The value of the sum of the arithmetic sequence from a₃ to a₆ is 38
What is an arithmetic sequence?An arithmetic sequence is a sequence in which the difference between two consecutive terms is a constant.
The first term of the sequence is 20, the common difference is 17 - 20 = 14 - 17 = 11 - 14 = 8 - 11 = 5 - 8 = 2 - 5 = -3
The sum from n = 3 to n = 6 of aₙ is found as follows;
The sequence is an arithmetic progression of the form aₙ = a + (n - 1)·d
Where;
aₙ is the value of the nth term
a = The first term
d = The common difference
From the sequence, we have;
a = 20, d = -3, from which we have;
aₙ = 20 + (n - 1) × (-3) = 20 - 3·(n - 1)
aₙ = 20 - 3·(n - 1)
From which we have;
a₃ = 20 - 3×(3 - 1) = 14
a₄ = 20 - 3×(4 - 1) = 11
a₅ = 20 - 3×(5 - 1) = 8
a₆ = 20 - 3×(6 - 1) = 5
a₃ + a₄ + a₅ + a₆ = 5 + 8 + 11 + 14 = 38
The value of the sum of the 3rd, 4th, 5th, and 6th value of the sequence is 38Learn more about arithmetic sequence or progression here:
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Do the following rectangles have the same perimeter, area, or both? a rectangle is labeled 4 centimeters along its left side and 5 centimeters along its top side. a rectangle is labeled 4 centimeters along its left side and 5 centimeters along its top side. a rectangle is labeled 10 centimeters along its left side and 2 centimeters along its top side. a rectangle is labeled 10 centimeters along its left side and 2 centimeters along its top side. choose 1 answer: choose 1 answer: (choice a) a same area only (choice b) b same perimeter only (choice c) c same area and perimeter
A local recreation center offers a yearly membership and charges
an additional fee for aerobics classes as shown in the table.
Number of classes (x)
1
5
10
15
Total cost (y)
270
290
315
340
a. Write an equation in slope-intercept form that represents the total cost of the membership.
b. Carly spent $500 one year. How many aerobics classes did she take?
An equation in slope-intercept form that represents the total cost of the membership is y = 5x + 265.
The number of aerobics classes that Carly took at $500 one year is 47 aerobics classes.
How to write an equation in slope-intercept form?In order to write the equation in slope-intercept form, we would have to determine the slope of the line representing the total cost of the membership.
Mathematically, the slope of any straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Substituting the given parameters into the formula, we have;
Slope, m = (290 - 270)/(5 - 1)
Slope, m = 20/4
Slope, m = 4
At point (1, 270), an equation of this line in slope-intercept form can be calculated by using this standard formula:
y = mx + c
Where:
m represents the slope.x and y are the points.c represents the intercept.Substituting the given points into the formula, we have;
y = mx + c
270 = 5(1) + c
Intercept, c = 270 - 5
Intercept, c = 265.
Therefore, the required equation is given by:
y = 5x + 265
For the number of aerobics classes at $500 one year, we have:
500 = 5x + 265
5x = 500 - 265
5x = 235
x = 235/5
x = 47 aerobics classes.
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6.2 in.
8 in.
I need help with this
What is the area of one of the triangles
What is the area of the entire square
Answer:
the area for the entire scale is 8 inches
the area for one of the triangles is 6.2 inches
Step-by-step explanation:
Answer:
Step-by-step explanation:
Area of the triangle is:
A = 1/2 * (Base * Height)
A = 1/2 * (b * h)
A = 1/2 * (8 * 6.2)
A = 1/2 * 49.6
A = 24.8
Area of the square is:
A = Base * Height
A = b * h
A = 8 * 6.2
A = 49.6
find the value of u
8^2 + u^2 = 17^2
Answer:
u = 15
Step-by-step explanation:
It appears that you have already created an equation to solve for u and just need help solving it
So we have 8² + u² = 17²
==> simplify exponents
64 + u² = 289
==> subtract 64 from both sides
u² = 225
==> take the square root of both sides
u = 15
asap
Calculate the value of x.
Answer:7.07 m
Step-by-step explanation:
ab=5
ab=bc
bc=5
(ab)^2+(bc)^2=(ac)^2
25+25=50
ac^2=50
ac=7.07
equation like that passes through (4,1) and perpendicular to y=1/2x-1
The equation of the line passing through (4,1) and perpendicular to y=1/2x-1 is y = -2x+9.
According to the question,
We have the following information:
A line passes through (4,1) and perpendicular to y=1/2x-1.
Now, the slope of the given line is 1/2.
We know that the slope of the perpendicular line is given by -1/m.
