The expression πr² = 6477 can be used to solve for the radius of the sphere.
What is a sphere?It is defined as three-dimensional geometry when half-circle two-dimensional geometry is revolved around the diameter of the sphere that will form.
[tex]\rm V = \dfrac{4}{3} \pi r^3[/tex]
Area of sphere A = 6477 square inches
A = 4πr²
A = 6477
4πr² = 6477
πr² = 6477
Thus, the expression πr² = 6477 can be used to solve for the radius of the sphere.
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Which of the following equations have complex roots?
Answer:
D
Step-by-step explanation:
Subtracting 2 from both sides and then dividing both sides by 3 gives that x² = -2/3, which indicates the roots are complex.
please help me asap thank you so so so much u are the most amazing
The smallest angle would be 19 degrees. So option D is correct.
What is the sum of the octagon?The sum of exterior angles of the regular octagon is 360 degrees.
Given;
The angles
x + 13 + 2x - 1 + 2x + 6 + 2x + 12 + 2x - 17 + 3x - 4 + 3x - 10 + 4x = 360
19x - 1 = 360
19x = 359
x = 18.89
The smallest angle would be
2x - 17 = 2(18.89) - 17 = 19
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[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{2x-20}{3}=2x \end{gathered}$}[/tex]
Multiply both sides of the equation by 3.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 2x-20=6x \end{gathered}$}[/tex]
Subtract 6x on both sides.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 2x-20-6x=0 \end{gathered}$}[/tex]
Combine 2x and −6x to get −4x.
[tex]\large\displaystyle\text{$\begin{gathered}\sf -4x-20=0 \end{gathered}$}[/tex]
Add 20 to both sides. Any value plus zero results in its same value.
[tex]\large\displaystyle\text{$\begin{gathered}\sf -4x=20 \end{gathered}$}[/tex]
Divide both sides by −4.
[tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{20}{-4} \end{gathered}$}[/tex]
Divide 20 by −4 to get −5.
[tex]\large\displaystyle\text{$\begin{gathered}\sf x=-5 \ \ \to \ \ \ Answer \end{gathered}$}[/tex]
{ Pisces04 }[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation: }[/tex]
[tex]\mathbf{\dfrac{2x - 20}{3} = 2x}[/tex]
[tex]\huge\textbf{SIMPLIFY IT or DISTRIBUTE:}[/tex]
[tex]\mathbf{\dfrac{2}{3}x - \dfrac{20}{3} = 2x}[/tex]
[tex]\huge\textbf{SUBTRACT 2x to BOTH SIDES:}[/tex]
[tex]\mathbf{\dfrac{2}{3}x - \dfrac{20}{3} - 2x = 2x - 2x}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{- \dfrac{4}{3}x - \dfrac{20}{3} = 0}[/tex]
[tex]\huge\textbf{ADD }\boxed{\rm{\bf \dfrac{20}{3}}}\huge\textbf{ to BOTH SIDES:}[/tex]
[tex]\mathbf{-\dfrac{4}{3}x - \dfrac{20}{3} + \dfrac{20}{3} = 0 + \dfrac{20}{3}}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{-\dfrac{4}{3}x = \dfrac{20}{3}}[/tex]
[tex]\huge\textbf{MULTIPLY }\boxed{\rm \bf {\dfrac{3}{-4}}}\huge\textbf{ to BOTH SIDES:}[/tex]
[tex]\mathbf{\dfrac{3}{-4}\times\dfrac{-4}{3}x = \dfrac{3}{-4}\times\dfrac{20}{3}}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{x = -5}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = -5}}}\huge\chekmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Which term describes the set of all possible input values for a function? O A. Range OB. Input O C. Output OD. Domain SUBMI
Answer:
D. domain
Step-by-step explanation:
domain is set of x-values
range is set of y-values
Input is the set of x-values, so it is the domain.
Which of the following could be the ratio between the lengths of the two legs of a 30-60-90 triangle?
Check all that apply.
Answer:c
options A and B
Step-by-step explanation:
the ratio between the lengths of the two legs of a 30-60-90 triangle
General ration of 30-6- 90 degrees triangle is
x : xsqrt(3) : 2x
When x=1 the ratio becomes 1 : 1 sqrt(3)
when x= 2sqrt(3) the ratio becomes
It becomes
Two sides of 30-60-90 triangle cannot be equal
so option c and option D are not possible
sqrt(2) is also not possible because we have sqrt(3) in general ratio
PLS MARK ME AS BRAINLIEST.
