A repeating decimal, also called a recurring decimal, is a number whose decimal representation eventually becomes periodic (i.e., the same sequence of digits repeats indefinitely). The repeating portion of a decimal expansion is conventionally denoted with a vinculum so, for example,
The minimum number of digits that repeats in such a number is known as the decimal period.
Repeating decimal notation was implemented in versions of the Wolfram Language prior to 6 as PeriodicForm[RealDigits[r]] after loading the add-on package NumberTheory`ContinuedFractions`.
All rational numbers have either finite decimal expansions (i.e., are regular numbers; e.g., ) or repeating decimals (e.g., ). However, irrational numbers, such as neither terminate nor become periodic.
Numbers such as 0.5 are sometimes regarded as repeating decimals since.
A publisher claims that the average salary paid at its company is $37,500 but it could differ as much as $4,500. Write and solve an absolute value inequality to determine the range of salaries at this company.
|x − 37500| ≤ 4500; The salaries range from $33,000 to $42,000
|x − 37,500| ≤ 4500; The salaries are less than $33,000 or greater than $42,000.
|x − 37500| ≥ 4500; The salaries range from $33,000 to $42,000
|x − 37,500| ≥ 4500; The salaries are less than $33,000 or greater than $42,000.
How do you rank an answer the brainliest? Really would like to know.
Which of the following is a radical equation?
Answer:
Option D. 7√x = 14
Step-by-step explanation:
By definition radical equation is an equation in which a variable is under radical.
Now we see the options given only in option D. x is variable under radical.
Therefore, 7√x = 14 is the radical equation.
Hence Option D. is the correct option.
All tutors that are employed at a local college must take a test and must score in the top 20%. if the scores are normally distributed with a mean of 78 and a standard deviation of 5, what is the cutoff score to be hired?
To solve this problem, we use the z statistic with formula:
z = (x – u) / s
or
x = s z + u
First we find the value of z at P = top 20%
z = 0.84
So the cut-off is:
x = 5 * 0.84 + 78
x = 82.2 (ANSWER)
In the figure, AB||CB. If CD:BA = 6:5 and the area of CED is 288, find the area of BEA
Answer:
The area of BEA is 200 square units.
Step-by-step explanation:
Given information: AB||CD and CD:BA = 6:5.
Let the length of sides CD and BA are 6x and 5x respectively.
If a transversal line intersect two parallel lines, then the alternative interior angles are equal.
[tex]\angle EAB=\angle EDC[/tex] (Alternate interior angles)
[tex]\angle EBA=\angle ECD[/tex] (Alternate interior angles)
[tex]\angle AEB=\angle DEC[/tex] (Vertically opposite angles)
By AAA property of similarity,
[tex]\triangle ABE\sim \triangle DEC[/tex]
The area of two similar triangles is proportional to the square of their corresponding sides.
[tex]\frac{Area(CED)}{Area(BEA)}=\frac{CD^2}{BA^2}[/tex]
[tex]\frac{288}{Area(BEA)}=\frac{(6x)^2}{(5x)^2}[/tex]
[tex]\frac{288}{Area(BEA)}=\frac{36x^2}{25x^2}[/tex]
[tex]\frac{288}{Area(BEA)}=\frac{36}{25}[/tex]
[tex]288\times 25=36\times Area(BEA)[/tex]
[tex]7200=36\times Area(BEA)[/tex]
Divide both sides by 36.
[tex]200=Area(BEA)[/tex]
Therefore the area of BEA is 200 square units.
Delia uses 3.5skeins of yard to knit one scarf how many scarves can she completed if she has 19skeins of yarn
Coach Stevens needs to purchase sprinklers to water the baseball field. The standard distance between bases is 90 feet and the infield is a perfect square.
Coach Stevens found one sprinkler that sprays a maximum distance of 50 feet.
If Coach Stevens placed the sprinkler on the pitcher's mound, would the water spray so that the entire infield was watered? Justify your response.
Answer:
So, if coach Stevens places as sprinkler of maximum distance 50 ft, he won't be able to cover the entire infield.
Step-by-step explanation:
Consider the infield as a polygon ABCDE.
It is given that each side AB, BC, CD, and DA is of length 90ft. It is also given that the infield is a perfect square.
Thus, the area of the square ABCD = 8100 ft.
Now consider the triangle BCD. Because of symmetry, the area of this triangle equals half the area of the square. Again, because of symmetry, the length of the base BD equals twice the length of the height EC.
Thus from to the formula of area of the triangle:
base × height = 4050 base × height = 8100 2(height) × height= 8100 height63.64 ft
Please answer with steps on how you solved it!
