Answer:
720
Step-by-step explanation:
Given : The word ABSENT
To Find: How many different 6-letter arrangements can be formed using the letters in the word ABSENT, if each letter is used only once?
Solution:
Number of letters in ABSENT = 6
So, No. of arrangements can be formed using the letters in the word ABSENT, if each letter is used only once = 6!
= [tex]6 \times 5 \times 4\times 3 \times 2 \times 1[/tex]
= [tex]720[/tex]
So, Option C is true
Hence there are 720 different 6-letter arrangements can be formed using the letters in the word ABSENT.
Final answer:
There are 720 different 6-letter arrangements that can be formed from the word ABSENT, by applying the permutation formula 6! = 720. The correct option is c.
Explanation:
The question asks: How many different 6-letter arrangements can be formed using the letters in the word ABSENT, if each letter is used only once? To answer this, we need to calculate the number of permutations of 6 letters taken from 6. This is a simple permutation problem where we use the formula for permutations which is n!, where n is the total number of items to choose from and ! denotes a factorial, meaning the product of all positive integers up to n.
Given that the word ABSENT has 6 letters and we are arranging all 6, we have 6! = 6×5×4×3×2×1 = 720. Therefore, there are 720 different 6-letter arrangements that can be formed using the letters in ABSENT, with each letter used only once.
Kellie is given the following information:
If two lines are perpendicular, then they intersect at a right angle. Lines A and B are perpendicular.
She concludes that lines A and B intersect at a right angle. Which statements are true? Check all that apply.
She used inductive reasoning.
She used the law of detachment.
Her conclusion is valid.
The statements can be represented as "if p, then q and if q, then r."
Her conclusion is true.
Answer:
She used inductive reasoning. (False)
She used the law of detachment. (True)
Her conclusion is valid. (True)
The statements can be represented as "if p, then q and if q, then r." (False)
Her conclusion is true. (True)
Step-by-step explanation:
p = Two lines are perpendicular
q = They intersect at Right angles.
Given: A and B are perpendicular
Conclusion: A and B intersect at right angle.
According to the law of detachment, There are two premises (statements that are accepted as true) and a conclusion. They must follow the pattern as shown below.
Statement 1: If p, then q.
Statement 2: p
Conclusion: q
In our case the pattern is followed. The truth of the premises logically guarantees the truth of the conclusion. So her conclusion is true and valid.
Answer:
it's b, c, e
Step-by-step explanation:
Klassen Toy Company, Inc., assembles two parts (parts 1 and 2): Part 1 is first processed at workstation A for 10 minutes per unit and then processed at workstation B for 20 minutes per unit. Part 2 is simultaneously processed at workstation C for 30 minutes per unit. Work stations B and C feed the parts to an assembler at workstation D, where the two parts are assembled. The time at workstation D is 15 minutes. a) The bottleneck of this process is workstation D , at 4 minutes per unit (enter your response as a whole number).
Answer:
The bottleneck of this process is Workstation C, at 30 minutes per unit.
Step-by-step explanation:
The throughput of each workstation is ...
A: 6 per hourB: 3 per hourC: 2 per hourD: 4 per hourSince each process must be executed once per finished product, the bottleneck is the station with the lowest throughput. It is clearly Workstation C.
The bottleneck of this process is workstation D, where the time per unit is 15 minutes.
Explanation:The bottleneck of this process is workstation D, where the time per unit is 15 minutes. This means that workstation D takes the longest time to complete one unit compared to other workstations. The bottleneck determines the maximum output rate of the entire process, as the other workstations cannot work faster than the slowest one.
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the center of a circle represent by the equation (x+9)^2+(y-6)^2=10^2 is___. options.... (-9,6), (-6,9), (6,-9) ,(9,-6)
Answer:
(-9, 6)
Step-by-step explanation:
It's all about pattern matching.
A circle centered at (h, k) with radius r has the equation ...
(x -h)^2 + (y -k)^2 = r^2
Comparing this pattern to the equation you have, you can see that ...
h = -9k = 6r = 10Then the center is (h, k) = (-9, 6).
Answer:
(-9, 6)
Step-by-step explanation:
i took the test
A probability experiment is conducted in which the sample space of the experiment is S={7,8,9,10,11,12,13,14,15,16,17,18}, event F={7,8,9,10,11,12}, and event G={11,12,13,14}. Assume that each outcome is equally likely. List the outcomes in F or G. Find P(F or G) by counting the number of outcomes in F or G. Determine P(F or G) using the general addition rule.
Answer:
F or G = {7,8,9,10,11,12,13,14}
n(F or G) = 8
n(S) = 12
By counting the no. of outcome
P(F or G) = n(F or G) / n(S)
P(F or G) = 8 /12
P(F or G) = 2/3
By using the general addition rule
P(F or G) = P(F) + P(G) - P(F and G)
= 6/12 + 4/12 - 2/12
= 2/3
An experimenter has prepared a drug dosage level that she claims will induce sleep for 80% of people suffering from insomnia. After examining the dosage, we feel that her claims regarding the effectiveness of the dosage are inflated. In an attempt to disprove her claim, we administer her prescribed dosage to 20 insomniacs and we observe Y , the number for whom the drug dose induces sleep. We wish to test the hypothesis H0 : p = .8 versus the alternative, Ha : p < .8. Assume that the rejection region {y ≤ 12} is used.