On July 1, 20x5, Augusta Enterprises issued bonds with a face value of $1,000,000. The bonds carry a face interest rate of 10 percent that is payable each July 1 and January 1.
a. Prepare the entry in journal form without explanation for the issuance assuming the bonds are issued at 97.
b. Prepare the entry in journal form without explanation for the issuance assuming the bonds are issued at 102.
Based on the price that Augusta Enterprises issued the bonds, the journal entries would be:
Date Account title Debit Credit
July 1, 20x5 Cash $97,000
Discount on Bonds payable $3,000
Bonds payable $1,000,000
Date Account title Debit Credit
July 1, 20x5 Cash $1,020,000
Premium on Bonds payable $20,000
Bonds payable $1,000,000
How are bonds recorded at premium and discount?The cash received from the discounted bond is:
= 1,000,000 x 97%
= $970,000
The cash received from the premium bond is:
= 1,000,000 x 102/100
= $1,020,000
The premium is:
= 1,020,000 - 1,000,000
= $20,000
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PLS HELP ME 17 MIN LEFT Solve the following equation: one third plus one third equals
one third,
two sixths,
two thirds,
or three thirds.
Complete the table below to solve the equation 2.5x − 10.5 = 64(0.5x).
x f(x) = 2.5x − 10.5 g(x) = 64(0.5x)
2
3
4
5
6
A newspaper started an online version of its paper 14 years ago. In a recent presentation to stockholders, the lead marketing executive stated, “The revenues for online ads are more than double that of the revenues for printed ads.”
Use the graph below to justify the lead executive’s statement.
Determine the approximate year that the two ad revenues were equal.
See Text Version
Two ocean beaches are being affected by erosion. The table shows the width, in feet, of each beach measured at high tide where 1995 is represented by year 0:
Year number Western Beach width (in feet) Dunes Beach width (in feet)
0 100 20
5 90 45
10 80 70
11 78 75
12 76 80
15 70 95
Describe the patterns shown by the erosion data measurements shown for each of the beaches in the table.
Between which years will the beaches have approximately the same width?
Assuming these rates remain constant, what can you do to get a better approximation of when the two beaches will have the same width?
The answers are as follows:
What is data?Data is information that has been translated into a form that is efficient for movement or processing.
1. By substituting the values x= 1, 2, 3..
We get the point where f(x)= g(x)
So, f(5)= g(5) =2
Hence, the value of x is 5.
2. As per the given data, during year 14,
revenue from online ads is approximately $4.2 million, whereas revenue from online ads is double than revenue from printed ads.
Also, both line intersect inbetween 7 and 8th year and both online ads and printed ads generated an approximate revenue of $2.2 million.
3. Western Beach erodes from 100 ft to 70 ft.
So, rate of erosion = 30 ft/15 yr = 2 ft/yr.
and, Dunes Beach builds up from 20 ft to 95 ft.
So, rate of buildup = 75 ft/15 yr = 5 ft/yr.
Hence, Dunes beach gets 5 feet every year, and every 5 years the beach loses 25 feet.
b) From the table, beaches will have the same width sometime in year 11 (2006).
c) If the rate remains constant then there is no same width cause of decrease in western beach and increase dunes beach.
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Bailey was practicing karate and kicked the target 6 out of 20 times. Express the number of times she kicked the target as a fraction of the total number of kicks , and reduce the fraction to the lowest terms.
Answer:
ok so here we know that Baily kicked the target 6 times out of 20 that is 6/20 and then you just reduce the fraction dividing it by 2 so it will be 3/10
Step-by-step explanation:
hope it helps :)
John deposits a certain amount that is compounded continuously at 8% interest. Find the number of years it takes to double the amount.
Answer:
about 8.66 years
Step-by-step explanation:
The multiplier of account value when interest is compounded continuously is ...
k = e^(rt)
where r is the annual interest rate, and t is the number of years.
SetupWe want to find t when k=2 and r=0.08. Putting these values in the formula gives ...
2 = e^(0.08t)
SolutionTaking logs of both sides, we have ...
ln(2) = 0.08t
t = ln(2)/0.08 = 0.693147/0.08 ≈ 8.66
It takes about 8.66 years to double the amount.
__
Additional comment
If the interest rate is expressed in integer numbers of percentage points (R%), then the doubling time is ...
t = 100·ln(2)/R ≈ 69.3147/R
Here, that is 69.3147/8 ≈ 8.66.