Jason bought a soft drink for $3 dollars and 9 candy bars. He spent a total of $30. How much did each candy bar cost?
solve
4x + 6 = 38
A. 144
B. 11
C. 8
D. 3.5
The length of a rectangle is the square root of 100 times an unknown number, x. The width is one-half an unknown number, y, less three-halves x. If the area of the rectangle is 125 cm2, find an equation that would give the width of the rectangle given the length.
What happens when you multiply a positive number by a positive number less than 1?
Find the value of y.
–2y + 16 + 6y = 44
a. 15
b. 7
c. 3.5
d. –6
Chance can wash the car in 2 hours, while Sandy can wash the same car in 4 hours. How many hours would it take for them to wash the car together?
A. 4/3
B. 3/4
C. 3
D. 4
Chance and Sandy together can finish the work in 4/3 hours.
What is the relation between time and efficiency?The relationship between time and efficiency is they are inversely proportional.
If one quantity increases other decreases and vice versa.
Given, Chance can wash the car in 2 hours.
∴ The efficiency of Chance is (1/2).
Sandy can wash the same car in 4 hours.
∴ The efficiency of Sandy is (1/4).
So, their combined efficiency is (1/2 + 1/4) = 3/4.
∴ Together they can finish the work in 4/3 hours.
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Given the function f(x)=-5x^2-x+20 find f(3)
f(3) = -5*3^2 - 3 + 20 = -5*9 - 3 + 20 = -45 - 3 + 20 = -28;
Answer: - 28
Step-by-step explanation:
f(x) = -5x^2 - x + 20
To find f(3), we simply put x = 3 and then simplify
f(3) = - 5(3)^2 - 3 + 20
= -5(9) - 3 + 20
= -45 - 3 + 20
= -48 +20
= -28
f(3) = -28
If y varies directly as x, and y = 12 when x = 15, find x when y = 21.
Please help not really sure what to do here.
Which of the binomials below is a factor of this trinomial?
x2 - 10x + 24
A. x + 4
B. x - 3
C. x - 4
D. x + 3
Answer:
Option (c) is correct.
(x-4) is a factor of given trinomial.
Step-by-step explanation:
Consider the give trinomial [tex]x^2-10x+24[/tex]
We have to find the factors of given binomial and choose the correct one from the given options.
Consider the given polynomial [tex]x^2-10x+24[/tex]
We will simplify the given quadratic equation using middle term split method,
-10x can be written as -4x-6x
Such that the product of term will give the product of the remaning terms,
Thus, the given trinomial becomes,
[tex]x^2-4x-6x+24[/tex]
Taking x common from first two terms and -6 common from last two terms, we have,
[tex]x(x-4)-6(x-4)[/tex]
Thus, take (x-4) common , we have,
[tex](x-4)(x-6)[/tex]
Thus, out of given factors (x-4) is a factor of given trinomial.
98,464 rounded to the nearest ten thousand is
What is the value of the expression “two less than six times the difference of a number and five” when n = 9?
Answer:
22
Step-by-step explanation:
The value of expression is 22.
Step-by-step explanation:
Given the statement “two less than six times the difference of a number and five” when n = 9. we have to find the value of expression formed by the above statement.
Difference of a number n and 5 gives (n-5)
Now, we have to write two less than 6 times the difference, we get the expression 6(n-5)-2
Here, the number n is 9
∴Value of expression is 6(9-5)-2=6(4)-2=24-2=22
Hence, the value of expression is 22.
The base of a box is a rectangle. The width of the box is half its length. The height of the box is 0.5m. Find the volume of the box if the area of the base is 1.08m² less than the combined area of the sides.
Answer:
Step-by-step explanation:
We assume the box is open-top.
If the width of the box is represented by w, then its length is 2w. The area of the base is then w·2w = 2w².
The combined area of the sides is the product of the perimeter of the base, 2(w+2w) = 6w and the height, 0.5, so is 3w.
Since the base area is 1.08 m² less than the lateral area, we have
... 2w² = 3w -1.08
... 2w² -3w +1.08 = 0 . . . . rearrange to standard form
... w² -1.5w +0.54 = 0 . . . make the leading coefficient 1 (divide by 2)
... (w -0.9)(w -0.6) = 0 . . . factor
The width of the box may be either 0.6 meters or 0.9 meters.
