Volume of the bead = Volume of the sphere - volume of the cylindrical hole = 242.95 mm³.
What is the Volume of a Sphere and a Cylinder?Volume of a sphere = 4/3πr³Volume of a cylinder = πr²hVolume of the bead = Volume of the sphere - volume of the cylindrical hole
= 4/3π(4³) - π(1²)(8)
= 268.08 - 25.13
Volume of the bead = 242.95 mm³
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Flying against the jetstream, a jet travels 2370 miles in 3 hours. Flying with the jetstream, the same jet travels 6350 miles in 5 hours. What is the rate of the jet in still air and what is the rate of the jetstream?
Velocity of jet in still air is
970
miles per hour and velocity of wind is
210
miles per hour.
Explanation:
Jet's velocity against wind is
3040
4
=
760
mile per hour and flying with wind it is
8260
7
=
1180
miles per hour.
Let the velocity of jet in still air be
x
miles per hour and velocity of wind be
y
miles per hour.
As such its velocity against wind is
x
−
y
and with wind is
x
+
y
and therefore
x
−
y
=
760
and
x
+
y
=
1180
Adding the two
2
x
=
1940
and
x
=
970
and
y
=
1180
−
970
=
210
Hence velocity of jet in still air is
970
miles per hour and velocity of wind is
210
miles per hour.
The speed of an aircraft in still air is 200kmh−1. The wind blows from the west at a speed of 85.0kmh−1.
1 Expert Answer
The speed of the plane in still air is 110 mph.
Multiply the headwind or tailwind component by your estimated flight time expressed as a decimal, such as "3.2 hours." Add the result (don't forget that tailwinds are negative numbers) to the geographic distance of your route. The resulting number will be total nautical air miles of your trip.
A shipping company will ship a package for $7.50 when the volume is no more than 15,000 cubic centimeters. Grace needs to ship a package that is 3x-5 centimeters long, 2x centimeters wide, and x + 20 centimeters tall. A.Write a polynomial expression to represent the situation if Grace plan as to spend a maximum of $7.50
B. Write and solve a system of equations
C. What should the dimensions of the package be to have the maximum volume?
The maximum volume is at x = 0.85 cm. The inequality is 6x³ + 110x² - 200x ≤ 15000
What is an inequality?
An inequality is an expression that shows the non equal comparison between two or more numbers and variables.
A shipping company will ship a package for $7.50 when the volume is no more than 15,000 cubic centimeters. Hence, if Grace plan as to spend a maximum of $7.50:
Volume (V) = (3x - 5)(2x)(x + 20) = 6x³ + 110x² - 200x
The inequality is:
6x³ + 110x² - 200x ≤ 15000
6x³ + 110x² - 200x - 15000 ≤ 0
x = 10
The maximum volume is at:
V' = 0
V' = 18x² + 220x - 200 = 0
x = 0.85 cm
The maximum volume is at x = 0.85 cm. The inequality is 6x³ + 110x² - 200x ≤ 15000
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the original price: $75 and percent of discount :30% what’s the
Answer:
The discount is 22.50 and the final price $52.50
Step-by-step explanation:
Discount = Original Price x Discount %/100
Discount = 75 × 30/100
Discount = 75 x 0.3
You save = $22.50
Final Price = Original Price - Discount
Final Price = 75 - 22.5
Final Price = $52.50
Suppose that f(x)=6/x^7 find the following
F’(2)
F’(-1)
Answer:
f’(2) = -21/128
f’(-1) = -42
Step-by-step explanation:
We are given a function:
[tex]\displaystyle \large{f(x)=\frac{6}{x^7}}[/tex]
We want to evaluate f’(2) and f’(-1). Keep in mind that f’(x) denotes or means the derivative of f(x). So what we are going to do first is to find the derivative of given function.
Derive the function, there are two ways to derive it, either using power rules or quotient rules. For this, I’ll demonstrate two methods.
Power Rules
If [tex]\displaystyle \large{f(x)=x^n}[/tex] then [tex]\displaystyle \large{f\prime (x)=nx^{n-1}}[/tex] where n is any real numbers.