The "rule of 72" is used to estimate the doubling time for periodically compounded interest at rate R%. That rule tells you the time is t ≈ 72/R. For most interest rates and compounding frequencies in a reasonable range, this gives a time within a reasonable amount of error.
For continuously compounded interest, we have shown the doubling time in years is 69.3147/R. (The exact value of the constant is 100·ln(2).) For the purpose here, a constant of 69.3 gives an estimate accurate to 3 sf.
Which of the following equations has the solution x = all real numbers?
O 4(3-x) + 7x = 4x + 12 + 2x
O 4(4-x) + 6x = x + 16 - 4x
O 3(4-x) + 6x = 4x + 12 - x
O 4(3-c) + 6x = 3x + 8x
Answer: 3(4-x) + 6x = 4x + 12 - x
Step-by-step explanation:
For the solution to be all real numbers, the left hand has to be identical to the right hand side.
1) [tex]4(3-x)+7x=12-4x+7x=12+3x[/tex], so wrong.
2) [tex]4(4-x)+6x=16-4x+6x=16+2x[/tex], so wrong.
3) [tex]3(4-x)+6x=12-3x+6x=12+3x=4x+12-x[/tex], so correct.
4) Wrong variable, so eliminate immediately.
A bus covered a distance of 331.25 km in 25 L of diesel. Find the distance covered by the bus in 1 L of diesel . please do answer in copy
Answer:
13.25km
Step-by-step explanation:
25 Litres = 331.25km
1 Litre =
[tex] \frac{331.25}{25} \\ = 13.25km[/tex]
Answer:
13.25 km
Step-by-step explanation:
25 litres = 331.25 km
1 litre =
331.25
25
=13.25 km
Draw a histogram and a box-and-whisker plot to represent the combined data, and answer the questions. Be sure to include the new graphs as part of your final submission.
How do the graphs of the combined data compare to the original graphs?
Compared to the original graphs, do the new graphs make it easier or more difficult to estimate the price of a book?
The new graphs would make it more difficult to estimate the price of a book.
How to create the combined graph?To do this, we simply combine the frequencies on Felix and Tyler's table.
When this is done, we have the following dataset
3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7, 8,8,8,8,9,9,9,9,9,9,9,9,9,11,11,13,13,13,13,15,15,15,16,16,18,18,18,18,18,19,19,19,19,19,19,29,32,32,36,36,36,38,38,64,64,66,66,66,68,68,69,75,75,76,76,76,76,76,78,78,79,82,82,86,86,86,89,96,96,97,97,99
Next, we create the box & whisker plot and the histogram using the new dataset
(see attachment for the graphs)
The new graphs would make it more difficult to estimate the price of a book.
This is so because the dataset used to create the graphs do not come from the same source
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how much is 0.54/0.2
Answer:
2.7 is the answer!!
Step-by-step explanation:
hope this helps :)
Draw u – v + w. please help !!!!!!!!!!
Here, we have to perform a sum of vectors and draw the resultant vector and the resultant vector will be <4, 0>.
How to illustrate the vector?If we see the image, we can write the vectors as:
w = <3, 3>
u = <-3, -4>
v = <-4, -1>
Now we want to sum:
u - v + w
u - v + w
= <-3, -4> - <-4, -1> + <3, 3>
= <-3 + 4 + 3, -4 + 1 + 3>
= <4, 0>
The graph of the resultant vector can be seen below.
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One jar filled with honey weighs 120 grams and one empty jar with half filled honey jar weighs 150 grams what is the weight of the jar
Answer:
90 grams
Step-by-step explanation
Full = 120
half filled + empty = 150
half of 120 = 60
Therefore, a jar weighs 150 - 60
= 90 grams
Tyler spent 17,700 seconds completing a 1,000 piece puzzle.
How many hours is this equivalent to? Answer choices are rounded
to the nearest hour.
O 288 hours
O 20 hours
5 hours
O124 hours
Which of the following are solutions to the equation below?
Check all that apply.
9x² - 6x + 1 =7
O A. x= 2√2
B. x = -√7+1
3
☐ C. X=
□ D. X=
√√7+1
3
+1
□ E. x = 2√2
3
O F. X= -√2+1
Answer: C and B
Step-by-step explanation:
[tex]9x^2 - 6x+1=7\\\\9x^2 - 6x-6=0\\\\x=\frac{-(-6) \pm \sqrt{(-6)^2 - 4(9)(-6)}}{2(9)}\\\\x=\frac{6 \pm \sqrt{252}}{18}\\\\x=\frac{1 \pm \sqrt{7}}{3}[/tex]
Name this triangle by its sides and angles. This is a(n) ____________________ triangle. a triangle with one right angle and three non-congruent sides obtuse, isosceles obtuse, scalene right, scalene right, isosceles
Answer:
c
Step-by-step explanation:
Choose the equation for the graph.
a) y = -x - 4 + 1
b) y=-x-4) - 1
c) y = -x + 4 + 1
d) y = -x + 4) - 1
e) y =
|x4| +1
Answer:
a
Step-by-step explanation:
The vertex is at (4,1).
