Answers
Answer:
Step-by-step explanation:
The circumference is the perimeter of a circle, which is equal to 131.88ft.
Circumference = [tex]2\pi r^{2}[/tex]
[tex]131.88=2\pi r^{2} \\r^{2} =\frac{131.88}{2\pi } \\r=\sqrt{20.989} \\r=4.581[/tex]
This means that the diameter is:
[tex]d=2r\\d=9.163[/tex]
So our area is:
[tex]A=\pi r^{2} \\A=\pi (4.581)^{2} \\A=65.940[/tex]
Hope this helped!
Related Questions
During a sale, the price of all computers in a store is being reduced by 25%. Albert is interested in a computer with an original cost of $650. Two weeks later, the sale price of this computer is reduced by an additional 5%. Albert thinks he can now get the computer for 30% off the original price. Find the sale price after the double reduction, and then the sale price after a single reduction of 30%. Is the double reduction (25% off and then 5% off) the same as or different than the single reduction (30% off)?
Answers
The sale price of the computer after a single reduction of 30% is $455.
The double reduction (25% off and then 5% off) and the single reduction of 30% are different.
The sale price after the double reduction is $463.13, while the sale price after a single reduction of 30% is $455.
What is a percentage?
The percentage is a way of expressing a fraction or proportion out of 100. It is commonly used in many different areas such as finance, math, science, and everyday life.
First, we need to find the sale price of the computer after the double reduction.
When the price of all computers in the store is reduced by 25%, the sale price of the computer that originally cost $650 becomes:
Sale price after first reduction ,
=> 650 - 25% 0f 650
=> 650 - [tex]\frac{25}{100}\times[/tex]650 = $ 487.5
Then, when the sale price is reduced by an additional 5%, the sale price of the computer becomes:
Sale price after double reduction
=> 487.5 - 5% of 487.5
=> 487.5 - [tex]\frac{5}{100}\times[/tex]487.5 = $463.13
Therefore, the sale price of the computer after the double reduction is $463.13.
Next, we need to find the sale price of the computer after a single reduction of 30%.
When the original cost of the computer is reduced by 30%, the sale price becomes:
Sale price after single reduction ,
=> 650- 30% of 650
=> 650 - [tex]\frac{30}{100}\times[/tex] = $455
Therefore, the sale price of the computer after a single reduction of 30% is $455.
The double reduction (25% off and then 5% off) and the single reduction of 30% are different.
The sale price after the double reduction is $463.13, while the sale price after a single reduction of 30% is $455.
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For each of the shapes below, state whether it is a regular polygon, an irregular
polygon or neither.
A
D
B
E
C
Answers
Each of the shapes below, The polygons are identified as:
A- Irregular polygon
B- Neither
C- Regular polygon
D- Regular polygon
E- Regular polygon
What is polygon?A polygon is a two-dimensional geometric shape that is defined as a closed figure with three or more straight sides and angles. Polygons can be convex or concave, depending on whether all of their interior angles are less than or greater than 180 degrees, respectively. Some common examples of polygons include triangles (3 sides), squares (4 sides), pentagons (5 sides), hexagons (6 sides), and octagons (8 sides). Polygons are frequently used in geometry, as they can be used to calculate areas, perimeters, and other properties of shapes.
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if (2x10^n)+(4.02x10^5), what is n?
Answers
The vaIue οf n = 5 .
What is an equatiοn?A mathematicaI statement knοwn as an equatiοn cοnsists οf twο aIgebraic expressiοns separated by equaI signs (=) οn either side.
It demοnstrates the equaIity οf the reIatiοnship between the printed statements οn the Ieft and right.
Left side equaIs right side in aII fοrmuIas.
Tο find the vaIues οf unknοwabIe variabIes, which stand in fοr unknοwabIe quantities, yοu can sοIve equatiοns.
A statement is nοt an equatiοn if it Iacks the equaIs sign.
When twο expressiοns have the same vaIue, a mathematicaI statement knοwn as an equatiοn wiII incIude the symbοI "equaI tο" between them.
Accοrding tο οur questiοn-
[tex]2 \times 10^{(n+5)} + 4.02 \times 10^5 = 2 x 10^{(n+5)} + 4.02 \times 10^n[/tex]
Subtracting [tex]2 \times 10^{(n+5)[/tex] frοm bοth sides:
[tex]4.02 \times 10^5 = 4.02 \times 10^n[/tex]
Dividing bοth sides by 4.02:
[tex]10^5 = 10^n[/tex]
Therefοre, n = 5.
