A manufacturer makes decorative globes out of silver in the shape of a solid sphere. Suppose each sphere has a radius of 4.5 cm. If silver is priced at $5.00 per cm3", how much will the silver cost to make one solid sphere?
Use 3.14 for , and do not round your answer.
Answer:
The silver will cost $1908.5125 to make one solid sphere
Step-by-step explanation:
The formula for the volume of a sphere is:
V = (4/3)πr^3
where r is the radius of the sphere.
Substituting the given value for the radius:
V = (4/3)π(4.5 cm)^3
= (4/3)(3.14)(91.125 cm^3)
= 381.7025 cm^3
The cost of the silver can be calculated by multiplying the volume by the cost per cm^3:
Cost = 381.7025 cm^3 × $5.00/cm^3
= $1908.5125
Which angles are congruent to each other? Select all that apply.
Answer:
1,2, and 4
Step-by-step explanation:
vertical angles theorem, which says that the vertical angles that are formed when two lines intersect are congruent.
Which table represents the function? Pls help me
A linear equation is an equation in which each term has at max one degree. The table that represents a linear function is Table 1. Thus, the correct option is A.
We have,
A linear equation is an equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c
Linear equation with two variables, when graphed on a cartesian plane with axes of those variables, give a straight line.
For the table to represent a linear function, the function must have a constant slope between any two points.
For the first table, the slope between the first two points is,
m = (7-3)/(2-1) = 4
The slope between the last two points is,
m = (15-11)/(4-3)
Hence, the table that represents a linear function is Table 1. Thus, the correct option is A.
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a. Use the appropriate formula to find the value of the annuity.
b. Find the interest.
Periodic Deposit
$7000 at the end of each year
Rate
6.5% compounded annually
Click the icon to view some finance formulas.
COD
Time
20 years
a. The value of the annuity $
(Do not round until the final answer. Then round to the nearest dollar as needed.)
According to the information, the interest earned on the annuity over the 20-year period is $78,066.89.
How to find the value of the annuity?To find the value of the annuity, we can use the formula:
V = PMT x [(1 + r)^n - 1] / rwhere:
PMT = periodic paymentr = interest rate per periodn = number of periodsIn this case, PMT = $7,000, r = 6.5% per year compounded annually, and n = 20 years.
First, we need to convert the annual interest rate to a periodic interest rate. Since the interest is compounded annually, the periodic interest rate is the annual rate divided by the number of periods in a year:
i = r / m
where,
m = number of compounding periods per year.
In this case, since the interest is compounded annually, m = 1, so:
i = 6.5% / 1 = 0.065
Now we can plug in the values and solve for V:
V = $7,000 x [(1 + 0.065)^20 - 1] / 0.065
V = $218,066.89
Therefore, the value of the annuity is: $218,066.89.
How to find the interest earned on the annuity over the 20-years period?To find the interest earned on the annuity over the 20-year period, we can subtract the total amount deposited from the total value of the annuity:
Interest = V - (PMT x n)Interest = $218,066.89 - ($7,000 x 20)Interest = $78,066.89Learn more about interest in: https://brainly.com/question/30393144
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The histogram represents data collected on the frequency of how far the tide rose, in feet, up the beach from the buoy. A histogram titled Tides For 15 Days with an x-axis labeled Measurement In Feet with intervals of 1 to 5, 6 to 10, 11 to 15, 16 to 20, and 21 to 25. The y-axis is labeled Frequency and starts at 0 with tick marks every one unit up to 7. There is a shaded bar above 1 to 5 that stops at 1, above 6 to 10 that stops at 3, above 11 to 15 that stops at 4, above 16 to 20 that stops at 4, and above 21 to 25 that stops at 3. Which statement best describes the spread and distribution of the data? The data is almost symmetric, with a maximum range of 24. This means that the tide frequently measured around 11 to 20 feet. The data is skewed, with a maximum range of 24. This means that the tide was frequently very high in the 16 to 25 feet range. The data is bimodal, with a maximum range of 24. This means that the tide was frequently between 6 to 10 or 21 to 25 feet. The data is symmetric, with a maximum range of 20. This means that the tide frequently measured around 1 to 5 feet.
The histogram is solved and the data is bimodal, with a maximum range of 24. This means that the tide was frequently between 6 to 10 or 16 and 20 feet.
Given data ,
Let the number of observations of each interval is:
1 to 5: 2 observations.
6 to 10: 5 observations.
11 to 15: 2 observations.
16 to 20: 6 observations.
21 to 25: 1 observations.