Eliminate b, c, dAlso, the graph opens down, so this eliminates e.
So, the answer is a.
A garden table and a bench cost $714 combined. The garden table costs $64 more than the bench. What is the cost of the bench?
Answer:
The bench costs $325
Step-by-step explanation:
let garden table = x
let bench = y
x = y+64
x+y = 714
y+y+64 = 714 (we know, x = y+64)
2y + 64 = 714
2y = 650
y = 325
Answer:
Bench: $325
Garden Table: $389
Step-by-step explanation:
g + b = 714 Eq. 1
g = b + 64 Eq. 2
g = cost of the garden table
b = cost of the bench
Replacing Eq.2 in Eq.1
(b+64) + b = 714
2b + 64 = 714
2b = 714 - 64
2b = 650
b = 650/2
b = 325
from the Eq. 2
g = b + 64
g = 325 + 64
g = 389
Check:
from the Eq. 1
g + b = 714
389 + 325 = 714
Find the y intercept of the line on the graph
Answer: y = -1
Step-by-step explanation:
When x = 0, y = -1
Also, you can think about it as when the graph of the line passes the y axis
A box with an open top is to be constructed from a 15 inch by 24 inch piece of cardboard by cutting squares of equal sides from the corners and folding up the sides. Find the dimensions of the box of the largest volume that can be constructed.
The dimensions of the box of the largest volume that can be constructed are
D=18,9,3
What are the dimensions?Generally, the equation for the lenght is mathematically given as
Lenght=(24-2x)
Widht= (15-2x)
Therefore
Volume =L*B*H
V=(24-2x)(15-2x)x
V=(360-48x-30x+4x)x
V=4x^3-78x^2+360x
Differnciating we have
dv/dx=12x^2-156x+360
put dv/dx=0
12(x^2-13x+30)=0
x^2-10x-3x+30=0
(x-10)(x-3)=0
root=10,3
Second diiferciation
d^v/dx^2=24x-156
[tex]lim _{x=3} =-84 < 0[/tex]
In conclusion,
L=24-2x
L=24-2x3
L=18in
w= 15-2x
w=15-2*3
w=9in
h=x
h=2in
Dimension=18,9,3
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Please help!!! Suppose we have two functions...
Answer:
4
Step-by-step explanation:
To find f(-1)g(-1) which is f(-1)*g(-1), first, we must find what are values of f(-1) and g(-1) first which can be found by substituting x = -1 in both functions.
[tex]\displaystyle{f(-1)=(-1)^2+1}\\\\\displaystyle{f(-1)=1+1 = 2}[/tex]
Now we know that f(-1) is 2, next, we find g(-1).
[tex]\displaystyle{g(-1) = 3(-1)+5}\\\\\displaystyle{g(-1)=-3+5 = 2}[/tex]
Now we know that g(-1) is 2 too. Since the question wants to find f(-1)g(-1), therefore 2*2 = 4.
Hence, the answer is 4.
Answer:
D) 4
Step-by-step explanation:
Given functions:
f(x) = x² + 1
g(x) = 3x + 5
Here, we're asked to find the value of both functions when the value of x is -1. Then, we multiply the functions in order to find the value of f(-1)•g(-1).
Note: f(-1) • g(-1) is equivalent to (f • g)(-1).
Method 1: f(-1) • g(-1)
Find the value of each function when x = -1.
f(-1) = (-1)² + 1 ⇒ f(-1) = 1 + 1 ⇒ f(-1) = 2
g(-1) = 3(-1) + 5 ⇒ g(-1) = -3 + 5 ⇒ g(-1) = 2
Multiply the functions together.
f(-1) • g(-1) ⇒ 2 • 2 ⇒ 4
Method 2: (f • g)(-1)
First, multiply the functions.
⇒ (x² + 1) • (3x + 5) [ Simplify using the Distributive Property: (a + b) • (c + d) = ac + ad + bc + bd. ]
⇒ x²(3x) + x²(5) + 1(3x) + 1(5)
⇒ 3x³ + 5x² + 3x + 5
Now, substitute -1 as the value of x.