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COMPLETE QUESTION-
if [tex](2\times10^n)+(4.02\times10^5)[/tex], what is n?
would your confidence intervals of parts a and c be valid if the distribution of the original population were not normal?
Answers
The 95% confidence interval for μ is (80.52, 82.68).
To find the 95% confidence interval for the population mean (μ), we can use the following formula
CI = X ± z* (σ / √n)
where X is the sample mean, σ is the population standard deviation (unknown), n is the sample size, and z* is the critical value from the standard normal distribution corresponding to the desired confidence level (in this case, 95%).
The critical value z* can be found using a standard normal distribution table or calculator, or using a statistical software. For a 95% confidence level, the z* value is 1.96.
Plugging in the values given, we get
CI = 81.6 ± 1.96 × (5.4 / √100)
Simplifying this expression, we get
CI = 81.6 ± 1.08
= (80.52, 82.68)
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The given question is incomplete, the complete question is:
A random sample of 100 observations from a normally distributed population possesses a mean equal to 81.6 and a standard deviation equal to 5.4 . Find a 95% confidence interval for μ
if two different students are randomly selected (i.e., without replacement), find the probability that both the first and second student studied.
Answers
The probability that both the first and second student studied = p²
To find the probability that both the first and second students studied when two different students are randomly selected, we can use the multiplication rule of probability.
What is the multiplication rule of probability?The multiplication rule of probability states that if the probability of event A is p(A), and the probability of event B, given that event A has occurred, is p(B|A), then the probability of the joint occurrence of A and B is given by p(A and B) = p(A) × p(B|A).
So, if we let A be the event that the first student studied, and B be the event that the second student studied, then we need to find the probability of the joint occurrence of A and B.
We can assume that the probability that any student studied is equal to some value p, and the probability that any student didn't study is equal to q = 1 - p. Since there are only two possibilities for each student (studied or not studied), then p + q = 1. So, we can use the complement rule of probability to write:
p(A) = probability that the first student studied = p, and
p(not A) = probability that the first student didn't study = q = 1 - p,
p(B|A) = probability that the second student studied, given that the first student studied = p, and
p(B|not A) = probability that the second student studied, given that the first student didn't study = p.To find the probability that both the first and second student studied, we need to find the probability of the joint occurrence of A and B. Using the multiplication rule, we get:
p(A and B) = p(A) × p(B|A) = p × p = p².
Which is the probability that both the first and second students studied.
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given a price of $11 per gift box, how many boxes of chocolate should choco lovers produce? gift boxes what will the profit or loss be per gift box? $ per gift box c. suppose that choco lovers raises the price to $13 per gift box. now how many boxes should choco lovers produce? gift boxes what will the new profit or loss be per gift box?
Answers
The boxes of chocolate should choco lovers produce= $11
What are numbers?A number is a numerical unit of measurement and labeling in mathematics.
The natural numbers 1, 2, 3, 4, and so on are the first examples.
Number words are a linguistic way to express numbers.
Most commonly, specific numbers can be represented using symbols known as numerals; for instance, the numeral "5" stands in for the number five.
Basic numerals are frequently grouped in a numeral system, which is an ordered manner to represent any number, because only a small number of symbols can be learned.
The most widely used number system is the Hindu-Arabic number system, which enables the depiction of any number using a combination of 10 basic numerical symbols, or "digits."
Hence, The boxes of chocolate should choco lovers produce= $11
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A student simplified the rational expression
using the steps shown.
Is the answer correct? Explain.
Answers
Step-by-step explanation & Answer
No, the answer is not correct
In the second step, the student did not use the quotient of powers property correctly. Instead, they should have subtracted inside the parentheses instead of dividing. This would have left them with [tex]x^{(\frac{4}{5} )}[/tex]. They should have then multiplied this power by [tex]^{\frac{1}{2} }[/tex] resulting in [tex]x^{(\frac{4}{10})}[/tex] which simplified is [tex]x^{(\frac{2}{5}) }[/tex] which is the correct answer.
That is just an example on how the answer is done.
can someone please help
Answers
Answer:
The circle x^2+y^2-2x-8y+17=0 has translated 5 units to the leftand 2units down.
Step-by-step explanation:
If we translate this circle to the left 5 units, and 2 units down,
we will subtract 5 from the center x coordinate and 2 for the center y coordinate
The center is (1,-4)
So the new center prime is (-4,-6)
Since a translation keep angles and measures,
Our radius will remain untouched so our new equation is
[tex](x + 4) {}^{2} + (y + 6) {}^{2} = 16[/tex]
In triangle ABC, point D lies on side BC such that ΔABD and ΔACD have the same perimeter. Points E and F are constructed on sides CA and AB in a similar manner, respectively, each dividing ΔABC into two triangles of equal perimeter. If BD=5, DC=3, and the perimeter of ΔABC is 18, what is the ratio of the area of ΔDEF to the area of ΔABC?
Answers
Answer:
10
Step-by-step explanation:
A box contains 40 pens. 30 of the pens are blue and the rest are green. One pen is taken out at random and replaced by Live of the other colour. Another pen is taken out at random and replaced by Live of the other colour. A Linal pen is taken out at random. (a) Work out the probability that all three pens are green
Answers
Work out the probability that all three pens are green p = 10/40 * 4/44 * 8/48 = 3/352.
a) p = 10/40 * 4/44 * 8/48 = 3/352
b) p = 3/352 + 30/40 * 24/44* 28/48
=3/352+ 203/704
= 209/704
= 19/64
c) p= 1 - 19/64
= 64/64 - 19/64
= 45/64
Probability is just the way that possible something is to occur.
Whenever we're uncertain about the result of an occasion, we can discuss the probabilities of specific results — how likely they are. The investigation of events administered by probability is called insights.
The probability of an occasion must be somewhere in the range of 0 and 1 and can likewise be composed as a rate.
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A circle has 360 degrees. A right angle turns through of a circle, or off. Degrees
Answers
A right angle turns through a circle, or off, which is equal to 90 degrees.
A circle is a shape that has no edges or corners.
It is a closed shape that is formed by a curve that is equidistant from a fixed point, known as the center.
A degree is a unit of measurement that is used to Bangles.
It is equal to of a circle, and there are 360 degrees in a circle.
A right angle is an angle that measures 90 degrees.
It is formed when two lines or rays meet at a point and create a square corner.
When a right angle turns through a circle, it covers one-quarter of the circle, which is equal to 90 degrees.
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HELPPPPPPPPPPPO!!!!!!!!!
Answers
Answer:
C
Step-by-step explanation:
What additional information would be sufficient, along with the given, to conclude that lmno is a parallelogram? check all that apply. ml ∥ no ml ⊥ lo lo ≅ mn ml ≅ lo mn ⊥ no
Answers
To conclude that quadrilateral LMNO is a parallelogram, we need either ML ∥ NO, LO ≅ MN, or ML ⊥ LO.
Since LO ∥ MN, we know that ∠LON = ∠OMN and ∠NOM = ∠LMO. To conclude that LMNO is a parallelogram, we need to show that opposite sides are parallel and equal in length.
The following statements would be sufficient to conclude that LMNO is a parallelogram:
ML ∥ NO: If ML is parallel to NO, then ∠LMO = ∠NOM, and since ∠NOM = ∠LMO, we have ∠LMO = ∠NOM = ∠NLO = ∠OML. Therefore, opposite angles are equal, and LMNO is a parallelogram.
LO ≅ MN: If LO is equal in length to MN, then we have LO = MN and ∠LON = ∠OMN. Therefore, triangle LON is congruent to triangle MON by the side-angle-side (SAS) congruence criterion. This implies that ∠LNO = ∠MNO and ∠LON = ∠MON. Since ∠LNO + ∠LON = 180° and ∠MNO + ∠MON = 180°, we have ∠LNO = ∠MON and ∠LON = ∠MNO. Therefore, opposite angles are equal, and LMNO is a parallelogram.
ML ⊥ LO: If ML is perpendicular to LO, then ∠LMO = 90° and ∠NOM = 90°. Therefore, opposite angles are equal, and LMNO is a parallelogram.
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The given question is incomplete, the complete question is:
In quadrilateral LMNO, LO ∥ MN. What additional information would be sufficient, along with the given, to conclude that LMNO is a parallelogram? Check all that apply. ML ∥ NO ML ⊥ LO LO ≅ MN ML ≅ LO MN ⊥ NO.
im training my robot to eat cuppy cupcakes every 7 days it eat 4 ill like to buy enough for the last 14 days
Answers
Rοunding up tο the nearest whοle cupcake, yοu shοuld buy 8 cupcakes tο ensure that yοur rοbοt has enοugh cupcakes tο last fοr the next 14 days.
What is equatiοn?An equatiοn is a mathematical statement that indicates that twο expressiοns are equal. It cοntains an equals sign (=) between twο expressiοns, with οne expressiοn οn each side οf the equals sign. Equatiοns can cοntain variables, cοnstants, cοefficients, and mathematical οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn.
Here,
If yοur rοbοt eats 4 cupcakes every 7 days, it means it eats 4/7 = 0.57 cupcakes per day (rοunded tο twο decimal places).
Tο buy enοugh cupcakes fοr the last 14 days, yοu need tο multiply the number οf days by the daily cοnsumptiοn rate:
0.57 cupcakes per day x 14 days = 7.98 cupcakes
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Complete question:
If your robot eats 4 cupcakes every 7 days. So to buy enough cupcakes for the last 14 days, how much cupcake is consumed daily?
if three students in mrs. Johansen's class said their favorite vacation was sightseeing, predict how many students are in her class based on this survey?
Answers
There are three students in Mrs. Johansen's class who like sightseeing. We cannot estimate the total number of students in the class based solely on this information.
What is the class based survey?It is not possible to accurately predict the total number of students in Mrs. Johansen's class based on the information provided. However, we can make an estimate based on the assumption that the three students who responded to the survey are representative of the entire class.
It is impossible to create an accurate projection of the total number of pupils in Mrs. Johansen's class without knowing more about the survey or the class.
However, assuming that the survey was distributed to all students in the class, we may create an approximation based on the proportion of students who stated that their favourite holiday was sightseeing. For example, if we believe that the three students who stated that their favourite holiday was touring reflect 25% of the whole class (i.e., one-fourth of the class), we may estimate that the class has about 12 students.
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The given question is incomplete. the complete question is given below:
If three students in Mrs. Johansen's class said their favourite vacation was sightseeing, what is a reasonable estimate for the total number of students in her class based on this survey?
report the level of significance. of ball bearings from this manufacturing process is 2.30 cm. based on the sample of 50 that you collected, is there evidence to suggest that the average diameter is greater than 2.30 cm? perform a hypothesis test for the population mean at alpha
Answers
Yes, there is evidence to suggest that the average diameter is greater than 2.30 cm.
To perform a hypothesis test for the population mean at alpha, use a two-tailed t-test. Assume the null hypothesis is that the average is equal to 2.30 cm and the alternative hypothesis is that the average is greater than 2.30 cm. Calculate the test statistic and then compare it to the critical value.
If the test statistic is greater than the critical value, then you can reject the null hypothesis and conclude that the average is greater than 2.30 cm.
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what is the value of
7p+ q/3
when p= 6 and q=12
a 14
b 36
c 42
d 46
Answers
7p + q /3
p = 6 and q = 12
7(6) + (12) / 3
42 + 12/ 3
54/3
18
18 is the correct answer, but isn't present as an option in the list.
Answer:D.46
Step-by-step explanation: because 7(6)+12/3
First 7(6)=42
Then 12/3=4
Finally 42+4=46
I need help with the last one which is prove AB and CD.
Answers
Answer:
because triangle ABD is congruent to triangle CBD
by CPCT
AB = CD
Ready
Chef Allen wants to know how much he will pay for different amounts of beans.
Plot two points that show the cost of
15 pounds and 20 pounds of beans,
Cost (dollars)
20
18
16
14
12
10
8
6
4
2
0
05
Cost of Beans
10 15 20 25 30 35 40 45 50
Beans (pounds)
Answers
The graph of the following function has been attached with the answer.
What Does Graphing Functions Mean?The procedure of graphing a function entails drawing the graph (curve) of the relevant function. While it is relatively straightforward to graph simple functions like linear, quadratic, cubic, etc., complex functions like rational, logarithmic, etc. call for knowledge and a comprehension of specific mathematical concepts.
In order to graph functions, one must first:
If possible, identifying the shape. A line would be the graph of a linear function of the type f(x) = axe + b, for instance; a parabola would be the graph of a quadratic function of the form f(x) = ax2 + bx + c.
Determining some of its points involves substituting some arbitrary values for x and then using the function to determine the corresponding values for y.
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By influencing some of its points' x values to random numbers, the function can be used to find the equivalent values for y.
What Does Graphing Functions Mean?Drawing the graph (curve) of the pertinent function is the first step in the process of graphing a function. While graphing basic functions like linear, quadratic, cubic, etc. is generally easy, complex functions like rational, logarithmic, etc. demand an understanding of and knowledge of particular mathematical concepts.
Prior to drawing a graph of a function, one must:
Identifying the form, if you can. For example, the graph of a linear function of the form f(x) = axe + b would be a line; the graph of a quadratic function of the form [tex]f(x)=ax^2+bx+c[/tex] would be a parabola.
By influencing some of its points' x values to random numbers, the function can be used to find the equivalent values for y.
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The graph is attached below,
Find the area of the regular trapezoid below
Answers
Answer:
54inch^2
Step-by-step explanation:
3×6=18
18÷2=9
6×6=36
36+9+9= 54
answer: 54inch^2
Directions: Rewrite each expression using positive exponents.
1. X-5
2. 3m-2
3. -7a-4b3
4. 9x6y-3
Answers
Answer:
1) X0=1
2) 19m2
3) there is something missing i think
4) 6x3y
How many ways can 8 people be assigned to 2 triple and 2 double rooms
Answers
Answer:
66 ways in the triple rooms, 28 ways in the double rooms
Step-by-step explanation:
In total: 8 people;
There are 2 triple rooms, so 3 people can live in one triple room:
In the first triple room:
8×7×6 = 336 / 3×2×1 = 56 ways (we have to divide the number of ways by the factorial, because the order of people doesn't matter)
In the second triple room:
5×4×3 = 60 / 3×2×1 = 10 ways (since we can't choose the same people from the first triple room)
In total: 56+10 = 66 ways
Now, double rooms:
Ir the first double room:
8×7 = 56 / 2×1 = 28 ways
In the second double room:
6×5 = 30 / 2×1 = 15 ways
In total: 28+15 = 43 ways
I don't know if I got this right, though...
1. FINANCIAL LITERACY Mika invests $1400 in an account with a 2% annual simple
interest rate, making no other deposits or withdrawals. What will his account
balance be after 6 months? 2 years?
2. FINANCIAL LITERACY Ardella invests $3100 in an account with a 3.2% annual
interest rate compounded monthly, making no other deposits or withdrawals.
What will Ardella's account balance be after 1 year? 3 years?
3. FINANCIAL LITERACY Marquis borrows $900 with a 3.8% annual interest rate
compounded continuously. If he does not make any payments, how much will
Marquis owe after 2 months? 18 months?
Example 4
4. FINANCIAL LITERACY Trina wants to invest $5000 at a bank offering three
different accounts. Account A earns 2.2% annual simple interest, Account B earns
2.2% interest compounded annually, and Account C earns 2.2% interest
compounded continuously. If no other deposits or withdrawals are made,
compare the balances of the accounts after each period of time.
a. 6 months
b. 1 year
c. 3 years
Answers
After answering the presented question, we can conclude that Account B: $5463.84 ($5000 multiplied by 1.0223) $5474.60 in Account C ($5000 x e(0.022 x 3))
what is interest ?In mathematics, interest is the amount of money earned or payable on an original investment or loan. You can use either simple or compound interest. Simple interest is calculated as a percentage of the initial amount, whereas compound interest is calculated on the principal amount plus any previously earned interest. If you invest $100 at a 5% annual simple interest rate, you will get $5 in interest every year for three years, for a total of $15.
Mika's account balance after 6 months would be $1413.33 ($1400 + $14.67 interest generated). His account balance after two years would be $1456 ($1400 + $56 interest earned).
Marquis would repay $907.02 after two months ($900 x e(0.038/12 x 2)). He would owe $1,033.72 after 18 months ($900 x e(0.038 x 1.5)).
a. 6 months later:
Account A: $5050 ($5000 + $55 earned in interest)
Account B: $5061 ($5000 multiplied by 1.0220.5).
$5061.68 in Account C ($5000 x e(0.022 x 0.5))
c. One year later:
Account A: $5100 ($5000 + $110 earned in interest)
Account B: $5112.20 ($5000 multiplied by 1.022).
$5113.85 in Account C ($5000 x e(0.022 x 1))
c. After three years:
Account A: $5330 ($5000 + $330 generated interest)
Account B: $5463.84 ($5000 multiplied by 1.0223)
$5474.60 in Account C ($5000 x e(0.022 x 3))
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What is the median of 1 3/4 and 1 2/3?
Answers
Answer:
Step-by-step explanation:
In numerical order:
[tex]1\frac{2}{3},1\frac{3}{4}[/tex]
Since there are only 2 scores the median(middle score) will be the same as the mean:
[tex](1\frac{2}{3}+ 1\frac{3}{4}) \div 2=(\frac{20}{12}+ \frac{21}{12}) \div 2=\frac{41}{12} \times \frac{1}{2} =\frac{41}{24}=1\frac{17}{24}[/tex]
myas rectangular yard is 10 feet wide and 15 feet long. how many square feet of grass does she need to plant if she wants to cover the entire yard?