Let the maximum range be represented as M
And , there are two similarly high bins for the histogram , hence the distribution can be said to be bimodal, with maximum range given as follows
M = 25 - 5
M = 21 - 1
M = 20
Hence , the histogram is solved
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URGENT!! ILL GIVE BRAINLIEST! ALONG WITH 100 POINTS!!!!!!!!
Match the given information with the equation for the line
-5x + 3y = -12
y = 3/2 x - 8
2y-x = -4
Y= -3/4x-2
Answer:
1. y = 3/2 x - 8
2. 2y-x = -4
3. y = -3/4x-2
4. -5x + 3y = -12
can someone help me on number 1
The segments AB and CD on item 1 are classified as follows:
Perpendicular.
When are lines parallel, perpendicular or neither?The slope, given by change in y divided by change in x, determines if the lines are parallel, perpendicular, or neither, as follows:
If they are equal, the lines are parallel.If their multiplication is of -1, they are perpendicular.Otherwise, they are neither.The slope of segment AB is given as follows:
m = (3 - 13)/(0 - (-2))
m = -10/2
m = -5.
The slope of segment CB is given as follows:
m = (3 - 0)/(10 - (-5))
m = 3/15
m = 1/5.
The multiplication of these slopes is given as follows:
-5 x 1/5 = -1.
As the multiplication of the slopes is of -1, the segments are perpendicular.
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What is the product of the matrices Matrix with 1 row and 3 columns, row 1 negative 3 comma 3 comma 0, multiplied by another matrix with 3 rows and 1 column. Row 1 is negative 3, row 2 is 5, and row 3 is negative 2.?
Matrix with 2 rows and 1 column. Row 1 is 9, and row 2 is 15.
Matrix with 1 row and 3 columns. Row 1 is 9 and 15 and 0.
Matrix with 3 rows and 3 columns. Row 1 is 9 comma negative 9 comma 0, row 2 is negative 15 comma 15 comma 0, and row 3 is 6 comma negative 6 comma 0.
[24]
The product of the matrices is [24].
Given is a row matrix and a column matrix, we need to find the product of both,
So,
A = [-3, 3, 0]
B = [tex]\left[\begin{array}{ccc}-3\\5\\-2\end{array}\right][/tex]
Now, the product will be =
AB = [-3, 3, 0] × [tex]\left[\begin{array}{ccc}-3\\5\\-2\end{array}\right][/tex]
AB = [9 + 15 + 0]
AB = [24]
Hence the product of the matrices is [24].
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write an equivilant fractions for 3 3/4 and 1 2/3 using a common denominator iready
The requried equivalent fraction for the equivalent fraction to 3 3/4 and 1 2/3, is 45/12, and 20/12.
To find a common denominator for 4 and 3, we can multiply them together to get 12.
So, we can convert 3 3/4 as:
3 3/4 = 12/4 + 3/4 = 15/4
Similarly, we can convert 1 2/3 as:
1 2/3 = 5/3
Therefore, the equivalent fractions for 3 3/4 and 1 2/3 using a common denominator of 12 are:
15/4 = 45/12 and 5/3 = 20/12
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Pls help
The shape below contains a rectangle and four semi circles.
The perimeter of the shape is 13π
The area of the shape is 48.125π square units
What are the perimeter and area of the shapes?The perimeter of the shape is calculated as follows:
The perimeter of shape = perimeter of the two semicircles of radius 2 + perimeter of the two semicircles of radius 4.5The perimeter of a semicircle = πr
The perimeter of shape = 2 * π * 2 + 2 * π * 4.5
The perimeter of shape = 13π
The area of the shape = area of the two semicircles of radius 2 + area of the two semicircles of radius 4.5 + area of the rectangle
Area of semicircle = πr²/2
The area of the shape = π * 2²/2 + π(4.5)²/2 + 4 * 9
The area of the shape = 48.125π square units
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Can someone please solve this y = 5x² + 2x + 7
The roots of the quadratic equation y = 5 · x² + 2 · x + 7 are contained by x = - 1 / 5 ± i √34 / 5.
How to solve a quadratic equation
In this problem we must solve a quadratic equation, whose roots must be found. This can be done by using algebra properties, by completing the square. First, write the entire quadratic equation:
y = 5 · x² + 2 · x + 7
Second, use algebra properties to find all roots:
y = 5 · [x² + (2 / 5) · x + 7 / 5]
y = 5 · [x² + (2 / 5) · x + 1 / 25] + 5 · (34 / 25)
y = 5 · (x + 1 / 5)² + 34 / 5
Third, use y = 0:
5 · (x + 1 / 5)² + 34 / 5 = 0
5 · (x + 1 / 5)² = - 34 / 5
(x + 1 / 5)² = - 34 / 25
x + 1 / 5 = ± √(- 34) / 5
x = - 1 / 5 ± √(- 34) / 5
x = - 1 / 5 ± i √34 / 5
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The measure of weights of 15 students is normally distributed with a sample mean of 6 and standard deviation of 5. Find the 95% confidence interval for the mean.
