The average of all integers from 11 to 35 is determined by summing the first and last integers and dividing by 2. The calculation is (11 + 35) / 2, which equals to 23.
Explanation:Calculating the Average of Integers
To calculate the average of all integers from 11 to 35, you sum up all the integers and then divide by the number of integers. Since the numbers form an arithmetic sequence, we can use the formula for the average, which is: (first term + last term) / 2. Therefore, the average is (11 + 35) / 2.
The calculation would then be 46 / 2, which equals 23. This value represents the mean or average of the integer set from 11 to 35. The concept of finding the average is a fundamental aspect of statistics and general mathematics that is commonly applied in various practical scenarios.
The average of all integers from 11 to 35 is 46.
Explanation:To find the average of all integers from 11 to 35, we first calculate the sum of all the integers from 11 to 35. Then, we divide the sum by the total number of integers (i.e., 35 - 11 + 1 = 25). The sum of the integers from 11 to 35 is (11 + 12 + 13 + ... + 35). We can simplify this sum by using the formula for the sum of an arithmetic series: Sn = (n/2)(a + l), where Sn is the sum of the series, n is the number of terms, a is the first term, and l is the last term. Plugging in the values, we get Sn = (25/2)(11 + 35) = 25(46) = 1150. Now, we can find the average by dividing the sum by the total number of integers: Average = 1150/25 = 46. Therefore, the average of all integers from 11 to 35 is 46.
WHAT THE VALUE OF 12.5X10 7
It takes nim 2 2/3 hours to weave a basket. He worked Monday through Friday , 8 hours a day. How many baskets can he make?
Answer:
15 baskets
Step-by-step explanation:
In order to solve this question, first we need to know the amount of hours that Nim was able to work.
If Nim worked Monday through Friday, 8 hours a day, then:
Monday to Friday = 5 days
1 day = 8 hours
5 days * 8 hours = 40 hours
Out of these forty hours, Nim needs 2 2/3 hours to weave a basket. Therefore:
40 / (2 2/3) =
40 / (8 /3) =
40 * 3/8 =
120/8 = 15
How to solve quadratic inequalities algebraically?
Solve ( x – 3)( x + 2) > 0.
Solve ( x – 3)( x + 2) = 0. By the zero product property,
Make the boundary points. Here, the boundary points are open circles because the original inequality does not include equality (see Figure 1).
Select points from the different regions created (see Figure 2).
See whether the test points satisfy the original inequality.
Since x = –3 satisfies the original inequality, the region x < –2 is part of the solution. Since x = 0 does not satisfy the original inequality, the region –2 < x < 3 is not part of the solution. Since x = 4 satisfies the original inequality, the region x > 3 is part of the solution.
Represent the solution in graphic form and in solution set form. The graphic form is shown in Figure 3.
The solution set form is { x| x < –2 or x > 3}.
Figure 1. Boundary points.Figure 2. Three regions are created.Figure 3. Solution to ExampleThe table shows the heights in inches of trees after they have been planted. Determine the equation which relates x and y.
Height In Pot, x | Height Without Pot, y
30 | 18
36 | 24
42 | 30
48 | 36
A. y = x - 6
B. y = x - 10
C. y = x - 12
D. y = x + 6
your job is to design a staircase that has a total rise of 11 feet and meets these design guidelines:
1) the slope of the staircase is between 0.55 and 0.85
2) twice the rise plus the run must be between 24 and 25 inches
3) there can be no irregular steps
4) each step must be the same size
how many risers and treads?
what size are they?
EXPLAIN DESIGN AND INCLUDE CALCULATIONS.
show how each design guideline is met.
What is the answer and steps?
Why are volumetric measurements defined as a cubed unit?
PLEASE HEP ME ANSWER THIS REALLY HARD QUESTION
What is the value in dollars of a stack of dimes that is 10 cm high? (1mm = 1 dime?
The value in dollars of a stack of dimes that is 10 cm high is $10.
What are nickles, dimes, quarters and cents?A dollar is further divided into some majorly used parts as:
A cent = 100th part of a dollar = $1/100 = $0.01
A nickle= 20th part of a dollar = $1/20 = $0.05
A dime = 10th part of a dollar = $1/10 = $0.10
A quarter = 4th part of a dollar = $1/4 = $0.25
If each dime is 1 mm then 10 dimes will be 1 cm high;
1 dime / 1 mm = x dimes / 10 mm Cross multiply
1 dime * 10 mm = x * 1 mm
10 dimes = x The mm
Since a dime is about 1 mm thick (10mm equals 1 cm), 10 cm high would be 100 dimes;
10 dimes = $1
$1 times 10 = $10
Hence, The value in dollars of a stack of dimes that is 10 cm high is $10.