Since the function is written in a fraction form, we’ll have to convert it to the x^n form using law of exponent.
[tex]\displaystyle \large{f(x)=\frac{6}{x^7} \to f(x)=6\cdot \frac{1}{x^7}}[/tex]
Law of Exponent I
[tex]\displaystyle \large{\frac{1}{a^n} = a^{-n}}[/tex]
Therefore:
[tex]\displaystyle \large{f(x)=6x^{-7}}[/tex]
Then derive the function using power rules:
Property of Differentiation I
[tex]\displaystyle \large{y=kf(x) \to y\prime = kf\prime (x)}[/tex] where k is a constant.
[tex]\displaystyle \large{f\prime (x)=6\cdot -7x^{-7-1}}\\\displaystyle \large{f\prime (x)=6\cdot -7x^{-8}}\\\displaystyle \large{f\prime (x)=-42x^{-8}}[/tex]
Quotient Rules
[tex]\displaystyle \large{y=\frac{f(x)}{g(x)} \to y\prime = \frac{f\prime (x)g(x)-f(x)g\prime (x)}{[g(x)]^2}}[/tex]
If f(x) = k or a constant then:
Property of Differentiation II
[tex]\displaystyle \large{y=k \to y\prime = 0}[/tex] for k is a constant.
[tex]\displaystyle \large{y=\frac{k}{g(x)} \to y\prime = \frac{0\cdot g(x)-kg\prime (x)}{[g(x)]^2}}\\\displaystyle \large{y\prime = \frac{-kg\prime (x)}{[g(x)]^2}}[/tex]
Therefore:
[tex]\displaystyle \large{f\prime (x)=\frac{-6\cdot 7x^{7-1}}{[x^7]^2}}\\\displaystyle \large{f\prime (x)=\frac{-42x^6}{x^{14}}}\\\displaystyle \large{f\prime (x)=-42x^{6-14}}\\\displaystyle \large{f\prime (x)=-42x^{-8}}[/tex]
Laws of Exponent used above:
[tex]\displaystyle \large{(a^n)^m = a^{nm}}\\\displaystyle \large{\frac{a^n}{a^m} = a^{n-m}}[/tex]
Therefore the derivative of function is:
[tex]\displaystyle \large{f\prime (x) = -42x^{-8}}[/tex] or [tex]\displaystyle \large{f\prime (x)=-\frac{42}{x^8}}[/tex]
Next is to substitute x = 2 and x = -1 in the derivative.
[tex]\displaystyle \large{f\prime (2)=-\frac{42}{2^8}}\\\displaystyle \large{f\prime (2) = -\frac{42}{256}}\\\displaystyle \large{f\prime (2)= -\frac{21}{128}}[/tex]
And:
[tex]\displaystyle \large{f\prime (-1)=-\frac{42}{(-1)^8}}\\\displaystyle \large{f\prime (-1) = -\frac{42}{1}}\\\displaystyle \large{f \prime (-1) = -42}[/tex]
Therefore, f’(2) = -21/128 and f’(-1) = -42.
The equation representa Function A and the graph represents Function B
Answer:
D) Slope of Funcation B = - Slope of Function A
Step-by-step explanation:
The equation for the line is:
y=mx+b
Where m is the slope and b is the y-intercept
In this question, we are only interested in the slope.
For function A, we can see that the equation is f(x) = -2x + 1
Going back to the equation, we can see that -2 is the slope
Now for function B, we need to find the slope by looking at the graph.
To do this, you need to remember that the slope is y/x, or rise over run. (This is saying that every time the y happens, the x also happens. For example, if the slope is 1/2, every time the line goes up 1 unit, it goes to the right 2 units)
So for the function, we can see that when you move to the right 1 unit (run), you also move up 2 units (rise), so the slope would be
2
Comparing the slope of both the functions
Function A is -2
and
Function B is 2
So the answer is D
Is quadrilateral ABCD angle is equals to 60 degrees Angle B is equals to 80 degrees and angle C is equals to 120° find angle d
Which expression is equivalent to the following complex fraction?