The 95% confidence interval for the mean is [3.23, 8.76].
What is the confidence of interval?
The confidence of interval of the mean is calculated as follows;
Confidence interval = σ ± (t-value x μ)
where;
σ is the sample meanμ is the standard errorThe standard error is calculated as follows:
μ = std / √n
μ = 5 / √15
μ = 1.29
Based on this value we will check the distrbution table, for the t-value of 95% confidence;
= 2.145.
Confidence interval = σ ± (t-value x μ)
= 6 ± (2.145 x 1.29)
= [3.23, 8.76]
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31, 92, 25, 69, 80, 31, 29
Median
Mode
Range
Answer:
Median: 31
Mode: 31
Range: 67
Step-by-step explanation:
Median: To find the median, we first need to arrange the numbers in order from smallest to largest:
25, 29, 31, 31, 69, 80, 92
The middle number is 31, so the median is 31.
Mode: The mode is the number that appears most frequently in the set. In this case, the number 31 appears twice, which is more than any other number. So, the mode is 31.
Range: The range is the difference between the largest and smallest numbers in the set. The smallest number is 25 and the largest number is 92, so the range is:
92 - 25 = 67.
Therefore, the median is 31, the mode is 31, and the range is 67.
Answer:
The median of the given set of numbers is 31, the mode is 31, and the range is 67.
Step-by-step explanation:
To find the median, we need to first arrange the numbers in order from smallest to largest:
25, 29, 31, 31, 69, 80, 92
There are seven numbers in the list, which means the middle number will be the fourth number: 31.
Therefore, the median is 31.
To find the mode, we need to determine which number appears most frequently in the list.
In this case, the number 31 appears twice, which is more than any other number in the list.
Therefore, the mode is 31.
To find the range, we need to subtract the smallest number from the largest number. The smallest number is 25 and the largest number is 92, so the range is:
92 - 25 = 67
Therefore, the range is 67.
Pls help, this is for geometry
I'm not 100 percent sure so please only rate after you see if it's right.
ANSWER: $1090
STEP 1:
The volume of one brick is given by multiplying its length, width, and height:
V = (7 1/4) in x 3 in x (2 1/4) in
V = (29/4) in x 3 in x (9/4) in
V = 2187/16 cubic inches
STEP 2:
The cost of one brick is given by multiplying the volume by the cost per cubic inch:
C = (2187/16 cubic inches) x $0.05/in^3
C = $1.09/brick
STEP 3: To find the cost of 1000 bricks, we simply multiply the cost of one brick by 1000:
Cost of 1000 bricks = 1000 x $1.09/brick
Cost of 1000 bricks = $1090
Therefore, the cost of 1000 bricks is $1090, rounded to the nearest cent.
PLEASE HELP. The steps to derive the quadratic formula are shown below:
Step 1 ax2 + bx + c = 0
Step 2 ax2 + bx = − c
Step 3
Provide the next step to derive the quadratic formula.
a times the quantity x squared plus b over a times x end quantity equals negative c
x(ax + b) = −c
x squared over a plus b over a times x equals negative c over a
x squared over a plus b over a equals negative c over a
Answer:
Step 3: Divide both sides of the equation in Step 2 by a to get x² + (b/a)x = -c/a.
What is the range of |x|-7?
Answer:
3 2/5 +(3/2+3/5)×6/5÷3/2-10 1/2× 2/2
Ravi is saving money to buy a game. The game costs $12, and so far he has saved one-fourth of this cost. How much money has Ravi saved?
Answer:
$3
Step-by-step explanation:
since $12 is 4/4 and he save 1/4 its 12÷4
Answer:
$3
Step-by-step explanation:
12 divided by 4 is 3
(3+3)+(3+3)
6+6
= 12
The vertices of a triangle are at (0,0), (8,8) and (4,12). What is the volume, in cubic units, of the figure created by rotating the triangle about y = x ?
The volume of the figure that was created by the triangle being rotated, would be 94. 83 units ³
How to find the volume ?When a triangle is rotated about y = x, a right circular cone is created. The formula is:
= π r² h / 3
We need to find the height and radius. The coordinates for the right circular cone are:
(0,0) - (0,0)
(8,8) - (8,8)
(4,12) - (12,4)
Using this, we find that the radius is 4 units. The height can be found by using any point such as ( 12, 4).