The volume is the product of width, length, and height
V = w·2w·0.5 = w²
V = 0.36 m³ . . . or . . . 0.81 m³. . . . . . (there are two possible answers)
Find the difference between the product of 21.33 and 2.04 and the sum of 1.115, 3.18, 22.0613, and 12.2384. A. 5.1318 B. 38.5947 C. 4.9185 D. 43.5132
To find the difference, first find the product of 21.33 and 2.04, then find the sum of 1.115, 3.18, 22.0613, and 12.2384, and finally subtract the sum from the product. The correct answer is 4.9185.
To find the difference between the product of 21.33 and 2.04 and the sum of 1.115, 3.18, 22.0613, and 12.2384, follow these steps:
Calculate the product of 21.33 and 2.04:The difference is 4.9185, which corresponds to option C in the given choices.
You and your friend are buying throw blankets with your names embroidered on them.The cost of the throw blanket is x dollars and the cost of each embroidered letter is y dollars.Your name has 6 letters and the total cost is $29.Your friend’s name has 3 letters and the total cost is $24.50.Find the cost of the throw blanket and the cost of each embroidered letter.
Answer:
Throw Blanket : $20
Embroidered Letter: $1.50
Step-by-step explanation:
Create a set of equations to solve this problem, where x is cost of throw blanket and y is cost of single embroidered letter.
My name:
[tex]x+6y=29\\x=29-6y[/tex]
Friend's name:
[tex]x+3y=24[/tex]
Substituting x into friend's name equation:
[tex](29-6y)+3y=24.5\\3y-6y=24.5-29\\-3y=-4.5\\y=1.5[/tex]
Substituting y into equation for x:
[tex]x=29-6(1.5)\\x=29-9\\x=20[/tex]
Suppose we did an experiment to gather data on the number of un-popped kernels of microwave popcorn. Half of the students in your class took home a bag, put it in the freezer overnight, and popped it the next day. The other half took the bag, left it on their kitchen counter overnight, and popped it the next day. Each group counted the number of un-popped kernels. Are these data paired or independent
The data collected on the number of un-popped kernels of popcorn, where one group's bags were frozen and the other's were left at room temperature, are considered independent. This is because each bag was only subjected to one condition and was not measured in both conditions, which would be necessary for paired data.
In the question provided, students collected data on the number of un-popped kernels of microwave popcorn where one group froze the popcorn while the other left it at room temperature. To determine whether the data are paired or independent, we need to understand the nature of the experiment setup.
Since every student’s popcorn was subject to a unique condition (frozen or room temperature) and they're not measured in both conditions, we can deduce that the data here are independent. This means that the outcome of one does not influence the outcome of the other.
In comparison to a scenario where the same item or subject is tested under two different conditions the popcorn experiment does not meet this criterion; that would be an example of paired data. An unpaired test such as the unpaired t-test may be appropriate here if we want to assess the effects of freezing on the number of un-popped kernels compared to leaving them at room temperature. Each bag of popcorn represents an independent sample from the population of all popcorn bags.
Mark borrowed $5,500 at 11.5 percent for five years. What is his monthly payment?
A. $131.50
B. $173.50
C. $120.95
D. $150.22
Answer:
C option is correct
Step-by-step explanation:
Given: payment borrowed (P)= $5,500
rate (r)=11.5 or 0.115
Time(t)= 5 years
Compound monthly(k)=12
To find : Monthly payment (M)
Formula used : [tex]M= P/(\frac{1-(1+\frac{r}{k})^{-kn}}{\frac{r}{k}})[/tex]
Solution : [tex]M= 5500/(\frac{1-(1+\frac{0.115}{12})^{-60}}{\frac{0.115}{12}})[/tex]
by solving we get, M =$120.95
therefore, option C is correct
Triangle RST has vertices R(2, 0), S(4, 0), and T(–3, –1). The image of triangle RST after a rotation has vertices
R'(0, –2), S'(0, –4), and T'(–3, –1). Which rule describes the transformation?
R0, 90°
R0, 180°
R0, 270°
R0, 360°
Answer:
It should be C aka 270°
Step-by-step explanation:
Answer:
3 option is correct.
Step-by-step explanation:
Given Triangle RST has vertices R(2, 0), S(4, 0), and T(–3, –1). The image of triangle RST after a rotation has vertices R'(0, –2), S'(0, –4), and T'(–3, –1).
We have to tell the rule describes the transformation.
A rotation is transformation that turns a figure about a fixed point. An object and its rotation are the same shape, but the figures may turned or rotate in different directions.
Here, the coordinates shift after rotation according to the rule
(2,0) → (0,-2) i.e (x, y) → (y, -x)
As, Rotation of 270º on coordinate axes.
(x, y) → (y, -x)
which match to the given rule.
hence, 3 option is correct.
George uses the diagram below to help determine 30% of 60. Which expression could George have used?