Answer:
cool
Step-by-step explanation:
32a³b²
_____
8ab²
Simplify the following expression.
Answer:
[tex]4a^{2}[/tex]
Step-by-step explanation:
We need to simplify the following expression:
[tex]y=\frac{32a^{3}b^{2}}{8ab^{2}}[/tex]
We know that: [tex]\frac{x^{a}}{x^{b}}=x^{a-b}[/tex]. Applying this rule, we have that:
[tex]y = \frac{32a^{3}b^{2}}{8ab^{2}} = 4a^{3-1}b^{2-2} = 4a^{2}[/tex]
Then, the solution is: [tex]4a^{2}[/tex]
The window shown is the shape of a semicircle with a radius of 6 feet. The distance from F to E is 3 feet and the measure of = 45°. Find the area of the glass in region BCIH, rounded to the nearest square foot.
Answer:
The area of the glass in region BCIH is 11 to the nearest feet²
Step-by-step explanation:
* Lets explain the figure
- The window is a semicircle with center G and radius 6 feet
- There is a small semicircle with center G and radius GF
∵ GE is 6 feet and EF is 3 feet
∵ GE = GF + FE
∴ 6 = GF + 3 ⇒ subtract 3 from both sides
∴ 3 = GF
∴ The radius of the small semicircle is 3 feet
∵ m∠BGC = 45°
- The area of sector BGC is part of the area of the semicircle
∵ The area of semi-circle is 1/2 π r²
∵ The measure of the central angle of the semicircle is 180°
∵ The measure of the central angle of the sector BGC is 45°
∴ The sector = 45°/180° = 1/4 of the semi-circle
∴ The area of the sector is 1/4 the area of the semicircle
∵ The area of the semicircle = 1/2 π r²
∵ r = 6 feet
∴ The area of the semicircle = 1/2 π (6)² = 1/2 π (36) = 18 π feet²
∴ Area of the sector = 1/4 (18 π) = 4.5 π feet²
- The small sector HGI has the same central angle of the sector BGC
∴ The area of the sector HGI is 1/4 The area of the small semicircle
∵ The area of the small semicircle = 1/2 π r²
∵ r = 3 feet
∴ The area of the small semicircle = 1/2 π (3)² = 1/2 π (9) = 4.5 π feet²
∴ Area of the sector HGI= 1/4 (4.5 π) = 1.125 π feet²
- The area of the glass in region BCIH is the difference between the
area of sector BGC and the area of the sector HGI
∴ The area of the glass in region BCIH = 4.5 π - 1.125 π ≅ 11 feet²
Answer:
11 feet to the nearest square foot.
Step-by-step explanation:
The area of sector BCG
= 45/180 * 1/2 π r^2
= 1/4 * 1/2 π r^2
= 1/8 * π * 6^2
= 4.5 π ft^2.
The radius of the inner semicircle is 6 - 3 = 3 feet.
The area of sector HIG = 1/4 * 1/2 π 3^2
= 1.125 π ft^2.
So the area of BCIH
= area of BCG - area HIG
= 4.5 π - 1.125 π
= 3.375 π
= 10.6 square feet.
if a*b represents the number of integers greater than a and less than b, what is the value of -2π*3√2
(a) 13 (b) 12 (c) 11 (d) 10
Answer:
11
Step-by-step explanation:
-2×pi is approximately-6.28
3×sqrt(2) is approximately 4.24
Now if you really need... just list out the integers between those two numbers and then count like so: -6,-5,-4,-3,-2,-1,0,1,2 3,4
That is 11 integers
The question is about finding the number of integers between -2π and 3√2. This involves understanding the definition of the function a*b, and then applying this to the given values. The correct answer is 11.
Explanation:The function a*b defined in this problem represents the number of integers greater than a and less than b.
When we substitute a with -2π and b with 3√2, we are basically finding the number of integers between -2π and 3√2.
Knowing that -2π is approximately -6.28, and 3√2 which is approximately 4.24, we count the integers that fall between these two numbers.
Our list of integers will be: -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4. Hence, the answer is 11 (option c).
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Desmond wants to sell his car that he paid $8,000 for 2 years ago. The car depreciated, or decreased in value, at a constant rate each month over a 2-year period. If x represents the monthly depreciation amount, which expression shows how much Desmond can sell his car for today? \
8,000 + 24x
8,000 - 24x
8,000 + 2x
8,000 - 2x
Answer:
8,000-24x
Step-by-step explanation:
Let
y ----> depreciated value of the car
x---> rate of depreciation
t ----> the time in months
we know that
The linear equation that represent this situation is
y=8,000-xt
For
t=2 years=2*12=24 months
substitute
y=8,,000-x(24)
y=8,000-24x
Dave and Ellen are newly married and living in their first house. The yearly premium on their homeowner's insurance policy is $450 for the coverage they need. Their insurance company offers a discount of 6 percent if they install dead-bolt locks on all exterior doors. The couple can also receive a discount of 2 percent if they install smoke detectors on each floor. They have contacted a locksmith who will provide and install dead-bolt locks on the two exterior doors for $50 each. At the local hardware store, smoke detectors cost $7 each, and the new house has two floors. Dave and Ellen can install them themselves. a. What discount will Dave and Ellen receive if they install the dead-bolt locks? Annual discount for deadbolts b. What discount will Dave and Ellen receive if they install smoke detectors? Annual discount for smoke detectors
Dave and Ellen could annually save $27 by installing dead-bolts and $9 by installing smoke detectors. This amounts to a significant discount on their homeowner's insurance premium.