= √ ( ( 12 - 8) ² + ( 4 - 8 ) ²)
= 5. 66 units
The volume would therefore be:
= π x 4² x 5. 66 / 3
= 94. 83 units ³
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Point: (3, 4)
Slope: -1
In slope intercept form
y = -x + 7
Step-by-step explanation:Slope-intercept form can give us valuable information about a graph.
Point-Slope Form
There are multiple ways to solve this problem; I am simply showing the way I use most often.
We can plug the known information into point-slope form and then simplify the equation into slope-intercept form. Point-slope is written as:
y - y₁ = m(x - x₁)In this equation, y₁ and x₁ are the y and x values we are given and m is the slope. So, plug in the information.
y - 4 = -1(x - 3)Then, simplify the right side by distributing the -1.
y - 4 = -x + 3Next, add 4 to both sides.
y = -x + 7The equation in slope-intercept form is y = -x + 7.
Slope-intercept Form
Slope-intercept form is written as y = mx + b, where m is the slope and b is the y-intercept. So, our equation, y = -x + 7, shows that the slope is -1 and the y-intercept is 7. Using this information, we can compare the line to other linear functions or graph the line if needed.
Answer:
y = -x + 7 is your correct answer
Step-by-step explanation:
CAN SOMEONE HELP WITH THIS QUESTION?
The value of the given summation is:
[tex]\sum (29a_i - 13b_i) ]= -30[/tex]
How to find the sum?Here we know that the sums are:
[tex]\sum a_i = -10\\\\\sum b_i = -20[/tex]
And we want to find the value of the sum:
[tex]\sum (29a_i - 13b_i)[/tex]
First we can distribute the sum to get:
[tex]\sum 29a_i + \sum - 13b_i[/tex]
And take the coefficients out of the sum:
[tex]29\sum a_i -13\sum b_i[/tex]
Now replace the known values:
[tex]29\sum a_i -13\sum b_i = 29*-10 - 13*-20 = -290 + 260 = -30[/tex]
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Help me Ive been on this question for a minute.
DM me on IG 1.rockkyy!!
The recursive formula is 5/6
What is recursive formula?You should know that a recursive formula is an equation used to describe a sequence in which terms are defined using one or more previous terms along with an initial condition.
The given parameters are
aₓ = a(n-1) + 2
Where aₓ = 2aₓ₋1
= 2*5(₃₋₁) = 5(3-1) + 2
= 10₂ = 10 + 2
Taking the log of both sides
Log₂10 - Log12 = 0
Dividing by 10 we have
10/12 = 5/6
therefore the recursive formula is 5/6
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The functions fand g are defined as follows.
f(x)=2x²-3x g(x)=-4x-1
Find f(-4) and g (5).
f(-4) = ?
g (5) = ?
Answer:
f(- 4) = 44 , g(5) = - 21
Step-by-step explanation:
to evaluate f(- 4) substitute x = - 4 into f(x)
f(- 4) = 2(- 4)² - 3(- 4) = 2(16) + 12 = 32 + 12 = 44
to evaluate g(5) substitute x = 5 into g(x)
g(5) = - 4(5) - 1 = - 20 - 1 = - 21
One owl hoots every 3 hours, and a second owl hoots every 8 hours, and a third owl hoots every 12 hours. If they all hoot together at midnight of the first day, how many times on the hour in 3 days will at least two owls not give a hoot.
The number of times on the hour in 3 days at least two owls will not hoot obtained using number theory are 69 times.
What is number theory?Number theory is the study of integers and functions of arithmetic.
The number of hours in 3 days = 72 hours
Number theory indicates that the multiples of the periods of hooting are;
The multiples of 8 are; 8, 16, 24, 32, 40, 48, 56, 64, 72
The multiples of 3 are; 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72
The multiples of 12 are; 12, 24, 36, 48, 60, 72
The common multiples of 3 and 8 are 24, 48, 72
The common multiples of 8 and 12 are 24, 48, 72
The number of times in 72 hours when at least 2 owls are hooting are therefore;
The times when only one owl is hooting are
8, 16, 32, 40, 56, 64, = 6 times only the second owl is hooting
3, 6, 9, 12, 15, 18, 21, 27, 30, 33, 36, 39, 42, 45, 51, 54, 57, 60, 63, 66, 69 = 21 times when only the first owl hoots
The times when non of the owls hoot are;
72 - 24 - 6 = 42 times
The number of times when at least two owls don't give a hoot = 42 + 6 + 21 = 69 timesLearn more on number theory here: https://brainly.com/question/4301692
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A scientist has 68 lbs of a material. In 40 years , there is 63.3 lbs left. How much will be there be left in 200 years?