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I’m stuck on this, what would be the answer?
Given: quadrilateral ABCD inscribed in a circle Prove: ∠A and ∠C are supplementary, ∠B and ∠D are supplementary Let the measure of = a°. Because and form a circle, and a circle measures 360°, the measure of is 360 – a°. Because of the ________ theorem, m∠A = degrees and m∠C = degrees. The sum of the measures of angles A and C is degrees, which is equal to , or 180°. Therefore, angles A and C are supplementary because their measures add up to 180°. Angles B and D are supplementary because the sum of the measures of the angles in a quadrilateral is 360°. m∠A + m∠C + m∠B + m∠D = 360°, and using substitution, 180° + m∠B + m∠D = 360°, so m∠B + m∠D = 180°. What is the missing information in the paragraph proof?
Quadrilateral ABCD is inscribed in a circle. Let the measure of arc BAD be a°. Arcs BCD and BAD form a circle and a circle measures 360°, then measure of arc BCD is 360°-a°.
The inscribed angle theorem states that an angle inscribed in a circle is half of the central angle that subtends the same arc on the circle.
Because of the Inscribed angle theorem,
[tex]m\angle A=\dfrac{a^{\circ}}{2};[/tex]
[tex]m\angle C=\dfrac{360^{\circ}-a^{\circ}}{2}.[/tex]
The sum of the measures of angles A and C is
[tex]\dfrac{a^{\circ}}{2}+\dfrac{360^{\circ}-a^{\circ}}{2}=180^{\circ}.[/tex]
Therefore, angles A and C are supplementary, because their measures add up to 180°.
Angles B and D are supplementary, because the sum of the measures of the angles in a quadrilateral is 360°.
m∠A + m∠C + m∠B + m∠D = 360°,
and using substitution,
180° + m∠B + m∠D = 360°, so m∠B + m∠D = 180°.
Answer: inscribed angle theorem
Answer:A
Step-by-step explanation:
Inscribed angle
Pls help me out here hope the points are good (no scams pls)
6/3 =2
15/3 =5
6/15 = 2/5
8/4 =2
20/4 =5
8/20 = 2/5
answer is B 2/5
Suppose Mrs. Reyes would like to save Php 1,000.00 at the end of each month for 9 months in a fund that gives 5% per annum compounded monthly. How much would the value of her savings be after 7 months?
After 7 months her savings will be 7117.64.
Step-by-step explanation:
Given :
Rate is r = 5% = 0.05
Compounding interval, n = 12
Solution :
Now,
[tex]\rm \dfrac{r}{n} = \dfarc{0.05}{12}[/tex]
[tex]\rm \dfrac{r}{n} = 0.004167[/tex]
Now first deposit duration is 7 months. Therefore, its value is [tex]\rm a_1 = 1000\times (1.004167)^7[/tex]
Now second deposit duration is 6 months. Therefore, its value is
[tex]\rm a_2 = 1000\times (1.004167)^6[/tex]
Now third deposit duration is 5 months. Therefore, its value is
[tex]\rm a_3 = 1000\times (1.004167)^5[/tex]
and so on.
The values are in geometric sequence where
[tex]\rm a = 1000\times (1.004167)[/tex]
[tex]\rm r = 1.004167[/tex]
We know that the sum of the geometric sequence is given by,
[tex]\rm S_n = \dfrac{a (r^n-1)}{(r-1)}[/tex] ------ (1)
Now put the values of a and r in equation (1),
[tex]\rm S_7=\dfrac{1000\times(1.004167)((1.004167)^7-1)}{(1.004167-1)}[/tex]
[tex]\rm S_7 = 7117.64[/tex]
After 7 months her savings will be 7117.64.
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A toy factory creates handmade train sets. One train car takes 0.4 hours to construct and 0.6 hours to paint. A section of wooden track requires 0.2 hours to construct and 0.1 hours to paint. A full train set with x train cars and y sections of wooden track takes 5.2 hours to construct and 4.2 hours to paint. Which system of equations can be used to find the number of train cars and number of sections of wooden track in a full train set?
To find the number of train cars and sections of wooden track in a full train set, we can set up a system of equations. The equations are 0.4x + 0.2y = 5.2 and 0.6x + 0.1y = 4.2.
Explanation:To find the number of train cars and number of sections of wooden track in a full train set, we can set up a system of equations based on the given information.
Let's use x to represent the number of train cars and y to represent the number of sections of wooden track.