Explanation:Dave and Ellen's annual homeowner's insurance premium is $450. If they install dead-bolts on all the exterior doors, they would receive a 6 percent discount, while smoke detector installations would fetch them a 2 percent discount. Let's calculate these discounts:
A. Dead-bolts discount: 6 percent of $450 translates to $(450*(6/100)) which equals $27.
B. Smoke detectors discount: 2 percent of $450would be $(450*(2/100)) that equals $9.
To summarize, the couple could annualy save $27 by installing dead-bolts and $9 by installing smoke detectors, which is a substantial reduction on the insurance premium.
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Dave and Ellen can save $27 annually by installing dead-bolt locks and $9 annually by installing smoke detectors. Total savings from both installations would be $36 annually.
Let's break down the problem step by step to calculate the discounts that Dave and Ellen will receive if they install dead-bolt locks and smoke detectors.
Part (a): Discount for Dead-Bolt Locks
1. Annual premium: $450
2. Discount for dead-bolt locks: 6%
The discount amount is calculated as follows:
[tex]\[ \text{Discount amount} = \text{Annual premium} \times \frac{\text{Discount percentage}}{100} \][/tex]
So, for the dead-bolt locks:
Discount amount for dead-bolt locks = 450 × [tex]\frac{6}{100} \][/tex]
Discount amount for dead-bolt locks = 450 × 0.06
Discount amount for dead-bolt locks = 27
Thus, Dave and Ellen will receive an annual discount of $27 if they install dead-bolt locks on all exterior doors.
Part (b): Discount for Smoke Detectors
1. Annual premium: $450
2. Discount for smoke detectors: 2%
The discount amount is calculated as follows:
[tex]\[ \text{Discount amount} = \text{Annual premium} \times \frac{\text{Discount percentage}}{100} \][/tex]
So, for the smoke detectors:
Discount amount for smoke detectors} = 450 × [tex]\frac{2}{100}[/tex]
Discount amount for smoke detectors} = 450 × 0.02
Discount amount for smoke detectors} = 9
Thus, Dave and Ellen will receive an annual discount of $9 if they install smoke detectors on each floor of their house.
In the 1980s an average mortgage rate was around 18.5 how much less per month would a 150000 30 year mortgage by today if the current rate were 5 %
Answer:
$1516.69 per month less
Step-by-step explanation:
The formula for the monthly payment A on a loan of principal P, annual rate r, for t years is ...
A = P(r/12)/(1 -(1 +r/12)^(-12t))
For the 18.5% loan, the monthly payment is ...
A = 150000(.185/12)/(1 -(1 +.185/12)^(-12·30)) ≈ 2321.92
For the 5% loan, the monthly payment is ...
A = 150000(.05/12)/(1 -(1 +.05/12)^-360) ≈ 805.23
The mortgage at 5% would be $1516.69 less per month.
Final answer:
To determine how much less per month a $150,000 30-year mortgage would be at a 5% interest rate compared to an 18.5% rate, calculate monthly payments for both scenarios and subtract the lower payment from the higher one.
Explanation:
The question asks to compare monthly mortgage payments in two different interest rate scenarios for a 30-year, $150,000 mortgage: first at an 18.5% interest rate which was the average in the 1980s, and second at the current rate of 5%. To find out how much less the monthly payment would be at 5% compared to 18.5%, we can use the formula for calculating monthly mortgage payments:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]
where:
M is your monthly payment.
P is the principal loan amount, $150,000 in this case.
i is your monthly interest rate. The annual rate needs to be divided by 12.
n is the number of payments (the number of months you will be paying the loan).
Calculating the monthly payment for an 18.5% interest rate over 30 years:
P = $150,000
i = 18.5% annual interest rate / 12 months = 1.5417% monthly interest rate
n = 30 years * 12 months/year = 360 payments
Doing the same calculation at a 5% interest rate:
P = $150,000
i = 5% annual interest rate / 12 months = 0.4167% monthly interest rate
n = 30 years * 12 months/year = 360 payments
After computing the monthly payments for both interest rates, we then subtract the monthly payment at 5% from the monthly payment at 18.5% to determine how much less it would be. As this is a high school-level mathematics problem, we use algebraic operations and functions to answer the question.
Help need help on this 3 math problems !!!
8. Determine whether the function shown is constant, linear, quadratic, or none of these. m(x)=13/6
A. Linear
B. Quadratic
C. None of these
D. Constant
6. Does the following equation determine y to be a function of x?
y2 = x + 3
A. No
B. Yes
C. Only when x = 1
D. Sometimes
16. Solve the system. y=1/7x-4 x=7y+1
A. No solution
B. (7, –3)
C. (–13, –2)
D. There are an infinite number of solutions
Answer:
8. D. Constant
6. A. No
16. A. No solution
Step-by-step explanation:
8. There is no "x" on the right side of the equal sign in the function definition. There is only the constant 13/6. The function shown is constant.