After 200 years, there will be 47.43 pounds left of the material.
How much will be there be left in 200 years?We know that we start with 68 pounds, and after 40 years there are 63.3 pounds left, so we have an exponential decay:
63.3 = 68*(b)^40
Where b defines how it decays, we can solve that equation for b to get:
(63.3/68)^(1/40) = b
0.9982 = b
Then the decay is:
f(x) = 68*(0.9982)^x
The amount left after 200 years will be:
f(200) = 68*(0.9982)^200 = 47.43
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If 5 + 5 is 9 what is 10 + 10
Answer: 20
Realistically : In this hypothetical scenario, if 5 + 5 equals 9, then the basic principles of mathematics are no longer applicable, and any further calculations cannot be accurately determined. However, in the real world, 5 + 5 equals 10, and therefore 10 + 10 would equal 20.
Answer:
20
Step-by-step explanation:
CAN SOMEONE HELP WITH THIS QUESTION?✨
The numeric value of the function f(x) at x = 5 is given as follows:
f(5) = 74.75.
How to obtain the function f(x)?The second derivative of the function f(x) is given as follows:
f''(x) = 2x + 6sin(x).
Integrating the second derivative, the first derivative of the function is given as follows:
f'(x) = x² - 6cos(x) + K.
When x = 0, y' = 2, hence the constant K is given as follows:
2 = -6 + K
K = 8.
Hence:
f'(x) = x² - 6cos(x) + 8.
Integrating the first derivative, the function is given as follows:
f(x) = x³/3 - 6sin(x) + 8x + K.
When x = 0, y = 4, hence the constant K is given as follows:
K = 4.
Then:
f(x) = x³/3 - 6sin(x) + 8x + 4.
The numeric value at x = 5 is given as follows:
f(5) = 5³/5 - 6sin(5) + 8(5) + 4
f(5) = 74.75.
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if A C B, then A n B = A U B
1) sometimes
2) never
3) always
if A C B, then A n B = A U B is always true
How to determine if A C B, then A n B = A U BThe statement "if A C B, then A n B = A U B" can be rephrased as "if A is a subset of B, then the intersection of A and B is equal to the union of A and B".
Every element of A is also an element of B. Therefore, the intersection of A and B contains all the elements of A.
On the other hand, the union of A and B contains all the elements of A and all the elements of B. Since A is a subset of B, all the elements of A are already included in B, so the union of A and B is just equal to B.
Therefore, we have:
A n B = A (since all the elements of A are in both A and B)
A U B = B (since A is a subset of B)
So A n B = A U B = B, which means that the original statement "if A C B, then A n B = A U B" is true
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15 POINTS HELP!!!
Al and Tim each have rectangular wooden decks on their homes. Al’s deck is 4 feet wide and has an area of 60 x+40 ft². Tim’s deck is 7 feet wide and has an area of 21x+14 ft². Determine an expression for the length of each deck. How many times the length of Tim's deck is Al’s deck?
The length of Tim's deck is 1/15th of the length of Al's deck.
Finding the expressions for the length of each deck.
For Al's deck:
Area of a rectangle = length × width
60x + 40 = length × 4
length = (60x + 40) / 4
length = 15x + 10 ft
For Tim's deck:
Area of a rectangle = length × width
21x + 14 = length × 7
length = (21x + 14) / 7
length = 3x + 2 ft
Now we can find no. of times the length of Tim's deck is Al's deck by dividing the length of Al's deck by the length of Tim's deck:
(15x + 10) / (3x + 2)
Simplifying this expression:
(3(5x + 3) + 1) / (3x + 2)
(3(5x + 3) / (3x + 2)) + (1 / (3x + 2))
15 + (1 / (3x + 2))
Therefore, the length of Tim's deck is 1/15th of the length of Al's deck.
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find f(g(2)), g(f(2)) given f(x)=3x+5 and g(x)=-7x+6
The two compositions give:
f(g(2)) = -19g(f(2)) = -71How to evaluate the compositions?Here we have two functions:
f(x) = 3x + 5
g(x) = -7x + 6
And we want to fin the two compositions:
f(g(2))
g(f(2))
First, let's find g(2) = -7*2+ 6 = -14 + 8 = -8
Then:
f(g(2)) = f(-8) = 3*-8 + 5 = -19
Now the other one:
f(2) = 3*2 + 5 = 11
Evaluating g in that:
g(11) = -7*11 + 6 = -77 + 6 = -71
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solve (2x - 3) (x + 2) = 0
Answer:
x=3/2
x=-2
Step-by-step explanation:
