The number of rhinestones per square centimeter on the surface of a disco ball is 448/274.167.
How to find the surface area of a sphere?Suppose that radius of the considered sphere is of 'r' units.
Then, its surface area S would be:
[tex]S = 4\pi r^2 \: \rm unit^2[/tex]
Given;
A disco ball has a circumference of 16.558 centimeters
448 rhinestones on its surface.
Now,
2pi*r=16.558
r=8.279/pi
Surface area of sphere=4pi*r^2
=4*68.541841
=274.167
Here, 448/274.167
Therefore, the surface area per square cm will be 448/274.167.
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To raise money for charity, Carmen and her friends start the Pampered Pooch Pet Wash. The first day they are open, they forget to put up posters and only raise a little money. The next day, they hang posters all over the neighborhood and raise $55.50. In all, Carmen and her friends raise $65.50 on the first two days they are open.
Julie will reach her goal 21 days before Mary.
What is division?Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
Mary and Julie both have a goal of raising $1000 for charity.
Mary raises money in every 4 days = $12.
In one day Mary raises money = 12/4
= $3
Mary needs time to reach her goal = 1000/3
= 333.33 ≈ 334 days
Julie raises money in every 6 days = $19
In one day Julie raises money = 19/6
= $3.1666 ≈ $3.2
Julie needs time to reach her goal = 1000/ 3.2
= 312.5 ≈ 313 days
Difference of the days between both of them to reach their goal
= 334 - 313 = 21 days
Julie will reach her goal first, 21 days before Mary.
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An antique dresser was $115, but is on sale for
30% off. If there is a 10% tax added to the sale
price, how much will the dresser cost?
Answer:
$88.55
Step-by-step explanation:
First find how much the 30% off discount will be.
115 x 0.30 = 34.5
Subtract it from original price
$115 - 34.5 = $80.5
Now find the 10% tax
80.5 x 0.10 = 8.05
Add that to the price
$80.5 + 8.05 = 88.55
The dresser's final sale price is $88.55
What is the value of root 216?
Answer: The square root of 216 is equal to approximately 6.485281.
Step-by-step explanation:
The square root of 216 is equal to the number that, when multiplied by itself, gives 216. The value of the square root of 216 can be found using several methods, including estimation, the long division method, and a calculator. Here, I'll provide a step-by-step explanation using estimation.
Step 1: Estimate the value of the square root.
One way to estimate the value of the square root of 216 is to find two perfect squares that are close to 216, and whose square roots are therefore close to the square root of 216. In this case, the perfect squares closest to 216 are 144 (12^2) and 225 (15^2). Since 216 is closer to 144, the square root of 216 is likely to be closer to 12 than to 15.
Step 2: Refine the estimate.
To refine the estimate of the square root of 216, we can average the two closest perfect squares and their square roots. In this case, the average of 12 and 15 is 13.5, and this is a better estimate of the square root of 216 than either 12 or 15 alone.
Step 3: Improve the estimate using a more precise method.
One method for finding an even more precise estimate of the square root of 216 is to use the Newton-Raphson formula for finding square roots. This formula involves repeatedly applying the following equation:
x_n+1 = (x_n + n/x_n) / 2,
where x_n is the nth estimate of the square root, and n is the number whose square root we are trying to find (in this case, n = 216). We can start with an initial estimate, such as x_0 = 13.5, and iterate the formula until the estimate converges to a desired level of precision.
Step 4: Use a calculator or other tools to find the exact value.
Finally, we can use a calculator or computer program to find the exact value of the square root of 216 to as many decimal places as desired. The exact value of the square root of 216 is equal to approximately 6.485281.
Suppose ABC is a right triangle, and cos (B) =a/c, which of the following much also be true ?