__
6. The equation will graph as a parabola that opens to the right. Solving for y, you get ...
y = ±√(x+3)
This is double-valued. A relation that gives two values for the same value of x is not a function.
__
16. In standard form, the two equations are ...
x -7y = 28x -7y = 1These equations are "inconsistent". There are no values of x and y that can make them both be true. Thus, there is no solution.
Write an equation of a parabola that opens to the left, has a vertex at the origin, and a focus at (–4, 0).
Answer:
[tex]y^{2}=-16x[/tex]
Step-by-step explanation:
we know that
The standard equation of a horizontal parabola is equal to
[tex](y-k)^{2}=4p(x-h)[/tex]
where
(h,k) is the vertex
(h+p,k) is the focus
In this problem we have
(h,k)=(0,0) ----> vertex at origin
(h+p,k)=(-4,0)
so
h+p=-4
p=-4
substitute the values
[tex](y-0)^{2}=4(-4)(x-0)[/tex]
[tex]y^{2}=-16x[/tex]
3) An open top box is to be constructed out of a 90 inch by 70 inch piece of cardboard by cutting squares out of the corners and then folding the side flaps up. If the squares all have sides of 15 inches, find the following.
a) Volume in cubic inches.
b) Volume in cubic feet.
c) Volume in cubic yards.
Answer:
a) The volume in cubic inches is 36000
b) The volume in cubic feet is 125/6
c) The volume in cubic yard is 125/162
Step-by-step explanation:
* Lets study the information of the problem to solve it
- The dimensions of the piece of cardboard are 90 inches by 70 inches
- The side of the cutting square is 15 inches
- The squares are cutting from each corner
∴ Each dimension of the cardboard will decrease by 2 × 15 inches
∴ The new dimensions of the piece of cardboard are;
90 - (15 × 2) = 90 - 30 = 60 inches
70 - (2 × 15) = 70 - 30 = 40 inches
- The dimensions of the box will be:
# Length = 60 inches
# width = 40 inches
# height = 15 inches
- The volume of any box with three different dimensions is
V = Length × width × height
∵ The length = 60 inches
∵ The width = 40 inches
∵ The height = 15 inches
∴ V = 60 × 40 × 15 = 36000 inches³
a) The volume in cubic inches is 36000
* Now lets revise how to change from inch to feet
- 1 foot = 12 inches
∵ 1 foot = 12 inches
∴ 1 foot³ = (12)³ inches³
∴ 1 foot³ = 1728 inches³
∵ The volume of the box is 36000 inches³
∴ The volume of the box in cubic feet = 36000 ÷ 1728 = 125/6
b) The volume in cubic feet is 125/6
* Now lets revise how to change from feet to yard
- 1 yard = 3 feet
∵ 1 yard = 3 feet
∴ 1 yard³ = (3)³ feet³
∴ 1 yard³ = 27 feet³
∵ The volume of the box is 125/6 feet³
∴ The volume of the box in cubic yard = 125/6 ÷ 27 = 125/162
c) The volume in cubic yard is 125/162
Answer:
3600 cubic inches , 2.08 cubic feet , 0.0771 cubic yards
Step-by-step explanation:
Here we are given that the open box has been constructed from a card board with length 90 inches and width 70 inches by
1. cutting a square card board
2. of each side 15 inches
Hence when we are done with folding it for our cuboid , we find our new
1. Length = 90-15-15 = 60 inches
2. width = 70-15-15 = 40 inches
3. Height = 15 inches
Now we know the volume of any cuboid is given as
V= Length * width * height
= 60*40*15
= 3600 cubic inches
Part 2 . Now let us convert them into cubic feet
1 cubic inch = 0.000578704 cubic feet
Hence 3600 cubic inches = 3600 * 0.000578704 cubic feet
=2.083 cubic feet
Part 3. Now let us convert them into cubic yards
1 cubic inch = 0.0000214335 cubic yards
Hence 3600 cubic inches = 3600 * 0.0000214335 cubic yards
= 0.0771 cubic yards
An ellipse has vertices at (0, #17) and foci at (0, ±15). Write the equation of the ellipse in standard form. Graph the ellipse.
ANSWER
[tex]\frac{ {x}^{2} }{ 64 } + \frac{ {y}^{2} }{ 289 } = 1[/tex]
See attachment for the graph
EXPLANATION
The standard equation of the vertical ellipse with center at the origin is given by
[tex] \frac{ {x}^{2} }{ {b}^{2} } + \frac{ {y}^{2} }{ {a}^{2} } = 1[/tex]
where
[tex] {a}^{2} \: > \: {b}^{2} [/tex]
The ellipse has its vertices at (0,±17).
This implies that:a=±17 or a²=289
The foci are located at (0,±15).
