Answer:
£30
Step-by-step explanation:
Percentage = Division
24 × 25% or 24 ÷ 4
= 6
6 + 24
= 30
Water is leaking from the bottom of a conical cup that is 20 inches across and 20 inches deep. Given that the cup loses 0. 5 cubic inches of water per minute, at what rate is the water level changing when the water is 8 inches deep?.
If water is leaking from the bottom of a conical cup that is 20 inches across and 20 inches deep. The rate that the water level changes when the water is 8 inches deep is: 3 /32π.
Rate of change of water leveldv/dt = rate of cup loss water per minutes=0.5
r = radius when the water is 8 inches deep
Hence,
20/10 = 8/r
r = 4
Volume of conical cup
v= 1/3πr²h
dv/dt=1/3πr² dh/dt
0.5 = 1/3π × (4)² dh/dt
dh/dt =3 /32π
Therefore the rate is 3 /32π.
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Create a division problem where both the divisor and the dividend are decimals. the quotient must be a whole number greater than 1. step by step please!
The Divisor is 1.5 , the Dividend is 4.5 and the quotient is 3.
As per the question we need to create a division problem where both the divisor and the dividend are decimals and the quotient must be a whole number greater than 1.
So, Let us suppose divisor as 1.5 . Now the dividend must be a decimal number which is greater than 1.5, let's say 5.5.
Now on dividing 5.5 by 1.5,
Divisor = 1.5
Dividend = 4.5
(Dividend/Divisor) = ( 4.5 / 1.5 ) = 3
Quotient = 3
On dividing dividend by divisor the quotient is 3 which is a whole number greater than 1.
So, we can conclude that the Divisor is 1.5 , the Dividend is 4.5 and the quotient is 3.
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Find the discriminant of
The discriminant of the quadratic equation is 11.1.
What is the discriminant?The discriminant is the expression that we could use to deduce the kind of roots that a quadratic equation would have. Note that when we say the roots of the equation, we are talking about the solutions of the quadratic equation. We shall now try to obtain the discriminant of this equation as we can see below.
The discriminant is given as;
√b^2 - 4ac
Given;
3x^2 - 10x + 2 = 0
a = 3
b = -10
c = 2
We have;
√(-10)^2 - 4(-3) (2)
√100 + 24
11.1
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Find the distance between each pair of points
The distance between each pair of points (-1,4) and (1,-1) exists √29 units after utilizing the distance formula.
What is meant by distance formula?It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.
The distance formula can be given as:
[tex]$\mathrm{d}=\sqrt{\left(\mathrm{x}_2-\mathrm{x}_1\right)^2+\left(\mathrm{y}_2-\mathrm{y}_1\right)^2}[/tex]
It is given that:
The distance between each pair of points (-1,4) and (1,-1)
Two points are (-1,4) and (1,-1)
To estimate the distance between the above two points utilize the distance formula:
[tex]$\mathrm{d}=\sqrt{(1-(-1))^2+(-1-4)^2}$$[/tex]
[tex]$\mathrm{d}=\sqrt{(1+1)^2+(-1-4)^2}$$[/tex]
The arithmetic operation can be described as the operation in which we do the addition of numbers, subtraction, multiplication, and division
d = √[(2)² + (-5)²]
simplifying the above equation, we get
d = √(4 + 25)
d = √29 units
Therefore, the distance between each pair of points (-1,4) and (1,-1) exists √29 units after utilizing the distance formula.
The complete question is:
Find the distance between each pair of points (-1,4) and (1,-1)
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The quadratic function − 0.379 ( x − 46 ) 2 + 2.62 ( x − 46 ) − 3.61 gives the percentage (in decimal form) of puffin eggs that hatch during a breeding season in terms of x , the mean sea surface temperature of the surrounding area, in degrees Fahrenheit.
a
.
What is percentage of puffin eggs that will hatch at
51°F? Round your answer to the nearest tenth of a percent.
b
.
For what mean temperature is the percentage of hatched puffin eggs a maximum? Round your answer to the nearest tenth of a degree.
°F
Find the percentage of hatched eggs at this temperature. Round your answer to the nearest tenth of a percent.
The percentage of puffin eggs that hatch given in decimal form by the quadratic function, f(x) = -0.379•(x - 46)² + 2.62•(x - 46) - 3.61, gives;
a. At 51 °F, 1.5% of the eggs will hatch
b. The temperature at which the maximum percentage of puffin eggs will hatch is approximately 49.5 °F
The maximum percentage of eggs that hatch is approximately 91.8 %
What is a quadratic function?A quadratic function is a polynomial of the second degree (degree 2) such that the highest power of the variables in a quadratic function is 2
The quadratic function is presented as follows;
f(x) = -0.379•(x - 46)² + 2.62•(x - 46) - 3.61
Where;
f(x) = The percentage of the eggs that hatch
x = The mean sea surface temperature of the area in degrees Fahrenheit
a. The percentage of the eggs that will hatch at 51° is therefore;
f(51) = -0.379•(51 - 46)² + 2.62•(51 - 46) - 3.61 = 0.015
The percentage of the eggs that hatch at 51° d is f(51) = 0.015 × 100% = 1.5%
b. The temperature for which the percentage of hatched puffin eggs is a maximum, is given by the maximum value of the quadratic function as follows;
At the maximum value of the quadratic function, f(x) = a•x² + b•x + c, we have;
x = -b/(2•a)
Therefore, where we have;
f(x) = -0.379•(x - 46)² + 2.62•(x - 46) - 3.61
At the maximum value;
x - 46 = -2.62/(2×(-0.379)) = 1310/379
x = 46 + 1310/379 ≈ 49.5°Which gives;
The mean temperature at which the percentage of hatched puffin eggs is a maximum is approximately 49.5°Second part;
The percentage of eggs that hatch at the temperature that gives the maximum percentage of eggs is the maximum percentage of eggs, which is found as follows;
f(46 + 1310/379) = -0.379•(1310/379)² + 2.62•(1310/379) - 3.61 ≈ 0.9179683
The maximum percentage of puffin eggs is therefore;
f(46 + 1310/379) ≈ 0.9179683 × 100 ≈ 91.8%Learn more about quadratic functions here:
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5. Find the distance from the point (0, -3) to the line y = x - 1.