Answer:
[tex]\frac{3}{10}\times 60\text{ or }\frac{30}{100}\times 60[/tex]
Step-by-step explanation:
Given expression,
30% of 60,
We know that,
Convert percentage to fraction :
[tex]a\% =\frac{a}{100}[/tex]
Thus,
[tex]30\% = \frac{30}{100}=\frac{3}{10}[/tex]
So, 30% of 60 = [tex]\frac{3}{10}\times 60[/tex]
Which is the required expression.
Triangle LMN is positioned inside rectangle LKPN as shown in the diagram. Which is the area of △LMN△LMN?
Answer:
Step-by-step explanation:
The area of the triangle inside the rectangle is calculated by using the formula for the area of a triangle, 1/2 * base* height. Given the base is the length of the rectangle and the height is the breadth of the rectangle, we substitute these measurements into the formula to determine the area. Area of triangle LMN is 15.6 square cm.
Explanation:To determine the area of the triangle inside the rectangle, we first need to understand the relationship between these two shapes. Given the base of the triangle, LN, is the same as the length of the rectangle, 6.5 cm, and the triangle is between the parallel lines of the rectangle, we can infer that the height of the triangle is the same as the breadth of the rectangle, which is 4.8 cm.
Now, the area of a triangle is given by the formula 1/2 * base * height.
Substituting the given measurements into this formula, we get
= 1/2 * 6.5 cm (base) * 4.8 cm (height)
= 0.5 * 6.5 cm (base) * 4.8 cm (height)
= 15.6 square cm
This will give us the area of the triangle LMN.
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The complete question is given below:
Triangle LMN is positioned inside rectangle LKPN as shown in the diagram. Which is the area of △LMN?
The length of rectangle and triangle are same, 6.5 cm. The breadth of rectangle is 4.8 cm. The triangle lies between the parallel lines of rectangle with base LN.
HELP! CONFUSED ON WHAT TO DO!
Marathon Training
Amanda and Kevin are training for a marathon. To prepare for this marathon they have been training and tracking their progress periodically. In the first week of training Kevin ran an average of 9.00 minutes per mile. Later, in week five of training he ran an average of 6.50 minutes per mile. In the first week of training Amanda ran an average of 10.00 minutes per mile. Later, in week seven of training she ran an average of 5.00 minutes per mile. Assuming that Kevin and Amanda continue to train and improve their times at the same rate your task is to determine which week they will have the same average minutes per mile. We will assume that the relationship is linear as they will be training for a maximum of 10 weeks. To complete this task follow the steps below.
1. Determine the equation of a line in standard form that represents Kevin’s training progress. His progress corresponds to the points (1, 9.00) and (5, 6.50). 2. Determine the equation of a line in standard form that represents Amanda’s training progress. Her progress corresponds to the points (1, 10.00) and (7, 5.00) 3. Solve the system of equations (showing work would be awesome!)
4. In which week will Kevin and Amanda have the same average minutes per mile?
5. If Kevin and Amanda continue to train until week 16, what will their times be? 6. Do you believe a linear model best represents the relationship of the time of the runners and the weeks that passed?(Hint: look at question 5). What do you think this says about problems in the real world? Justify your thoughts in 3-4 sentences.
Sorry it's this long, but please, I really don't know where to start or what to use to solve! I really need the help to understand. If you can't answer all, it's OK, but at least 2 or more would be great, so that way, I'll know to where to start!
Of all rectangles with a perimeter of 21 21, which one has the maximum area? (give the dimensions.) let a be the area of the rectangle. what is the objective function in terms of the width of the rectangle, w?
To find the rectangle with the maximum area, we need to find the dimensions and write the objective function in terms of the width of the rectangle.
Explanation:To find the rectangle with the maximum area, we need to find the dimensions of the rectangle that will give us the maximum area. Let's assume the width of the rectangle is w. Since the perimeter of the rectangle is given as 21, we can write the equation:
2w + 2l = 21
We can rearrange this equation to solve for l:
2l = 21 - 2w
l = (21 - 2w)/2
The area of the rectangle can be calculated as:
A = w * l
Substituting the expression for l we obtained earlier:
A = w * (21 - 2w)/2
Expanding and simplifying this equation will give us the objective function in terms of the width w.
Ezekiel was having a pizza party, so he bought 7 pizzas, each with 8 slices. Unfortunately, word of his party got out, and the party got out of control. Now, Ezekiel is trying to figure out how many people showed up. If he assumes that on average each person ate 3 1/2 slices, and if all the pizza was eaten, how many people would Ezekiel guess showed up?