The time to construct 1 train car is 0.4 hours, so the time to construct x train cars is 0.4x hours.The time to paint 1 train car is 0.6 hours, so the time to paint x train cars is 0.6x hours.The time to construct 1 section of wooden track is 0.2 hours, so the time to construct y sections of wooden track is 0.2y hours.The time to paint 1 section of wooden track is 0.1 hours, so the time to paint y sections of wooden track is 0.1y hours.The total time to construct a full train set is 5.2 hours, so we have the equation 0.4x + 0.2y = 5.2.The total time to paint a full train set is 4.2 hours, so we have the equation 0.6x + 0.1y = 4.2.The system of equations that can be used to find the number of train cars and number of sections of wooden track in a full train set is:
0.4x + 0.2y = 5.2
0.6x + 0.1y = 4.2
Find the slope and y intercept
We have 5 dice, 4 of these dice are the same, the fifth is not. find it!
The dice are illustrations of patterns
The fifth die that is different from the other four dice is die D
From the question, we have the following highlights
The pattern on all the 5 dice include 4, 5 and 6When the patterns are ordered, dice A, B, C and E have their pattern to be in a clockwise directionDie D has its pattern to be in a counterclockwise directionHence, the fifth die that is different from the other four dice is die D
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what's 4/5 + 6/5 equals
Translate each word phrase into an algebraic expression.
The perimeter of a rectangle 24 units long and w units wide.
whats the area of a cardboard In one carton if the length is 9 inches height is 9inches width is 4 inches and is 240 ml as well as also in a 946 ml container and a 1.89 L container?
Assuming that the cardboard forms a regular rectangle, therefore the area of the cardboard is simply taken to be the product of length and width. Therefore:
A = l w
A = (9 inches) * (4 inches)
A = 36 square inches = 36 inches^2
Juanita is 13 years older than her cousin. The sum of their ages is no less than 103 years.
What is the youngest age Juanita's cousin can be?
Answer:
45
Step-by-step explanation:
I can confirm, the first guy is right (I did the test)
explain how you can tell the frequency of a data value by looking at the dot plot
If there are 62 values in a data set, how many classes should be created for a frequency histogram?
Franklin waters' annual gross pay is $55,400. He takes a married exemption of $4,000. His state income tax rate is 3.5 percent. How much will he pay annually in state tax?
F(x) =8+2x and g(x) =1/2x the value of f/g(5)
simplify
3m^-2
over
5n^-3
does anyone understand how to do this? Solve r4<−5 or −2r−7 ≤ 3 . The solution is _or_
The given problem consists of solving two inequalities. The first one, r4<−5, is invalid since the 4th power of any real number cannot be a negative number. For the second inequality, −2r−7 ≤ 3, the solution is r ≥ -5.
Explanation:The subject of this question is Mathematics, specifically relating to solving inequalities. To answer your question, let's solve the two given inequalities independently. Starting with the first one, r4<−5, this inequality is invalid as the 4th power of any real number (r) cannot be less than -5. Moving on to the second inequality, −2r−7 ≤ 3, we first add 7 to both sides to isolate the term with the variable, giving us -2r ≤ 10. Dividing both sides by -2 (remember to flip the inequality sign when multiplying or dividing by a negative number) gives us r ≥ -5. Therefore, the solution to the given inequalities is r ≥ -5.
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Jackie is wrapping a birthday present. The gift box is in the shape of a rectangular prism. It has a length of 8 inches, a width of 10 inches, and a height of 3 inches. What is the minimum amount of wrapping paper she will need to completely cover the box?
Answer:
D
Step-by-step explanation:
how do I do this problem ??
How do you make $2.161616 as a fraction and a mixed number
Solve x2 = 144
Select one:
a. 72
b. 12
c. ±12
d. −12
So I chose B which I thought was correct but it was wrong
Power is the result of multiplying two numbers together. The solution of the x²=144 is ±12. The correct option is C.
What is power?Power is the result of multiplying two numbers together such that both numbers are equal to each other. Power is typically expressed by a base number and an exponent. The base number indicates the number being multiplied. The exponent, which is a little number printed above and to the right of the base number, indicates the number of times the base number is multiplied.
The solution of the given expression can be written as,
x² = 144
x² = 12×12 or -12×-12
x = √(12×12) or √(-12×-12)
x = 12 or -12
x = ±12
Thus, the solution of the x²=144 is ±12. This is because the multiplication of two positive numbers is positive, also, the sum of the two negative numbers is positive.
Hence, the solution of the x²=144 is ±12
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