Answer:
option 1 --> sec A = c/a
option 3 --> sin(b) = b/c
option 4 --> Sin(A) = a/c
Step-by-step explanation:
Since cos is adjacent, we know the legs are a and b and the hypotenuse is c
For angle B
sin (opposite over hypotenuse) = b/ctan (opposite over adjacent) = b/acsc (hypotenuse over opposite) = c/bsec (hypotenuse over adjacent) = c/bcot (adjacent over opposite) = a/bFor Angle A
sin = a/ccos = b/ctan = a/bcsc = c/asec = c/bcot = b/aWhat value for x makes the equation −13(x + 11) + 12x = -26 true
Answer:
x= -177
Step-by-step explanation:
−13(x + 11) + 12x =-26
x=-177
i don’t understand how to get answer
Answer:
You probably know that it is a good idea to brush your teeth every day. What does this do that helps prevent tooth decay?
Step-by-step explanation
8x - 7y = 56
plot on the graph
Answer: put tow points, 1 on the x-axis (horizontal) and the other 1 on y-axis (vertical).
x = 7
y = -8
and you make a straight line , connecting them
Gracie deposited $20,000 into an account that compounds interest weekly at a rate of 1.56%. Each week, her bank withdraws $200 from the account and puts that amount into her mortgage account. How long will it take until the account has a balance of $0? Round to the nearest tenth of a year.
It takes 2 years for the account balance to come down to 0.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].
Given that, principal =$20,000, rate of interest =1.56%, n=52 and W=$200.
Use the formula, [tex]P=W\frac{1-(1+\frac{r}{n})^{-nt} }{\frac{r}{n} }[/tex]
[tex]20000=200\frac{1-(1+\frac{0.0156}{52})^{-52t} }{\frac{0.0156}{52} }[/tex]
[tex]100=\frac{1-(1+0.0003)^{-52t}}{0.0003}[/tex]
[tex]0.03=1-(1.0003)^{-52t}[/tex]
[tex]0.97=(1.0003)^{-52t}[/tex]
Take log on both the side, we get
-52t·log(1.0003)=log0.97
So, t=2 years
Therefore, it takes 2 years for the account balance to come down to 0.
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factor the following:
(a-b)*z+3(b-a)^2
The factored expression of (a-b) * 2 + 3(b-a)^2 is (-2 + 3(b - a))(b - a)
How to factor the expressionFrom the question, we have the following parameters that can be used in our computation:
(a-b)*z+3(b-a)^2
Express properly
So, we have
(a-b) * 2 + 3(b-a)^2
Rewrite as
-2(b - a) + 3(b - a)^2
Factor out b - a from the expression
So, we have
(-2 + 3(b - a))(b - a)
Hence, the factored expression is (-2 + 3(b - a))(b - a)
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(-2,1) (-8,-5) round nearest tenth
The slope of line from the points given is 1
What is the slope of lineThe slope of a line is a measure of how steep the line is and the direction it is going. In mathematical terms, it is defined as the ratio of the change in the y-coordinate (rise) to the change in the x-coordinate (run) between two points on the line. Slope is often represented by the letter "m". If (x₁, y₁) and (x₂, y₂) are two points on the line, the slope can be calculated using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
In this problem, we can take the two points and calculate the slope.
m = (y₂ - y₁) / (x₂ - x₁)
Substituting the values into the formula to find the slope;
m = -5 - 1 / -8 - (-2)
m = 1
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Complete Question; Calculate the slope of the line (-2, 1) and (-8, -5)
Each student in a math class has to buy the items in the table. Write an expression in simplest form that represents the
total cost for x students.
Item
Calculator
Notebook
Pack of pencils
11.55
9.65x+0.65x+1.25x
11.55x
x(9.65+0.65+1.25)
Cost
$9.65
$0.65
$1.25
The expression in simplest form that represents the total cost for x students is 11.55x, the correct option is C.
What is an expression?Expression in mathematics can be defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that a student in a math class has to buy the items in the table.
Now,
x(9.65+0.65+1.25)
=9.65x+0.65x+1.25x
=11.55x
Therefore, the expression in simplest form will be 11.55x.
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The average of your first 6 tests is 82. If your test average after your seventh test is an 80. 5, what did you score on the seventh test?.
The score on the seventh test is 71.5
"Information available from the question"
The average of your first 6 tests is 82.
If your test average after your seventh test is an 80. 5
To find the score on the seventh test.
Now, According to the information:
Average of 6 test is 82
We know that :
Average = Sum of all test / Total no. of test => 82 = Sum of all test / 6
Sum of all test = 492
Let the seventh test be 'x'
So, Sum of seventh test is = 492 + x
Average = [tex]\frac{492+x}{7}[/tex]
80.5 = [tex]\frac{492+x}{7}[/tex]
=> 80.5 × 7 = 492 + x
x = (80.5 × 7) - 492
=> x = 563.5 - 492
x = 71.5
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Someone please help me!!
Answer:
84 units
Step-by-step explanation:
The darkest shaded face has 12 full units. Times that by the width or the lightest shade area (7) you get the answer 84 units.
12(7) = 84
solve this problem pls a question of inequality
Answer:
x > - 6
Step-by-step explanation:
[tex]\frac{x}{2}[/tex] > - 3 ( multiply both sides by 2 to clear the fraction )
x > - 6
Janice is at her favorite store checking out. She wants to buy a few shirts (s) that cost $14 each and a pair of jeans that cost $32. She wants to spend less than $88. How many shirts can she buy without going over her limit? Write an inequality to represent the scenario. Then, solve.
The number of shirts that Janice can buy without going over her limit is; 3 shirts
How to solve Inequality word problems?The number of shirts she can buy is denoted as s.
Cost of each shirt = $14
Cost of a pair of jeans = $32
She wants to spend less than $88.
Thus, the inequality that depicts this problem is;
14s + 32 < 88
Subtract 32 from both sides to get;
14s < 56
Divide both sides by 14 to get;
s < 4
Thus, maximum number of shirts will be 3 shirts
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Help with geometry. Given ABC is congruent to MNO. m < A = 51 , m < N = 67 , and m < B = (2x + 7) What is the value of x?
The value of x is given as follows:
x = 30.
What are similar triangles?Similar triangles are triangles that share these two features presented as follows:
Congruent angle measures.Proportional side lengths.For the two similar triangles, we have that B and N are equivalent angles, hence they are congruent and the value of x is given as follows:
2x + 7 = 67
2x = 60
x = 60/2
x = 30.
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The table shows the height of water in a pool as it is being filled. A table showing Height of Water in a Pool with two columns and six rows. The first column, Time in minutes, has the entries, 2, 4, 6, 8, 10. The second column, Height in inches, has the entries, 8, 12, 16, 20, 24. The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water in the pool? The height of the water increases 2 inches per minute. The height of the water decreases 2 inches per minute. The height of the water was 2 inches before any water was added. The height of the water will be 2 inches when the pool is filled.
The correct statement that describes how the slope relates to the height of the water in the pool is: The height of the water increases 2 inches per minute, the correct option is A.
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
where (x₁, y₁) and (x₂, y₂) are the two points that you are trying to find the slope between.
We are given that;
The time in minutes: 2, 4, 6, 8, 10
Height in inches: 8, 12, 16, 20, 24
Now,
The slope of the line through the points is 2, which means that for every 1 unit of time (in minutes) that passes, the height of the water in the pool increases by 2 units (in inches).
Therefore, by the given slope answer will be height of the water increases 2 inches per minute.
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Which function will approach positive infinity the fastest?
O f(x)= 100(1.5)*
O f(x) = 100x5 + 200x³ + 100
Of(x) = 200(1.45)*
O f(x) = 200x3 + 100x² + 100
Answer:
Step-by-step explanation:
fx
what should a good residual plot look like if the regression line fits the data well?
A good residual plot should have the points randomly scattered around the horizontal line with no discernible pattern.
This indicates that the model is well fit to the data. The residuals should also be equally distributed on either side of the horizontal line. This can be seen as the sum of the residuals being equal to 0, or mathematically expressed as the sum of the residuals (e) being equal to 0, where [tex]e = y - ŷ[/tex], where y is the observed value and ŷ is the predicted value. The equation can be expressed as Σe=0.
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Complete the equation of the line through
(
−
8
,
−
2
)
(−8,−2)left parenthesis, minus, 8, comma, minus, 2, right parenthesis and
(
−
4
,
6
)
(−4,6)left parenthesis, minus, 4, comma, 6, right parenthesis
The linear function through the points (-8,-2) and (-4,6) is given as follows:
y = 2x + 14.
How to define a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change of the linear function.The intercept b represents the value of y when x = 0.Given two points, the slope is calculated as the change in y divided by the change in x, hence:
m = (6 - (-2))/(-4 - (-8))
m = 8/4
m = 2.
Hence:
y = 2x + b.
When x = -8, y = -2, hence the intercept b is obtained as follows:
-2 = 2(-8) + b
b = 14.
Hence the equation is:
y = 2x + 14.
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What type of graph is shown, and what is the growth factor?
linear function; growth factor of 2
linear function; growth factor of 4
exponential function; growth factor of 2
exponential function; growth factor of 4
The graph is a linear function with a growth factor of 4
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The graph has the shape of a straight line, so it is linear.
The graph starts at point (0, 0). It passes through point (1, 4).
slope = 4/1 = 4
The slope is 4. Growth factor is the same as slope for a linear function.
Hence, the graph is a linear function with a growth factor of 4
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Find the measure of the missing angle
Answer:
a = 149 degrees
Step-by-step explanation:
Angles must add up to 180 degrees so,
180 - 31 = 149.
factor each polynomial by grouping
^(3)+4x^(2)+2x+8
4b^(3)-6b^(2)+10b-15
2m^(3)+4m^(2)+6m+12
7r^(3)-35r^(2)+6r-30
10a^(3)+4a^(2)+5a+2
The required factor each polynomial by grouping are factored.
What are polynomials?A polynomial is an algebraic expression in which the operators "+" and "-" are used to separate terms, and the exponents of the variables are consistently non-negative integers. Polynomials include, for instance, x² + x + 5, y² + 1, and 3x³ - 7x + 2.
According to question:1)1) [tex]x^3+4x^2+2x+8[/tex]
can be factored by grouping as:
[tex]x^3 + 2x + 4x^2 + 8[/tex]
= [tex]x(x^2+2) + 4(x^2+2)[/tex]
= [tex](x+4)(x^2+2)[/tex]
2) [tex]4b^3-6b^2+10b-15[/tex]
can be factored by grouping as:
[tex]2b^2(2b-3)+5(2b-3)[/tex]
=[tex](2b-3)(2b^2+5)[/tex]
3)[tex]2m^3+4m^2+6m+12[/tex]
can be factored by grouping as:
[tex]2m^2(m+2) + 6(m+2)[/tex]
= [tex](2m^2+6)(m+2)[/tex]
= [tex]2(m^2+3)(m+2)[/tex]
4) [tex]7r^3-35r^2+6r-30[/tex]
can be factored by grouping as:
[tex]7r^2(r-5)+6(r-5)[/tex]
=[tex](7r^2+6)(r-5)[/tex]
[tex]10a^3+4a^2+5a+2[/tex]
can be factored by grouping as:
[tex]2a^2(5a+2)+1(5a+2) = (2a^2+1)(5a+2)[/tex]
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The average temperatures for two of the world's hottest places are given. Determine which location has the warmer average temperature and by how many degrees Fahrenheit
Location A: 85.3°F and Location B: 29.3°C
The location with the warmer average temperature is
(Round to the nearest tenth of a degree as needed.)
which is warmer by about F
Location A has the warmer average temperature, by about 0.6°F (rounded to one decimal place).
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
To compare the temperatures of Location A and Location B, we need to convert the temperature of Location B from Celsius to Fahrenheit. We can use the formula:
°F = (°C × 9/5) + 32
Substituting the given temperature of Location B, we get:
°F = (29.3 × 9/5) + 32 = 84.74°F (rounded to two decimal places)
So, the average temperature of Location A is 85.3°F and the average temperature of Location B is 84.74°F (rounded to two decimal places).
Therefore, Location A has the warmer average temperature, by about 0.6°F (rounded to one decimal place).
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Can somebody help with number 8 find the value of each variable using the properties of a Parallelogram p
Answer: (9,8) A
Step-by-step explanation: how the mandle 10 30 6 150 144
What is the value of 300m in miles
Answer:
Step-by-step explanation:0.18
Find the volume.
(Pls help…. I’ve tried many times but ain’t near the answer)
The volume of the composite figure is equal to 1395 square inches.
How to determine the volume of the composite figure
In this problem we need to determine the volume of a composite figure, which is the result of combining the volumes of a right prism and a pyramid, whose volume formulas are listed below:
Pyramid
V = (1 / 3) · w · l · h
Prism
V = w · l · h
Where:
w - Width, in inchesl - Length, in inchesh - Height, in inchesNow we proceed to determine the volume of composite solid:
V = (9 in) · (15 in) · (7 in) + (1 / 3) · (15 in) · (9 in) · (10 in)
V = 1395 in³
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In many classes, a passing test grade is 60 (A = 60). Using the formula A = 10 R,
what raw score (R) would a student need to get a passing grade after her score is
adjusted?
A student need a raw score of 36.
How to determine the raw score (R) of the student?
We can find the raw score (R) of the student by substituting A = 60 into the the formula and then solve for R. That is:
A = 10√R
√R = 60/10
√R = 6
R = 6²
R = 36
Thus, a student need a raw score of 36 to get a passing grade after her score is adjusted.
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What is the value of 50g in tbsp?
The conversion rate for grams to tablespoons is 1 gram is equal to 0.2 tablespoons. This conversion is useful for both converting small amounts of ingredients in recipes and converting larger amounts of ingredients in recipes.50 grams is equal to 10 tablespoons."
This means that 50 grams is equal to 10 tablespoons. To calculate the value of 50 grams in tablespoons, we can use the following formula:50 grams x 0.2 tablespoons = 10 tablespoons.The value of 50 grams in tablespoons is 10 tablespoons.To convert from grams to tablespoons, the basic formula is to multiply the weight in grams by 0.2. This conversion is useful for converting small amounts of ingredients in recipes, as many recipes call for weights in grams rather than tablespoons. For example, if a recipe calls for 20 grams of butter, this would be equal to 4 tablespoons. To convert from tablespoons to grams, the basic formula is to multiply the weight in tablespoons by 5. This conversion is useful for converting larger amounts of ingredients in recipes, as many recipes call for weights in tablespoons rather than grams. For example, if a recipe calls for 8 tablespoons of sugar, this would be equal to 40 grams. To summarize, the value of 50 grams in tablespoons is 10 tablespoons. This conversion is useful for both converting small amounts of ingredients in recipes and converting larger amounts of ingredients in recipes.
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using diagonals from a common vertex, how many triangles could be formed from a 21-gon?
Total 816 triangles that can be formed using diagonals from a common vertex of a 21-gon.
What are Diagonals?In mathematics, a diagonal is a line joining two vertices of a polygon or solid whose vertices do not lie on the same edge. Diagonals are generally defined as oblique lines or slanted lines connecting the vertices of a shape. A diagonal is defined as a horizontal shape with sides/edges and corners.
Solution of the given problem:
Firstly, choose 3 vertices of 21-gon which are not adjacent to each other.
Secondly, connect all three vertices to a common vertex.
Now, there are 18 vertices that are not adjacent to common vertex and there are now 18 diagonals that can be drawn to the common vertex up to these vertices.
To form a triangle using these diagonals, we need to choose 3 of these 18 vertices, this can be calculated using the binomial coefficient formula:
18 choose 3 = 18! / (3! * (18 - 3)!) = (18 * 17 * 16) / (3 * 2 * 1) = 816
Thus, total 816 triangles can be formed.
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