⇒ 3(-1)³ + 5(-1)² + 3(-1) + 5 [ Exponents first. }
⇒ 3(-1) + 5(1) -3 + 5 [ Multiply the numbers. ]
⇒ -3 + 5 - 3 + 5 [ Simplify. ]
⇒ 4
Therefore, the product of both functions when x = -1 is 4.
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in a random sample of 36 criminals convicted of a certain crime, it was determined that the mean length of sentencing was 50 months, with a standard deviation of 5 months. construct and interpret a 90 % confidence interval for the mean length of sentencing for this crime.
The answer is 90% of the crime is between 48.63 and 51.37
How to solve for the confidence intervalThe sd = 5 months
n = 36
Mean length = 50
1- 0.90
= 0.1
Critical value = alpha/2 = 1.645
Margin of error
E = 1.645 x 5/√36
= 1.37
The upper and lower limits are50 - 1.37 + 50 + 1.37
= (48.63, 51.37)
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15. Which one of the following is a geometric sequence?
O A. 0, 1, 2, 3,...
O B. 2, -3, 92, -18/4
O C. -7, 10, 23, 36, ...
O D. 8, 4, 2, 1, 1/2, ¹/4....
in the x-y plane, what is the y- intercept of the graph of the equation y=6 (x-1/2) (x+3)
The y-intercept on the x-y plane is (0, -9).
How to get the y-intercept?To get the y-intercept we just need to evaluate in x = 0.
Here we have:
y = 6*(x - 1/2)*(x + 3)
Evaluating the given equation in x = 0 we get:
y = 6*(0 - 1/2)*(0 + 3) = -9
Then the y-intercept on the x-y plane is (0, -9).
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Answer:
-9
Step-by-step explanation:
What is this expression in simplified form?
Answer:
See below
Step-by-step explanation:
= (-7)(11)(√(3*10) ) = - 77 √(30)
The following table shows the data collected from a random sample of 100 middle school students on the number of hours they do household chores every week:
Weekly Duration of Household Chores
Time (in hours) 0–1 2–3 4–5 6–7
Number of Students 32 64 3 1
There are 1,500 students in the school. Based on the sample proportion, how many students in the school would be expected to do household chores for at least two hours every week?
A 480
B 960
C 1020
D 1440
The students in the school would be expected to do household chores for at least two hours every week with 1020 students.
We have given
Time (in hours) 0– 1 2–3 4–5 6–7
Number of Students 32 64 3 1
What is the random sample?A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen.
The keyword is at least, this means anything under that number will not qualify.
So that leaves 68 out of the 100 sample students.
So if you want to have the same thing but with 1,500 students.
Take off the 2 zeros at the end of 1500 and multiply by 68 to get your answer.
This is because there are 2 zeros in 100, so to cancel out the 2 zeros in 100, take out the 2 zeros in 1500 making it a lot easier.
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Consider the following data on the estimated cost (in millions of dollars) resulting from traffic congestion for different urban areas. The following are the data for the 13 largest U.S. urban areas.
The mean is $5.769 million and the standard deviation is $3.905 million.
What is the mean?The mean is the average of a data set.
What is the standard deviation?The standard deviation shows the measure of the dispersion from the mean.
Data and Calculations:Urban Area Total Cost Squared Difference
(millions of dollars) (x - u)²
New York 16 104.65
Los Angeles 13 52.27
Chicago 7 1.51
Washington, D.C. 5 0.59
Houston 5 0.59
Dallas, Fort Worth 4 3.13
Detroit 4 3.13
Miami 4 3.13
Phoenix 4 3.13
Philadelphia 4 3.13
San Francisco 3 7.67
Boston 3 7.67
Atlanta 3 7.67
13 Total 75 198.27
Mean = 5.769 (75/13) 15.251 (198.27/13)
Standard Deviation = 3.905 (square root of 15.251)
Question Completion:Urban Area Total Cost
(millions of dollars)
New York 16
Los Angeles 13
Chicago 7
Washington, D.C. 5
Houston 5
Dallas, Fort Worth 4
Detroit 4
Miami 4
Phoenix 4
Philadelphia 4
San Francisco 3
Boston 3
Atlanta 3
Calculate the mean and standard deviation for this data set (in millions of dollars). (Round your answers to three decimal places.) mean $ million standard deviation $ million
Thus, the mean is $5.769 million and the standard deviation is $3.905 million.
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