Answer:I think it might be D but i'm not 100% sure
Answer my question #4
Answer:
11. 432,500 12. KF & ND
Step-by-step explanation:
11.
80,000 + 75,000 + 105,000 + 82,500 + 90, 000 = 432,500 people
( it says "about" so it doesn't have to be exact but a reasonable guess)
12. The two stadiums most similar in attendance is Kyle Field and Notre Dame
The problem is write you answer using ONLY positive exponents
Answer:
z^10/z^5 = z^5
Step-by-step explanation:
if it is divide, you minus, so z^10/z^5 is z^5.
Find the length of each arc shown in red. Leave your answer in terms of pi. 110 4in
The length of the arc shown in red is
Step-by-step explanation:
step 1
Find the circumference of the circle The circumference is equal to we have substitute
step 2
Find the length of the arc in red Remember that the length of the circumference subtends a central angle of 360 degrees so by proportion find the length of the arc by a central angle of 110 degrees Simplify
the quotient of the product of 32 and 15 and the difference of 17 and 9 as a numerical expression?
Answer:
(32×15)/(17 -9)
Step-by-step explanation:
The term "quotient" refers to the result of division. The term "product" refers to the result of multiplication. The term "difference" refers to the result of subtraction.
__
Here, we want the quotient of a product and a difference. This means the product will be divided by the difference. The product is the product of 32 and 15, so its value is (32×15). The difference is the difference of 17 and 9, so its value is (17 -9).
Then the desired numerical expression is ...
[tex]\boxed{\dfrac{32\times15}{17-9}}[/tex]
______
Additional comment
The result of evaluating this expression is ...
(32×15)/(17 -9) = 480/8 = 60
__
For quotients and differences, the order of the operands matters. Our convention is that "the quotient of A and B" means "A/B", and "the difference of A and B" means "A-B".
In general English usage (not specific to a formal math problem), the term "difference" often is used to mean "the positive difference." That is, the wording "the difference between 3 and 4" would generally refer to the value 1 (not -1).
Find the average of this set of numbers.16, 20, 30, 30
A) 14
B) 15
C) 25
D) none of the above
Answer:
D) none of the above
Step-by-step explanation:
To find an average, you add up all of the numbers and divide by how many numbers there were. for example, in this equation, the sum of all of the numbers was 96. then I divided 96 by 4(the amount of numbers shown)
what’s the answer to 22= b/2 -2
b would equal 48
_________________
show how you know, thank you :)
~giving brainliest!~
Answer:
V≈180.96
Step-by-step explanation:
What is the domain for the following function?
y=-x+1
x²+x-6
X-
O A. {X-1
O B. (x*-3
O c. {# -3;x # 2)
OD. x+0)
Which statement about these triangles is true.
Picture Below
Answer:
For me I think it is a number 3
Step-by-step explanation:
The statement about these triangles which is true there are exactly three isosceles triangles, the correct option is B.
What is the right triangle?A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse. The angle of a right angle is always 90 degrees.
We are given that;
4 triangle figure
we can answer the question by counting how many triangles belong to each category. We have:
Three acute triangles: B, D, and E.
Three isosceles triangles: A, D, and E.
Two right triangles: A and C.
Two scalene triangles: B and C.
Therefore, the statement that is true about these triangles is:
Therefore, by the given triangle answer will be There are exactly three isosceles triangles.
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What is 8x25 to ding out the answer please
Please I need help please help
Answer: 8x25= 200
Step-by-step explanation: 200
Answer:
8×25
=200 is the answer ok
Mrs. Bradford, a tailor, received 25 meters of fabric as a gift. She used 3 meters of fabric to make herself a long skirt. She plans to turn the rest of the fabric into smaller girls' dresses that she can sell. If she needs 110 centimeters of fabric for every dress, how many dresses can she make?
Answer:
20 dresses
Make sure to label
Step-by-step explanation:
there is 100 centimeters in 1 meter she has 2200 centimeters of fabric left and need 110 for each dress she can make 20 dresses
Sunshine Rental rents a motorcycle at a daily rate of $57.99 plus 48 cents per mile. City Rentals
rents the same motorcycle at $58.95 plus 46 cents per mile. For what mileage is the cost the same?
Answer:
48 miles
Step-by-step explanation:
To find the mileage when both cost the same, first form two equations for the total cost for each rental place.
Let the mileage be m.
Sunshine Rental
Daily rate= $57.99
Total cost= $(57.99 +0.48m)
City Rentals
Daily rate= $58.95
Total cost= $(58.95 +0.46m)
Let's equate both equations together.
When both costs the same,
57.99 +0.48m= 58.95 +0.46m
0.48m -0.46m= 58.95 -57.99
0.02m= 0.96
Solve for m:
m= 0.96 ÷0.02
m= 48
The cost is the same at 48 miles.
Margo is creating a pencil caddy in the shape of a triangular prism. She is determining how much wood she needs to build the caddy. Her design is shown below.
The total amount of wood Margo needs to build her pencil caddy is
square inchesMargo is creating a pencil caddy in the shape of a triangular prism. She is determining how much wood she needs to build the caddy. Her design is shown below.
The total amount of wood Margo needs to build her pencil caddy is
square inchesMargo is creating a pencil caddy in the shape of a triangular prism. She is determining how much wood she needs to build the caddy. Her design is shown below.
The total amount of wood Margo needs to build her pencil caddy is
square inchesMargo is creating a pencil caddy in the shape of a triangular prism. She is determining how much wood she needs to build the caddy. Her design is shown below.
The total amount of wood Margo needs to build her pencil caddy is
square inchesMargo is creating a pencil caddy in the shape of a triangular prism. She is determining how much wood she needs to build the caddy. Her design is shown below.
The total amount of wood Margo needs to build her pencil caddy is
square inchesMargo is creating a pencil caddy in the shape of a triangular prism. She is determining how much wood she needs to build the caddy. Her design is shown below.
The total amount of wood Margo needs to build her pencil caddy is
square inchesMargo is creating a pencil caddy in the shape of a triangular prism. She is determining how much wood she needs to build the caddy. Her design is shown below.
The total amount of wood Margo needs to build her pencil caddy is
square inchesv
solve x/3+y/4=2
2x/3+3y/4=5
Step-by-step explanation:
please mark me as brainlest
Answer:
Step-by-step explanation:
[tex]\dfrac{x}{3}+\dfrac{y}{4}=2\\\\\\\text{Multiply the whole equation by the LCM of 4 , 12 which is 12}\\\\ 12*\dfrac{x}{3}+12*\dfrac{y}{4}=12*2\\\\\\4x + 3y=24 \ -------------------(i)[/tex]
[tex]\dfrac{2x}{3}+\dfrac{3y}{4}=5\\\\\\\text{Multiply the whole equation by 12}\\\\12*\dfrac{2x}{3}+12*\dfrac{3y}{4}=5*12\\\\\\[/tex]
8x + 9y = 60 -------------------------(ii)
Multiply equation (i) by (-2)
(i)*(-2) -8x -6y = -48
(ii) 8x +9y = 60 {Now add. x will be cancelled}
3y = 12 {Divide both sides by 3}
y = 12/3
y = 4
Substitute y = 4 in equation (i)
4x + 3*4 = 24
4x + 12 = 24
4x = 24 - 12
4x = 12
x = 12/4
x = 3
[tex]\boxed{x = 3 \ ; \ y = 4}[/tex]
9. If triangle GFE - triangle GHJ, find the value of x.
Answer:
2
Step-by-step explanation:
→ Find the scale factor
12 ÷ 7.5 = 1.6
→ Form an equation
x + 6 = 1.6 ( 2x+ 1 )
→ Solve
x = 2
PLSS HELP ME
12/12 + 12/12 + 7/12=_____
2 7/12
This is because 12/12 is equal to 1/1 or 1. So 12/12 + 12/12 = 2.
2 + 7/12= 2 7/12
Answer:
31
-----
12
Step-by-step explanation:
12 12 7 31
---- + ------- + ----- = -------
12 12 12 12
Add the numerators together (top number) and keep the denominator the same (bottom number)
I hope this helps!
In the figure; Triangle ABC is isosceles with BC=AC . If ∠A = 70, find the values of x and y . Give reasons for your answer.
Captionless Image
Answer:
∠B = 70 and ∠C = 40
Step-by-step explanation:
The image is not loading for me but with isosceles triangles there will two angles that are the same and one different angle.
All the angles will add up to equal 180 degrees.
In this case the different angle would angle C as the two same lines meet at that point.
From this you can that angle A and B are the same, both 70, so angle C would be:
180 (all the angles of a triangle added together) - 70 - 70 = 40
I'm assuming that x and y are angles B and C as they are not stated so they would be: ∠B = 70 and ∠C = 40.
Here is a diagram to demonstrate this:
Which of the following describes this?
Answer:
Step-by-step explanation:
irrational number
Answer:
Irrational number
Step-by-step explanation:
It is a never-ending and non-repeating number.
Tim had 85$ to spend on 6 books. After buying them he had 13$. How much did each book cost. Write using two step equations
Answer:
he spent 12 dollars on each book
Step-by-step explanation:
minus 13 from 85 you get 72 and then divide 72 by 6
Answer:
12$ each
Step-by-step explanation:
Tim had 85$ to spend on 6 books.
After buying them he had 13$.
85$ - 13$ = 72$How much did each book cost.
72$ / 6books = 12$ each bookDetermine whether the statement makes sense or does not make sense, and explain your reasoning.
A candidate received the majority of first-place votes and lost the election.
Choose the correct answer below.
A. The statement does not make sense because the candidate with the majority of the first place votes using the plurality method is the winner.
B. The statement does not make sense because the candidate with the majority of the first place votes in an election is always the winner.
C. The statement makes sense because the Borda count method using preference ballots can result in a situation where this can happen.
D. The statement makes sense because the plurality method can result in a situation where this can happen.
A candidate received the majority of first-place votes but loses hows that A. The statement does not make sense.
What is plurality voting?It should be noted that plurality voting simply means when each voter is allowed to vote for only one candidate.
In this case, a candidate received the majority of first-place votes will win the election. Here, the majority of the first place votes using the plurality method is the winner.
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The electrical current, in amperes, in a circuit varies directly as the voltage. When 18 volts are applied, the current is 6 amperes. What is the current when 51 volts are applied?
Answer:
Step-by-step explanation:
6 Ampheres or 6A
Step-by-step explanation:
I = Current (unit is Amphere or A)
V = Voltage (unit is Volt or V)
R = Resistance ( unit is Ohm or Ω)
Formulas:
V=IR ; when getting the voltage
R=V/I; when getting the resistance
I=V/R; when getting the current
Solution of the Problem:
First, you have to get the resistance using the first given senario.
Distribute the given values (Voltage=15 Volts or 15V and Current= 5 Ampheres or 5A) to the formula on how to get the resistance.
R=V/I = 15 Volts/5 Ampheres
= 3 Ohms or 3Ω
Now, you have the value of the resistance which is 3 Ohms or 3Ω and the given value of voltage which is 18 Volts or 18V for the second senario.
I=V/R = 18 Volts/ 3 Ohms
= 6 Ampheres or 6A
So, the value of the current is 6 Ampheres or 6A
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Write the value of (2 +√ 2) (2 -√3)
[tex]\left(2 + \sqrt 2 \right)\left(2-\sqrt 3 \right)\\\\=4- 2\sqrt 3 + 2 \sqrt 2 - \sqrt 6\\\\=0.91484.....[/tex]
A closet contains 5 cases of laundry detergent. Each case contains 12 bottles. Each bottle contains 3 liters of detergent.
How many liters of laundry detergent in all are in the closet?
Each bottle in the case is 3 litres in capacity, we found the total number of bottles to be 60, hence the number of litres is 180 litres
Capacity of ItemsGiven Data
Number of Cases of Detergent = 5Number of Bottles on the closet = 5*12 = 60 bottlesRequired : the total litres
If each bottle is 3 litres in capacity and we have 60 bottles
Then the total amount in litres is
= 60*3
= 180 litres
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