This implies that:c=±15 or c²=225
We use the following relation to find the value of b²
[tex] {a}^{2} - {b}^{2} = {c}^{2} [/tex]
[tex] \implies \: 289 - {b}^{2} = 225[/tex]
[tex] - {b}^{2} = 225 - 289[/tex]
[tex] - {b}^{2} = - 64[/tex]
[tex] {b}^{2} = 64[/tex]
We substitute into the formula for the standard equation to get:
[tex]\frac{ {x}^{2} }{ 64 } + \frac{ {y}^{2} }{ 289 } = 1[/tex]
At the local pet store, zebra fish cost $1.80 each and neon tetras cost $2.00each. Of Sameer bought 14 is for a total cost of $26.80, not including tax, how many of each type of fish did he buy?
. Need help !!! on 2 math questions
The height in feet of a ball dropped from a 150 ft. Building is given by h(t) = –16t2 + 150, where t is the time in seconds after the ball is dropped. Find h(2) and interpret its meaning. Round your answer to the nearest hundredth.
A. h(2) = 86.00 means that after 2 seconds, the height of the ball is 86.00 ft.
B. h(2) = 3.04 means that after 2 seconds, the height of the ball has dropped by 3.04 ft.
C. h(2) = 3.04 means that after 2 seconds, the height of the ball is 3.04 ft.
D. h(2) = 86.00 means that after 2 seconds, the height of the ball has dropped by 86.00 ft.
15. The perimeter of a triangle is 69 cm. The measure of the shortest side is 5 cm less than the middle side. The measure of the longest side is 5 cm less than the sum of the other two sides. Find the lengths of the sides.
A. 16 cm; 21 cm; 32 cm
B. 15 cm; 21 cm; 33 cm
C. 15 cm; 22 cm; 32 cm
D. 17 cm; 21 cm; 31 cm
Answer:
Part 1) Option A. h(2) = 86.00 means that after 2 seconds, the height of the ball is 86.00 ft.
Part 2) Option A. 16 cm; 21 cm; 32 cm
Step-by-step explanation:
Part 1)
we have
[tex]h(t)=-16t^{2}+150[/tex]
where
t ----> is the time in seconds after the ball is dropped
h(t) ----> he height in feet of a ball dropped from a 150 ft
Find h(2)
That means ----> Is the height of the ball 2 seconds after the ball is dropped
Substitute the value of t=2 sec in the equation
[tex]h(2)=-16(2)^{2}+150=86\ ft[/tex]
therefore
After 2 seconds, the height of the ball is 86.00 ft.
Part 2) The perimeter of a triangle is 69 cm. The measure of the shortest side is 5 cm less than the middle side. The measure of the longest side is 5 cm less than the sum of the other two sides. Find the lengths of the sides
Let
x----> the measure of the shortest side
y ----> the measure of the middle side
z-----> the measure of the longest side
we know that
The perimeter of the triangle is equal to
P=x+y+z
P=69 cm
so
69=x+y+z -----> equation A
x=y-5 ----> equation B
z=(x+y)-5 ----> equation C
substitute equation B in equation C
z=(y-5+y)-5
z=2y-10 -----> equation D
substitute equation B and equation D in equation A and solve for y
69=(y-5)+y+2y-10
69=4y-15
4y=69+15
4y=84
y=21 cm
Find the value of x
x=21-5=16 cm
Find the value of z
z=2(21)-10=32 cm
The lengths of the sides are 16 cm, 21 cm and 32 cm
Raise the quality in parentheses to the indicated exponent, and slim lift the resulting expression with positive exponents.
For this case we have the following expression:
[tex](\frac {-27x ^ 0 * y ^ {- 2}} {54x ^ {- 5} * y ^ {- 4}}) ^ {- 2} =[/tex]
By definition we have to:
[tex]a^0= 1[/tex]
So:
[tex](\frac {-27y ^ {- 2}} {54x ^ {- 5} * y ^ {- 4}}) ^ {- 2} =[/tex]
Simplifying:
[tex](\frac {-y ^ {- 2}} {2x ^ {- 5} * y ^ {- 4}}) ^ {- 2} =[/tex]
By definition of power properties we have to:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
So, rewriting the expression we have:
[tex]\frac {-y ^ {- 2 * -2}} {4x ^ {- 5 * -2} * y ^ {- 4 * -2}} =\\\frac {-y ^ {4}} {4x ^ {10} * y ^ {8}} =[/tex]
SImplifying:
[tex]\frac {-y ^ {4-8}} {4x ^ {10}} =\\\frac {-y ^ {- 4}} {4x ^ {10}} =\\- \frac {1} {4x ^ {10} y^ {4}}[/tex]
Answer:
[tex]- \frac {1} {4x ^ {10} y ^ {4}}[/tex]
Find the ratio, reduced to lowest terms, of the volume of a sphere with a radius of 5 inches to the volume of a sphere with a radius of 10 inches. The ratio is (Type an integer or a simplified fraction)
Answer: The ratio is [tex]1:8\ or\ \dfrac{1}{8}[/tex]
Step-by-step explanation:
Since we have given that
Radius of first sphere = 5 inches
Radius of second sphere = 10 inches
We need to find the ratio of volume of first sphere to volume of second sphere:
As we know the formula for "Volume of sphere ":
[tex]Volume=\dfrac{4}{3}\pi r^3[/tex]
So, it becomes,
Ratio of first volume to second volume is given by
[tex]\dfrac{4}{3}\pi (5)^3:\dfrac{4}{3}\pi (10)^3\\\\=5^3:10^3\\\\=125:1000\\\\=1:8[/tex]
Hence, the ratio is [tex]1:8\ or\ \dfrac{1}{8}[/tex]
The ratio of the volume of a sphere with a radius of 5 inches to the volume of a sphere with a radius of 10 inches is 1/8.
Explanation:To find the ratio of the volume of a sphere with a radius of 5 inches to the volume of a sphere with a radius of 10 inches, we can use the formula for the volume of a sphere, which is V = (4/3)πr³. Let's calculate the volumes of the two spheres:
For the sphere with a radius of 5 inches:
V1 = (4/3)π(5)³ = (4/3)π(125) = 500π inches³
For the sphere with a radius of 10 inches:
V2 = (4/3)π(10)³ = (4/3)π(1000) = 4000π inches³
Therefore, the ratio of the two volumes is:
R = V1/V2 = (500π)/(4000π) = 1/8
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Create a question with this scenario you could ask that could be answered only by graphing or using logarithm.
David estimated he had about 20 fish in his pond. A year later, there were about 1.5 times as many fish. The year after that, the number of fish increased by a factor of 1.5 again. The number of fish is modeled by f(x)=20(1.5)^x.
Answer:
After how many years is the fish population 100?
x=3.97 years
Step-by-step explanation:
The fish population increases by a factor of 1.5 each year. We have the equation that represents this situation
[tex]f (x) = 20 (1.5) ^ x[/tex]
Where x represents the number of years elapsed f(x) represents the amount of fish.
Given this situation, the following question could be posed
After how many years is the fish population 100?
So we do [tex]f (x) = 100[/tex] and solve for the variable x
[tex]100 = 20 (1.5) ^ x\\\\\frac{100}{20} = (1.5)^x\\\\ 5= (1.5)^x\\\\log_{1.5}(5) = log_{1.5}(1.5)^x\\\\log_{1.5}(5) = x\\\\x =log_{1.5}(5)\\\\x=3.97\ years[/tex]
Observe the solution in the attached graph
Suppose θ is an angle in the standard position whose terminal side is in Quadrant IV and cotθ = -6/7 . Find the exact values of the five remaining trigonometric functions of θ. Find the exact values of the five remaining trigonometric functions of θ.
let's recall that on the IV Quadrant the sine/y is negative and the cosine/x is positive, whilst the hypotenuse is never negative since it's just a distance unit.
[tex]\bf \stackrel{\textit{on the IV Quadrant}}{cot(\theta )=\cfrac{\stackrel{adjacent}{6}}{\stackrel{opposite}{-7}}}\qquad \impliedby \textit{let's find the \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{6^2+(-7)^2}\implies c=\sqrt{36+49}\implies c=\sqrt{85} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf tan(\theta )=\cfrac{\stackrel{opposite}{-7}}{\stackrel{adjacent}{6}}\qquad \qquad sec(\theta )=\cfrac{\stackrel{hypotenuse}{\sqrt{85}}}{\stackrel{adjacent}{6}}\qquad \qquad csc(\theta )=\cfrac{\stackrel{hypotenuse}{\sqrt{85}}}{\stackrel{opposite}{-7}}[/tex]
[tex]\bf sin(\theta )=\cfrac{\stackrel{opposite}{-7}}{\stackrel{hypotenuse}{\sqrt{85}}}\implies \stackrel{\textit{and rationalizing the denominator}}{\cfrac{-7}{\sqrt{85}}\cdot \cfrac{\sqrt{85}}{\sqrt{85}}\implies -\cfrac{7\sqrt{85}}{85}} \\\\\\ cos(\theta )=\cfrac{\stackrel{adjacent}{6}}{\stackrel{hypotenuse}{\sqrt{85}}}\implies \stackrel{\textit{and rationalizing the denominator}}{\cfrac{6}{\sqrt{85}}\cdot \cfrac{\sqrt{85}}{\sqrt{85}}\implies \cfrac{6\sqrt{85}}{85}}[/tex]
Answer:
These are the five remaining trigonometric functions:
tanθ = - 7/6secθ = (√85) / 6cosθ = 6(√85) / 85sinθ = - 7(√85) / 85cscθ = - (√85)/7Explanation:
Quadrant IV corresponds to angle interval 270° < θ < 360.
In this quadrant the signs of the six trigonometric functions are:
sine and cosecant: negativecosine and secant: positivetangent and cotangent: negativeThe expected values of the five remaining trigonometric functions of θ are:
1) Tangent:
tan θ = 1 / cot (θ) = 1 / [ -6/7] = - 7/62) Secant
sec²θ = 1 + tan²θ = 1 + (-7/6)² = 1 + 49/36 = 85/36sec θ = ± (√85)/ 6
Choose positive, because secant is positive in Quadrant IV.
sec θ = (√85) / 6
3) Cosine
cosθ = 1 / secθ = 6 / (√85) = 6 (√85) / 854) Sine
sin²θ + cos²θ = 1 ⇒ sin²θ = 1 - cos²θ = 1 - [6(√85) / 85] ² =sin²θ = 1 - 36×85/(85)² = 1- 36/85 = 49/85
sinθ = ± 7 / (√85) = ± 7(√85)/85
Choose negative sign, because it is Quadrant IV.
sinθ = - 7 (√85) / 85
5) Cosecant
cscθ = 1 / sinθ = - 85 / (7√85) = - (√85) / 7Find the area under the standard normal curve to the left of z=−2.94 and to the right of z=−2.28. Round your answer to four decimal places, if necessary.
Answer:
The area under the standard normal curve to the left of z=−2.94 and to the right of z=−2.28 is 0.9903 square units.
Step-by-step explanation:
We need to find the area under the standard normal curve to the left of z=−2.94 and to the right of z=−2.28.
The standard normal table represents the area under the curve.
[tex]P(z<-2.94)\cup P(z>-2.28)=P(z<-2.94)+P(z>-2.28)[/tex] .....(1)
According to the standard normal table, we get
[tex]P(z<-2.94)=0.0016[/tex]
[tex]P(z>-2.28)=1-P(z<-2.28)=1-0.0113=0.9887[/tex]
Substitute these values in equation (1).
[tex]P(z<-2.94)\cup P(z>-2.28)=0.0016+0.98807=0.9903[/tex]
Therefore the area under the standard normal curve to the left of z=−2.94 and to the right of z=−2.28 is 0.9903 square units.
The area under the standard normal curve to the left of z = −2.94 and to the right of z = −2.28 is 0.9903 square units.
What is normal a distribution?It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.
The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.
The area under the standard normal curve to the left of z = −2.94 and to the right of z = −2.28 will be
The standard normal table represents the area under the curve.
[tex]\rm P(z < -2.94) \cap P(z > -2.28) = P(z < -2.94) + P(z > -2.28)[/tex] ...1
According to the standard normal table, we have
[tex]\rm P(z < -2.94) = 0.0016\\\\P(z > -2.94) = 1- P(z < -2.94) = 1-0.0113 = 0.9887[/tex]
Substitute these values in equation 1, we have
[tex]\rm P(z < -2.94) \cap P(z > -2.28) = 0.0016 + 0.9887 = 0.9903[/tex]
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Someone can you please help me on number 74
Answer:
9t^3 +t^2
Step-by-step explanation:
The perimeter of the figure is the sum of the lengths of the sides. The side lengths are represented by the polynomials shown, so the perimeter (P) is their sum:
P = (4t^3 -5) + (4t^3 -5) + (t^2 +9) + (t^3 -t^2 -11) + (t^2 +12)
Rearranging to group like terms:
P = (4t^3 +4t^3 +t^3) + (t^2 -t^2 +t^2) + (-5 -5 +9 -11 +12)
P = 9t^3 +t^2
The perimeter of the figure is represented by the polynomial 9t^3 +t^2.
Answer:
[tex]9t^3+t^2[/tex]
Step-by-step explanation:
We are given a figure of a polygon with mentioned side lengths and we are to find the perimeter of it.
For that, we will simply add the given side lengths and simplify them.
Perimeter of polygon = [tex] ( 4 t ^ 3 - 5 ) + ( 4 t ^ 3 - 5 ) + ( t ^ 2 + 9 ) + ( t ^ 2 + 1 2 ) + ( t ^ 3 - t ^ 2 - 1 1 ) [/tex]
= [tex] 4 t ^ 3 + 4 t ^ 3 + t ^ 3 + t ^ 2 - t ^ 2 + t ^ 2 - 5 - 5 + 9 - 1 1 + 1 2 [/tex]
Perimeter of polygon = [tex]9t^3+t^2[/tex]
XTAX=1. determine their canon- 1. Write the following quadratic forms as V(x) ical forms, find the modal matrices (i.e. the matrices of unit eigenvectors) of the corresponding transformations and write down explicite expressions for canonical cOordinates (y1, 2, y3) in terms of the original coordinates (x1, X2, X3). State what surfaces these quadratic forms correspond to: = > (a) -a x + 4x12 4x1x38x231; (b) 3-33 + 4xrj224x3122a3= 1; (c) 4a7 2x1 2x1X36x2a3 = 1. 2. Solve the following systems of differential equations using the matrix exponential technique 3x 4 (a) x(0) = 5, y(0) = 1; 4x-3y 3.x y(0) = 9, y(0) = 3; -2x 6x2y
Answer:
678
Step-by-step explanation:
Chords and arcs. Can someone please help me with this and explain???20 points
Answer:
89
Step-by-step explanation:
So the line segment CD is 12.7 and half that is 6.35. I wanted this 6.35 so I can look at the right triangle there and find the angle there near the center. This will only be half the answer. So I will need to double that to find the measure of arc CD.
Anyways looking at angle near center in the right triangle we have the opposite measurement, 6.35, given and the hypotenuse measurement, 9.06, given. So we will use sine.
sin(u)=6.35/9.06
u=arcsin(6.35/9.06)
u=44.5 degrees
u represented the angle inside that right triangle near the center.
So to get angle COD we have to double that which is 89 degrees.
So the arc measure of CD is 89.
A survey asked 816 college freshmen whether they had been to a movie or eaten in a restaurant during the past week. The following information was obtained: 385 freshmen had been to neither a movie nor a restaurant, and 268 had been to a movie. If 96 of those who had been to a movie had not been to a restaurant, how many of the surveyed freshmen had been to the following?