Slope of perpendicular line = -1/(1/2)
Slope of perpendicular line = -2
Equation of the required line:
(y-y') = m(x-x')
(y-1) = -2(x-4)
y-1 = -2x+8
y = -2x+8+1
y = -2x+9
Hence, the equation of the line passing through (4,1) and perpendicular to y=1/2x-1 is y = -2x+9.
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Determine if the statements are true or false
The standard form of 4.4 x 10-4 is 0.00044.
The standard form of 6.39 x 105 is 63,900,000.
The standard form of 3.02 x 10° is 3,020,000,000.
The statements are true or false.
The standard form of 4.4 x 10-4 is 0.00044.
= 4.4 * 10^-4
= 4.4/10^4
= 4.4/10000
0.00044 = 0.00044
This statement is true.
The standard form of 6.39 x 10^5
= 6.39 * 100000
= 639*1000
639000 ≠ 63,900,000
This statement is false
The standard form of 3.02 x 10^10 is 3,020,000,000.
= 3.02 * 10^10
= 3.02 *10000000000
= 3,020,000,0000
This statement is false.
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Determine if the triangles below are similar. If so, state the reason and write the similarity statement.
QRS is similar to _______.
A. Similar due to AA . Triangle QRS is similar to triangle VUT.
B. Similar due to SSS and a scale factor of 0.29. Triangle QRS is similar to triangle VUT.
C. Not similar
D. Similar due to SSS and a scale factor of 3.5. Triangle QRS is similar to triangle TUV.
E. Similar to due SAS and a scale factor of 0.29. Triangle QRS is similar to triangle TUV.
The correct statement is "Similar, due to SSS and a scale factor of 0.29. Triangle QRS is similar to triangle VUT".
What is similarity in triangles?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures.
Given that, two triangles Δ QRS and Δ VUT
We have,
QR/VU = RS/UT = QS/VT = 2/7 = 0.29
Hence, the two triangles are similar by SSS property with a scale factor of 0.29
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please I need help in this question
Answer:
Step-by-step explanation:
A is an integer by 10 as even and by 3 as odd as timed would be in power also by 3 then, B, in scientific writing is.... 140 OBVI
what is 28.5dived by 11 equal explain how you got the answer.
The solution to the statement is 2.591
How to determine the solution to the statement?From the question, we have the following mathematical statement that can be used in our computation:
what is 28.5dived by 11 equal
Rewrite the statement properly
So, we have
what is 28.5 divided by 11 equal
This means that we divide 28.5 by 11
So, we have the following representation
28.5/11
Evaluate the quotient
28.5/11 = 2.591
Hence, the result is 2.591
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Amanda wants to purchase a new printer and is comparing printing speeds between two different printers. Printer a can print 400 pages in 40 minutes, and printer b can print 760 pages in the same amount of time. How many more pages per minute can printer b print than printer a?.
Answer:
9 More Pages Per Minute
Step-by-step explanation
Printer A: 400/40 = 10
Printer B: 760/40= 19
Difference Between Printers: 19-10= 9
what would the answer be and this is the last question u get brainlist for givnig the answer
Answer:
8.56
Step-by-step explanation:
d=2
r=d/2
r=1
area of the circle=πr², but we also have to subtract the square from it
a=π2²
a= 12.56
now the area of the square is 2*2
the area of the shape 12.56-(2*3)
the area of the shape is 8.56
Factor the polynomial: -2x³ - 4x² - 6x
Answer:
−2x (x² + 2x + 3)
The product of twice a number and six is the same as the difference of eleven times the number and 7/6. find the number
Answer:
2x X 6 = 11x - 7/6
12x = 11x - 7/6
12x - 11x = -7/6
x = - 7/6
Step-by-step explanation:
let the unknown be x
twice of the number is 2x multipled by 6
2x(6) equating to eleven times the number 11x minus 7/6
gives an equation as in step 1
multiply 6 by 2x to give a more simple equation
collect like terms so you have an equation as in step 3
simplify to get your final answer
13#A toy manufacturer wants to see how long, on average, a new toy captures children's attention. He tests 11 children selected at random and finds that their mean attention span is 22 minutes with a standard deviation of 5 minutes. If we assume that attention spans are normally distributed, find a 90% confidence interval for the mean attention span of children playing with this new toy. Give the lower limit and upper limit of the 90% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas. )Lower limit:Upper limit:
The lower limit of the confidence interval is 18.80 and the upper limit of the confidence interval is 25.19
Confidence interval = sample mean ± margin of error
Margin of error = z*population standard deviation/[tex]\sqrt{n}[/tex]
The level of confidence is represented by z==2.12
the size of the sample n=11
sample mean= 22
confidence interval = sample mean ± z*population standard deviation/[tex]\sqrt{n}[/tex]
upper limit of confidence interval = sample mean + z*population standard deviation/[tex]\sqrt{n}[/tex]
=22+2.12*5/[tex]\sqrt{11}[/tex]=25.19
lower limit of confidence interval = sample mean - z*population standard deviation/[tex]\sqrt{n}[/tex]
=22-2.12*5/[tex]\sqrt{11}[/tex]=18.80
Therefore, the lower limit of the confidence interval is 18.80 and the upper limit of the confidence interval is 25.19
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a neonate order is 0.03 mg/kg of a 1:10,000 solution. the patient weighs 4.4 lb. how many milliliters of the solution will be needed?
600 milliliters of the solution will be needed.
Given:
Let x be the solution needed.
A neonate order is 0.03 mg/kg of a 1:10,000 solution. the patient weighs 4.4 lb.
4.4 lb = 1.99581 kg
4.4 lb ≈ 2 kg
neonate order = 2*0.03
= 2*3/100
= 6/100
= 0.06 mg
1 : 10000 = 0.06 : x
1/10000 = 0.06/x
x = 0.06 * 10000 / 1
= 0.6*1000
= 6*100
= 600 milliliters.
Therefore 600 milliliters of the solution will be needed.
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One cable company charges $50 per month for their basic plan, plus $75
installation. A second company charges $55 per month, but offers free
installation. For what number of months is the first plan cheaper than the
second plan?
Write your answer as a number, with no symbols, spaces, or words.
Your answer
Step-by-step explanation:
One cable company charges $50 per month for their basic plan, plus $75 installation. A second company charges $55 per month, but offers free installation. For what number of months is the first plan cheaper than the second plan?
50m + 75 < 55m
subtract 50m from both sides:
50m + 75 -50m < 55m - 50m
75 < 5m
divide both sides by 5:
75/5 < 5m/5
15 < m
or m > 15
so:
The first plan cheaper than the second plan after 16+ months
Alphabet: abcdefghijklmnopqrstuvwxyz if add = 9, bad = 7, and cad = 8 what is the value of ada?.
If "add" = 9 , "bad" = 7 , "cad" = 8 , then the value of "ada" is 6 .
In the question ,
alphabets are given ,
the alphabets are a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z .
and the value of "add" is 9,
form above we can see that , the alphabet "a" is in the first position , so value of "a" = 1 ,
"d" is at 4th position , so the value of "d" = 4 .
So , "add" = a + d + d = 1+4+4 = 9
similarly we have , "bad" = b + a + d = 2+1+4 = 7
and "cad" = c + a + d = 3+1+4 = 8
hence , the value of "ada"
"ada" = a + d + a = 1+4+1 = 6 .
Therefore , the value of "ada" is 6 .
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For the quadratic equation x2 + 4x - 5 = - x2 + 7
which is a,b,c
The coefficients of the quadratic equation are:
a = 2, b = 4, c = -12
What are the coefficients of the quadratic equation?
The general quadratic equation is:
a*x^2 + b*x + c = 0
In this case, we have the quadratic equation:
x^2 + 4x - 5 = -x^2+ 7
Let's move all the terms to the left side, then we will get:
x^2 + 4x - 5 + x^2 - 7 =0
Now group like terms:
x^2 + x^2 + 4x - 5 - 7 =0
2x^2 + 4x - 12 = 0
Comparing this with the general quadratic equation we can see that:
a = 2
b = 4
c = -12
These are the coefficients.
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Which arrangement shows −27/5 , −4.1 , −5 3/5 , and −3 in order from least to greatest?
A. −4.1, −27/5 , −3 , −5 3/5
B. −4.1 , −27/5 , −5 3/5 , −3
C. −5 3/5 , −27/5 , −4.1 , −3
D. −5 3/5, −3 , −4.1 , −27/5
The solution of numbers in their ascending order is Option C.
−5 3/5 , −27/5 , −4.1 , −3
What is Ascending Order?
When numbers are arranged in ascending order, they are done so from least to largest. We must first compare the numbers before we may arrange them in any order. Compare first, then order. Numbers arranged in ascending order: Determine how many digits each number has.
Given data ,
The numbers in the set S is S = { -27/5 , -4.1 , -5 3/5 , -3 }
Now , the fractions -27/5 and -5 3/5 can be simplified as
-27/5 = -5.4
-5 3/5 = -28/5
= -5.6
And , the numbers in the set S = { -5.4 , -4.1 , -5.6 , -3 }
The larger negative numbers are smaller in value
So , the numbers in their ascending form will be
-5.6 < -5.4 < -4.1 < -3
And ,
-5 3/5 < -27/5 < -4.1 < -3
Hence , the ascending form of the numbers is -5 3/5 , -27/5 , -4.1 , -3
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Write an equation of the line that passes through (7, 10) and is perpendicular to the line y = -x - 9.
Equation of the line that passes through (7, 10) and is perpendicular to the line y = x - 9 is y = -x + 17.
Given,
The equation, y = x - 9
Slope = m = 1
Slope of line perpendicular to given line = -1/m = -1/1 = -1
Let the equation of line be y = mx + c
Passes through A(7,10)
10 = -1(7) + c
10 = -7 + c
c = 10 + 7
= 17
Therefore, the equation of line is y = -x + 17
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If I am 165 centimeter tall. And Roberto is 1.7 meters tall who is taller?
Answer:
"Centi" means hundred so, a centimeter is a meter times 100. Divide 165 centimeters by 100 to convert it to meters. 165/100=1.65. If you are 1.65 meters, and Roberto is 1.7 meters tall, Roberto is taller.
Hope this helped!
Directions: Determine if the given equations are parallel, perpendicular, or neither. 3x + 2y = 8 and 2x + 3y = -12
the european and mediterranean population is declining as a proportion of the total u.s. population and will be less than 50% of the population by:
3x - y = 17
4x + y = -3
Answer:
x = 7, y = 4
Step-by-step explanation:
simultaneous equation:
3x-y=17
4x+y=-3
Solving for x: add the two equations together to cancel out y (-y + y = 0)7x = 14divide both sides by 7 to get the value of 1 xx = 7solving for y: substitue the value of x (7) into any equation (we'll use the top one for ease)3(7) - y = 17so in other words; 21 - y = 17subtract 21 from both sides to get the value of -y-y = -4therefore, y = 4What is the yield on a corporate bond with a $1000
face value purchased at a discount price of $950, if
it pays 6% fixed interest for the duration of the
bond?
The yield on a corporate bond with a face value of $1000 after removal of discount would be =$60.
What is interest rate?Interest rate can defined as the payment received by an individual after investing a particular amount of money for a given period of time.
The principal amount after removal of $950 discount = $1000
The rate of interest (R) = 6%
The time of investment (T) = 1
Then the simple interest;
= P × T × R/100
= 1000 × 1 × 6/100
= 6000/100 = $60
Therefore, the yield of the corporate bond would be extra $60.
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solve for x.
3/4 (-4.2 - x) = 5
Answer: x = -10.8666667
Step-by-step explanation:
which is the solution set for ?
- 4 (-x+a)+5<8
The solution of the given function is x < 3 + 4a.
What is a function?
A function is uniquely represented by the set of all pairings (x, f (x)), known as the function graph, which is a popular way of visualizing the function. When the domain and codomain are real number sets, each pair may be thought of as the Cartesian coordinates of a point in the plane. Functions are frequently employed in science, engineering, and the majority of mathematical areas. Most disciplines of mathematics say that functions are "the major subjects of investigation." If the domain and codomain set of two functions f and g are the same and their output values agree over the whole domain, they are equivalent.
The solution of the given function is
-4(-x+a)+5<8
or, 4x - 4a + 5 < 8
or, x < 8 - 5 + 4a
or, x < 3 + 4a
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find the exponential equation using points (-1,6) and (2,3/4)
Answer: 3
Step-by-step explanation:
You are solving a system of equations y1 = abx1 and y2 = abx2, so plug the x and y coordinates into the equations to solve for a and b:6 = ab1 & 3/4 = ab-2Since a = 6/b, we can use this in the second equation to solve for b:3/4 = (6/b)b-23/4 = 6/b36/(3/4) = b38 = b32 = b,which means that a = 3.Now we just input our a and b values into y = abx, so our equation is y = 3*2x. I hope this helps
how large a sample is needed if we wish to be 96% confident that our sample proportion in the question (7) will be within 0.02 of the true fraction of the voting population.
The sample size for estimating the proportion is 2637.
Given,
How many people should be included in the sample if we want to have 96% confidence that our sample proportion will be within 0.02 of the true fraction of the voting population given the data?
E = 0.02
c = 96% = 0.96
[tex]\hat p[/tex] or P = 0.5 (We have no idea about P, in this case, take P = 0.5)
[tex]\hat p[/tex] = 1 - [tex]\hat p[/tex] = 0.5
Now,
α = 1 - c = 1 - 0.96 = 0.04
α/2 = 0.04/2 = 0.02
⇒ α/2 = 2.054 (using z table)
The sample size for estimating the proportion is given by,
[tex]n = Z^2_\alpha _/_2P(1-P)/E^2[/tex]
= (2.054/0.02)2 * 0.5 * 0.5
= 2636.8
= 2637
Hence, the size of sample is 2637.
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