the picture below.
let's bear in mind that the standard deviation measures deviation in a dataset, so is a measure of how much the data fluctuates, so a dataset of 3 , 1000, will have a much higher deviation value than a same total of 450 , 553.
10. A blood alcohol content (BAC) of 0.08 g/100 mL means
uppose that the rela
S={(-1, -9), (-9, 1), (3, 1)}
ve the domain and range of S.
rite your answers using set notation.
domain =
range =
Help me please
Answer:
Domain = {-9, -1, 3}Range = {-9, 1}Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Use the diagram find the image of c under the translation described by the translation rule
(X,y) (x+11,y-8)
○ B
○ A
○ D
○ E
3.4-2.8d+2.8d-1.3Combine like terms to create an equivalent expression.
The given expression is
3.4 - 2.8d + 2.8d - 1.3
By collecting like terms, we have
- 2.8d + 2.8d + 3.4 - 1.3
= 0 + 2.1
= 2.1
circle C has centre D and equation
x^2+y^2+2x-8y+8=0
A line is drawn through the point P (4,6),so that it touches the circle C at the point T
Show that PT=square root 20
find the equation of the circle centre P which passes through the point T
The equation of the circle center P which passes through the point T is [tex](x-4)^{2} + (y-6)^{2} = 20[/tex]
Here, we are given a circle with center D and equation as-
[tex]x^{2}+ y^{2}+2x -8y + 8 =0[/tex]
Comparing this to the general form of equation of a circle which is [tex]x^{2}[/tex] + [tex]y^{2}[/tex]+ 2gx + 2fy + c = 0, we get-
g = 1, f = -4 and c = 8
thus, the center of the circle is (-1,4) and radius =[tex]\sqrt{ (1+16-8)}[/tex] = 3
Now, since PT is a tangent to the circle, DP will e perpendicular to PT.
We can find the length of PD using the distance formula as we know P(4,6) and D(-1,4)
= [tex]\sqrt{(4+1)^{2} +(6-4)^{2} }[/tex]
= [tex]\sqrt{(5)^{2} +(2)^{2} }[/tex]
= [tex]\sqrt{25 +4 }[/tex]
=[tex]\sqrt{29}[/tex]
Thus, in triangle, PDT by using Pythagoras theorem, we will have-
[tex]PT^{2} + DT^{2} = PD^{2}[/tex]
since DT is the radius of the circle, DT = 3
⇒ [tex]PT^{2} + 3^{2} = (\sqrt{29}) ^{2}[/tex]
[tex]PT^{2} + 9 = 29[/tex]
[tex]PT^{2} = 29 - 9[/tex]
[tex]PT^{2} = 20[/tex]
[tex]PT = \sqrt{20}[/tex]
Thus, we've proved that the length of PT is [tex]\sqrt{20}[/tex] units.
Now, the circle with center P, passing through T will have radius = [tex]\sqrt{20}[/tex]
so r = [tex]\sqrt{20}[/tex] and (h,k) = (4,6)
Thus, the equation of the circle will be-
[tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex]
[tex](x-4)^{2} + (y-6)^{2} = (\sqrt{20}) ^{2}[/tex]
[tex](x-4)^{2} + (y-6)^{2} = 20[/tex]
Thus, the equation of the circle center P which passes through the point T is [tex](x-4)^{2} + (y-6)^{2} = 20[/tex]
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Steve has a new credit card with an APR of 11.99% and a credit limit of $1800. The minimum monthly payment is 6.5 % of the new balance. If Steve buys $550 dollars in school supplies at the beginning of the month, what will Steve’s new balance be at the end of the month? Explain your answer rounded to the nearest cent
Steve's new credit card balance at the end of the month and after making the minimum monthly payment will be $519.39.
What is a credit card balance?A credit card balance is an amount the cardholder owes to the credit card issuer at the end of a credit period.
The credit card balance consists of purchases, finance charges, and repayments.
Credit card's APR = 11.99%
Credit limit = $1,800
Minimum monthly payment = 6.5%
Purchase at the beginning of the month = $550
Credit card interest for the month = $5.50 ($550 x 11.99% x 1/12)
New balance = $555.50
Minimum payment = $36.11 ($555.50 x 6.5%)
Balance after the minimum payment = $519.39 ($555.50 - $36.11)
Thus, If he buys $550 in school supplies at the beginning of the month, Steve’s new balance at the end of the month is $555.50, which he can reduce to $519.39 by making the required minimum monthly payment.
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Help me answer this please!!!
Answer:2 choice
Step-by-step explanation:you use the rise over run technique with 2 points, it should give you rise 1 run 4 since the line is decreasing its a negative. For the y-int its the point where the line crosses Y int which is (0,-2) answer is -2
list 3 points that are on the line 2x=6y+4
The three Points that lie on the given line 2x=6y+4 are (5,1) , (8,2) and (11,3).
The given equation of line is given below,
2x=6y+4 equation 1
We need to find the points that lie on the given line.
Point 1 :
Put x = 5 in equation 1
2(5) = 6y + 4
6y = 6
y=1
So, Point (5,1) lie on the given line.
Point2:
Put x = 8 in equation 1
2(8) = 6y + 4
6y = 12
y=2
So, Point (8,2) lie on the given line.
Point 3 :
Put x = 11 in equation 1
2(11) = 6y + 4
6y = 18
y=3
So, Point (11,3) lie on the given line.
Thus, Points (5,1) , (8,2) and (11,3) lie on the line 2x=6y+4 .
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Find the sum of the first 31 terms of the following series, to the nearest integer. 4, 11,18,... 4,11,18,...
The sum of the first 31 terms of the arithmetic series is 114.
What is arithmetic series?
In mathematics, arithmetic series is the sequence of the number whose common difference between the two consecutive number is always constant. And the sum of the series is depend on the first term as well as on the last term.
According to the question, the given series is an arithmetic series. In the common difference is same.
The given series is:
4, 11, 18,....4, 11, 18,....4, 11, 18,....
To know the sum of the given series, first calculate the sum of the first three numbers. And later multiply by ten.
Using standard formula for the sum of the arithmetic series:
[tex]S_{3} =\frac{(first term + last term)}{2} = \frac{4+18}{2} =11[/tex]
Therefore to calculate the sum of the 31 terms:
s(31 terms) = 10(11) + first term = 110 + 4 = 114
Hence, the sum of the first 31 terms of the arithmetic series is 114.
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Blake was assigned the problem below. Analyze his work and determine if it is correct.If it is wrong, describe all mistakes.Problem:53x-5 = ( 625 )#*?53x-s5 "(x+2)3x-5 = 4 (x+7)3x-5= 4x+7-3x-3xS = x +7-7-7x= -12
1) Let's solve that exponential equation
Converting the bases:
2) Since we are on the same base let's just calculate the exponents.
3) Blake has committed a mistake when He didn't apply the distributive property properly. He didn't multiply the 7 by 4. He subtracted the x variables wrongly and added -7 to -5.
When He started operating the exponents.
The depth of a local lake averages 26 ft, which is represented as |−26|. In February, it measured 5 ft deep, or |−5|, and in July, it was 18 ft deep, or |−18|. What is the difference between the depths in February and July?
21 feet
23 feet
8 feet
13 feet
The difference between the depths in February and July is D. 13 feet.
How to illustrate the information?From the information illustrated, it was stated that the depth of a local lake average 26 ft is represented as |−26|. In February, it measured 5 ft deep, or |−5|, and in July, it was 18 ft deep, or |−18|.
Therefore, it should be noted that the depth in July is -18.
Therefore, the difference between the depths in February and July will be:
= -5 - (-18)
= -5 + 18
= 13
Therefore, the difference is 13 feet.
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what is the inequality of 1< x <5 on a number line.
When we write an inequality in the form:
[tex]1We are indicating the both are true: x is greater than 1 and x is less than 5. This means that x is between 1 and 5 (not including neither ends).In a number line, we can draw it, mark the endpoints (1 and 5) and then we highlight the parts at which the x is, which is in the middle:
Notice that we marked the endpoints as empty dots, which indicates that the endpoints are not included in the interval.
Write the given transformation in vector notation (please help its due in 20 mins)
Answer:
-1, 1
Step-by-step explanation:
The translation is 1 unit left and 1 unit up.
find the value of k given both points lie on a line passing through the orgin (-12,-2) and (k,8)
The value of k given that both points lie on a line passing through the origin is 48.
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope,\;m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope,\;m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Since both points lie on a line which passes through the origin, we can logically deduce the following points:
Point (x, y) = (0, 0)
Substituting the given points into the formula, we have;
Slope, m = Δy/Δx
Slope, m = (-2 - 0)/(-12 - 0)
Slope, m = -2/-12
Slope, m = 1/6
At point (-12, -2) and (k, 8), we have:
1/6 = (8 - (-2))/(k - (-12))
1/6 = (8 + 2)/(k + 12)
1/6 = 10/(k + 12)
k + 12 = 10(6)
k + 12 = 60
k = 60 - 12
k = 48
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Pierce is making a rectangular frame for a photo collage that has a perimeter of 72.2 inches. The length of the frame is 20.3 inches.
Write an equation to find the width of the frame, x.
Enter the correct equation in the box.
An equation to find the width of a rectangular frame with perimeter 72.2inches and length 20.3 inches is given by 2( 20.3 + x ) = 72.2 .
As given in the question,
Pierce is making a rectangular frame for a photo collage.
Perimeter of a rectangular frame is equal to 72.2 inches.
Length of the rectangular frame is equal to 20.3 inches
Perimeter of the rectangle = 2(length + width) __(1)
Let x inches be the width of the frame
Equation with x width of the frame is given
2(20.3 + x) = 72.2
Therefore, an equation to find the width of a rectangular frame with perimeter 72.2inches and length 20.3 inches is given by 2( 20.3 + x ) =72.2.
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Your cousin gave you $13.78 with which
to buy a present. This covered 2/3 of the
cost. How much did the present cost?
The cost of the present is $20.67
Given,
The cost of the present = x
Amount given by cousin = $13.78
Amount given by cousin is 2/3 of x.
That is,
13.78 = 2/3 of x
Lets find x
13.78 = 2/3 × x
13.28 = 2x/3
Multiply with 3 on both sides
13.78 × 3 = (2x/3) × 3
We get,
41.34 = 2x
Divide 2 on both sides
That is,
41.34/2 = 2x/2
We get,
x = 20.67
Here, x is the cost of the present
Therefore, the cost of the present is $20.67
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please solve the inequality in the picture shown below i will give brainliest
[tex]\frac{3}{4} -\frac{1}{2} p > \frac{5}{4} \\\frac{3}{4}(4)-\frac{1}{2} p(4) > \frac{5}{4} (4)\\3-2p > 5\\-2p > 5-3\\-2p > 2\\\frac{-2p}{-2} > \frac{2}{-2} \\p < -1[/tex]
when you divide or multiply by a negative number the signs <> change directions.
←
The retail cost of a TV is 10% more than its wholesale cost. Therefore, the retail cost is
The retail cost is
times the wholesale cost.
Answer:
1.1
Step-by-step explanation:
You want the multiplier of the wholesale cost that makes the retail cost be 10% more.
MultiplierThe retail cost is said to be ...
retail cost = (wholesale cost) + 10% × (wholesale cost)
= (wholesale cost) × (1 +10%)
= (wholesale cost) × 1.10
The retail cost is 1.10 times the wholesale cost.
given a number line C=11 and D=13 CD=?can u help me solve this problem?
The diagram of the number line is shown below
Thus, the distance CD which is the distance between point D and point C is
13 - 11 = 2
CD = 2
A garden table and a bench cost $830 combined. The garden table costs $80 more than the bench. What is the cost of the bench?
The most appropriate choice for linear equation will be given by-
The cost of bench is $375
What is linear equation?
A one degree equation is called a linear equation.
Here,
Let the cost of the bench be $x
cost of garden table = $(x + 80)
Total cost of bench and garden table= $(x + x + 80)
= $(2x + 80)
By the problem,
2x + 80 = 830
2x = 830 - 80
2x = 750
x = [tex]\frac{750}{2}[/tex]
x = $375
So,
The cost of bench is $375
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If f(x) = 3x - 1 and g(x) = x + 2, find (f- g)(x).
A. 3-2x
B. 4x+1
C. 2x-3
D. 2x-1
HELP ASAP 30 POINTS 9TH GRADE MATH. WILL GIVE BRAINIEST IF CORRECT
Solve.
Question 1.
-4x + 17 ≥ 9.
Question 2.
| 5 + z | + 3 = 10.
Question 3.
Match to the correct one
5y + 2 = 5y + 8. 1. All real numbers
2 (y + 4) = 2y + 8. 2. No solutions
5y + 2 = 2y + 8 3. Infinity many solutions.
Question 4.
Solve for x.
x - 4 ≥ 5. SHOW YOUR WORK.
question 5.
solve for x.
12x = 4 (2x -3) - 12.
SHOW YOUR WORK.
Question 7.
Solve for x
3(x + 2) = 3x + 2
For the given problems we have:
1) The solution of the inequality is:
x ≤ 2
2) The absolute value equation has two solutions:
z= 2
z = -12
3) The correct matches are:
5y + 2 = 5y + 8 this has no solutions2*(y + 4) = 2y + 8 this has infinite solutions5y + 2 = 2y + 8 This has a single solution.How to solve the different operations?Remember that solving means to isolate the variable in one side of the expression.
1) We have the inequality:
-4x + 17 ≥ 9
-4x ≥ 9 - 17
x ≤ -8/-4
x ≤ 2
This is the solution of the inequality.
2) We have the absolute value function:
|5 + z| + 3 = 10
|5 + z| = 10 - 3 = 7
We can decompose this into:
5 + z = 7
5 + z = -7
Then the two solutions are:
z = 7 - 5 = 2
z = -7 - 5 = -12
3) The correct matches here are:
5y + 2 = 5y + 8 this has no solutions, these are parallel lines.2*(y + 4) = 2y + 8 this has infinite solutions (all real numbers).5y + 2 = 2y + 8 This has a single solution.Learn more about inequalities:
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30% of 3000
I know how to do it but I just need to be sure
Answer:900
Step-by-step explanation: 1. set up an equation
x= (p * n)/100 when x= the answer p= the percentage and n= the total number
2. plug in the numbers
x= (30 * 3000)/100
3.solve
x= (30*3000)/100
x= (90000)/100
x= 900
M2 U2 Practice 6
Given: the equation of line lis y = -x +4
Write the equations of the lines passing through the point (6,7) that are (a) perpendicular to line I, and (b) parallel to
line l.
Lines that are parallel to one another on a plane do not intersect or meet at any point. They are always equidistant from one another and parallel. Non-intersecting lines are parallel lines. Parallel lines can also be said to meet at infinity.
What formula should you use to represent the line that passes through the given points?How to determine a line's equation from two points:
Using the slope formula, determine the slope.
To find the y-intercept (b), use the slope and one of the points.
You can obtain the equation for a line by entering the values of m and b into the slope-intercept form of the line (y = mx + b).
y = -x/3 + 5 is the equation that depicts the line that crosses through the coordinates (-6, 7) and (-3, 6).
3 Answers What is the slope of the line passing through (- 7 2 and 6 7? by Certified Tutors
The slope of the equation would be nine.
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