ANSWER FASTTTTT
Answers
To cover the entire yard, Mya needs to plant 150 square feet of grass.
Mya's rectangular yard is 10 feet wide and 15 feet long. To find the area of the yard, we need to multiply the width by the length:
Area of yard
= width x length
= 10 ft x 15 ft
= 150 square feet
Therefore, Mya needs to plant 150 square feet of grass to cover the entire yard
A rectangular yard is a type of outdoor space that is often used for gardening, outdoor activities, or as a place for relaxation. To calculate the area of a rectangular yard, you need to know its dimensions, which are typically expressed in feet or meters. The area of a rectangular yard can be found by multiplying its length by its width. The formula for the area of a rectangle is A = L x W, where A represents the area, L represents the length, and W represents the width. Once you have calculated the area of the yard, you can use this information to determine how much grass or other landscaping materials you need to cover the area.
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The area A of a rectangular swimming pool is given by the equation A=12w-w^2, where w is the width of one side. Write an expression for the other side of the pool.
Answers
Answer: y=mx+c
Step-by-step explanation:
How do I solve this ??
Answers
The match would be given as
[tex]\left[\begin{array}{ccc}18\\-24\\\end{array}\right]=[/tex][tex]A=3\left[\begin{array}{ccc}6\\-8\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}-24\\36\\\end{array}\right]=[/tex][tex]D=3\left[\begin{array}{ccc}-8\\12\\\end{array}\right][/tex]
How to solve the matrixIn mathematics, a matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. Matrices are used extensively in various branches of mathematics such as linear algebra, calculus, and statistics, as well as in fields such as physics, engineering, and computer science.
1. [tex]A=3\left[\begin{array}{ccc}6\\-8\\\end{array}\right] =\\[/tex]
We are to multiply the values that are in the matrix by 3. This is a 1 x 2 matrix
3 * 6 = 18, 3 * -8 = -24
Hence we would have
[tex]\left[\begin{array}{ccc}18\\-24\\\end{array}\right][/tex]
2. [tex]D=3\left[\begin{array}{ccc}-8\\12\\\end{array}\right] =[/tex]
we will multiply as:
3 * -8 = -24
3 * 12 = 36
Hence [tex]\left[\begin{array}{ccc}-24\\36\\\end{array}\right][/tex]
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The vertices of a rectangle are plotted.
A graph with both the x and y axes starting at negative 7, with tick marks every one unit up to 7. The points negative 4 comma 2, 5 comma 2, 5 comma negative 3, and negative 4 comma negative 3 are each labeled.
What is the perimeter of the rectangle?
10 units
18 units
28 units
45 units
Answers
Answer:
Answer is 28
Step-by-step explanation:
Length = 5
Width = 9
Perimeter = length*2 + width*2
Perimeter = 5*2 + 9*2
Perimeter = 10 + 18 = 28
what is the pattern of the sequence 10, 11, 21, 32?
Example:
Sequence- 2, 6, 18, 54
Pattern- x3
Answers
The pattern of the sequence is "add increasing multiples of 9 starting with 1."
To find the pattern in the sequence 10, 11, 21, 32, follow these steps:
1. Identify the differences between consecutive terms:
11 - 10 = 1
21 - 11 = 10
32 - 21 = 11
2. Notice that the differences are increasing by 9 (10 - 1 = 9 and 11 - 10 = 1).
3. Based on this observation, the pattern can be described as adding a value that increases by 9 each time:
10 + 1 = 11
11 + 10 = 21
21 + 11 = 32
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Lauri spent 5% of x hours at her part-time job. What is x if 5% of x is about 10 hours? Explain how you estimated and which property of equality you used to find x.
Answers
To estimate x, we can use the fact that 5% is approximately equal to 1/20. Therefore, if 5% of x is about 10 hours, then we can estimate that 1/20 of x is also about 10 hours.
Multiplying both sides of the equation 1/20 x = 10 by 20, we get x = 200.
To check our answer, we can verify that 5% of 200 hours is indeed about 10 hours.
We used the multiplication property of equality to solve for x, which states that we can multiply both sides of an equation by the same non-zero number without changing the solution. In this case, we multiplied both sides by 20.