Answer:
the answer is 90
Step-by-step explanation:
296-96=90
If jobs arrive every 15 seconds on average, what is the probability of waiting more than 30 seconds?
Answer: 0.14
Step-by-step explanation:
Given: Mean : [tex]\lambda=15\text{ per seconds}[/tex]
In minutes , Mean : [tex]\lambda=4\text{ per minute}[/tex]
The exponential distribution function with parameter [tex]\lambda[/tex] is given by :-
[tex]f(t)=\lambda e^{-\lambda t}, \text{ for }x\geq0[/tex]
The probability of waiting more than 30 seconds i.e. 0.5 minutes is given by the exponential function :-
[tex]P(X\geq0.5)=1-P(X\leq0.5)\\\\=1-\int^{0.5}_{0}4e^{-4t}dt\\\\=1-[-e^{-4t}]^{0.5}_{0}\\\\=1-(1-e^{-2})=1-0.86=0.14[/tex]
Hence, the probability of waiting more than 30 seconds = 0.14
The probability of waiting more than 30 seconds for a job, when jobs arrive every 15 seconds on average, can be calculated using the Poisson distribution model. The probability is approximately 13.5%.
Explanation:This problem involves the concept of Poisson distribution, which is a mathematical concept used to model events such as the arrival of customers in a given time interval. Since the question states that jobs arrive every 15 seconds on average, we can use this information to calculate the probability of waiting more than 30 seconds.
In a Poisson distribution, the average rate of arrival (λ) is 1 job every 15 seconds. This rate can be converted to a rate per 30 seconds by multiplying by 2, giving us λ=2. The probability that no jobs arrive in a 30-second interval in a Poisson distribution is given by the formula:
P(X=0) = λ^0 * e^-λ / 0! = e^-2 ≈ 0.135
This means that the probability of waiting more than 30 seconds is approximately 0.135, or 13.5%.
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According to a study, 86% of K-12 schools or districts in a country use digital content such as ebooks, audiobooks, and digital textbooks. Of these 86%, 11 out of 20 use digital content as part of their curriculum. Find the probability that a randomly selected school or district uses digital content and uses it as part of their curriculum. The probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is nothing.
Answer: Our required probability is 47.3%.
Step-by-step explanation:
Since we have given that
Probability of schools or district in a country use digital content = 86% = 0.86
Probability of schools or district uses digital content as a part of their curriculum out of 86% = [tex]\dfrac{11}{20}[/tex]
So, Probability that a selected school or district uses digital content and uses it as a part of their curriculum is given by
[tex]\dfrac{86}{100}\times \dfrac{11}{20}\\\\=0.86\times 0.55\\\\=0.473\\\\=47.3\%[/tex]
Hence, our required probability is 47.3%.
The probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is 47.3% and this can be determined by using the given data.
Given :
According to a study, 86% of K-12 schools or districts in a country use digital content such as ebooks, audiobooks, and digital textbooks.Of these 86%, 11 out of 20 use digital content as part of their curriculum.The probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is given by:
[tex]=\dfrac{11}{20}\times \dfrac{86}{100}[/tex]
Now, multiply 11 by 86 and also multiply 20 by 100 in the above expression.
[tex]=\dfrac{11\times 86}{20\times 100}[/tex]
SImplify the above expression.
[tex]=\dfrac{946}{2000}[/tex]
= 0.473
So, the probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is 47.3%.
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The average annual salary for 35 of a company’s 1200 accountants is $57,000. This describes a parameter.
yeah it does because $68,000 is a numerical description of a sample of annual salaries. so it is only a PARAMETER
--mark brainliest please! thank you and i hope this helps
(CO 3) The weights of ice cream cartons are normally distributed with a mean weight of 20.1 ounces and a standard deviation of 0.3 ounces. You randomly select 25 cartons. What is the probability that their mean weight is greater than 20.06 ounces? 0.553 0.748 0.252 0.447
Final answer:
To find the probability of the mean weight of 25 randomly selected ice cream cartons being greater than 20.06 ounces, we can use the Central Limit Theorem. By calculating the standard error, finding the z-score, and using a z-table or calculator, we can determine the probability.
Explanation:
To find the probability that the mean weight of 25 randomly selected ice cream cartons is greater than 20.06 ounces, we can use the Central Limit Theorem. According to the Central Limit Theorem, the distribution of sample means from a population with any distribution will be approximately normal, as long as the sample size is large enough.
First, we need to find the standard error of the mean (SE). The formula for SE is SE = standard deviation / √(sample size). In this case, the standard deviation is 0.3 ounces and the sample size is 25. So, SE = 0.3 / √25 = 0.06 ounces.
Next, we calculate the z-score, which measures how many standard deviations the mean is from the population mean. The formula for z-score is z = (sample mean - population mean) / standard error. In this case, the sample mean is 20.06 ounces, the population mean is 20.1 ounces, and the standard error is 0.06 ounces. So, z = (20.06 - 20.1) / 0.06 = -0.67.
We can use a z-table or a calculator to find the probability associated with the z-score. From the table or calculator, we find that the probability of getting a z-score greater than -0.67 is approximately 0.748. Therefore, the probability that the mean weight of the 25 ice cream cartons is greater than 20.06 ounces is approximately 0.748.