Distance from point (0, -3) to the line y = x - 1 = [tex]\sqrt{2}[/tex]
Given:
Point =(0,-3) => x = 0; y = -3
Line = y = x - 1 => a= 1, b= -1, c=-1
How is the distance from the point to the line calculated?
Let us consider the distance to be d,
[tex]d= \frac{ax+by+c}{\sqrt {a^{2}+b^{2}} } \\\\=\frac{1(0)-1(-3)-1}{\sqrt{2} } \\\\=\frac{2}{\sqrt{2} } = \sqrt{2}[/tex]
What is the distance from a point to a line?
The distance between a point and a line in Euclidean geometry is the shortest path between any two points on an infinite straight line. The length of the line segment connecting the point to the closest point on the line, measured perpendicularly to the line, is the distance between them.If the variances of the dependent and independent variables are equal, then Deming regression, a form of linear curve fitting, produces orthogonal regression, in which each data point's degree of fit error is expressed as the angle of the point from the regression line.To learn more about distance from a point to a line, refer:
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water is leaking from an inverted conical tank at a rate of . water is also being pumped into the tank at a constant rate. the tank has height and the diameter at the top is . if the water level is rising at a rate of when the height of the water is , find the rate at which water is being pumped into the tank. hint: let denote the rate (in ) at which the tank is being filled, and let denote the volume (in ) of water in the tank. then rate in - rate out , so it suffic
The rate of the water being pumped into the tank is 289,753 cm3/min
d = 4m
∴ r = 2m
h = 6m
Therefore r = h/3
The formula for the volume of the cone is:
V=(1/3)π•r2h
substitute:
V=(1/3)π (h/3)2h
V=(1/27)π h3
Derive both sides with respect to time:
dV/dt = (1/9) π h2• dh/dt
When h= 2 meters = 200 cm when dh/dt = 20
dV/dt = (1/9) π (200)2• (20)
dV/dt = (800,000/9) π ~ 279,252.68
Meaning the volume of water is increasing at a rate of 279,252.68 cm3/min.
However, it's leaking out at a rate of 10,500 cm3/min. Therefore the rate of the water being pumped into the tank is:
279,252.68 + 10,500 = 289,752.68 ~ 289,753 cm3/min
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Can someone help me pleaseeeeee
Answer:
a) 225 meters
b) -162°C
Step-by-step explanation:
a) 5 meters per second for 45 seconds. 5*45 = 225 meters
b) cooled by 18°C per hour over a 9 hour period. -18*9 = -162°C
Answer:
a) 225 meters.
B) -2 °
Step-by-step explanation:
a If it is moving 5 meters per second, then in one second it moves 5 meters, in 2 seconds it move 10 meters, in 3 seconds it move 15 minters.
So to find how much it moved in 454 seconds we would multiply 45 x 5 = 225
B) In 9 hours it cooled 18 degrees 18/9 = 2. This means that is cooled 2 degrees per hour.
Anyone know the answer for this
NEED HELP ASAP. GETS BRAINIEST GET A 100 POINTS
Is the Fibonacci sequence arithmetic, geometric, or neither? Explain how you know.
Look at quotients . What do you notice about this sequence of numbers?
The 15th through 19th Fibonacci numbers are 610, 987, 1597, 2584, 4181. What do you notice about the quotients ?
Answer:
there are different kind of sequence number and just multiply the fractions.
Step-by-step explanation:
multiply fractions aND you will get the answer.
An architect
makes a model
of a new house
with a patio
made with
pavers. In
the model, each
paver in the
1
patio is in.
4
1
long and in.
6
wide. The actual
2
9
ft
1
The constant of proportionality is
(Type the ratio as a simplified fraction.)
3
ft
a. What is the constant of proportionality that relates the length of
a paver in the model and the actual length? Write an equation that
represents this relationship.
Answer - The constant proportionality constant of proportionality between the actual dimensions of the pavers and the model is 9. The proportionality constant for the area is 81.
Step-by-step explanation: To solve this problem, let's transform all quantities to the same units (inches)
The actual dimensions of the pavers are:
Then we divide the real dimensions between those of the model:
Width:
Long =
Then, the constant of proportionality between the actual dimensions of the pavers and the model is 9.
Actual length = model length * (9)
The "A" area of a paver is the product of its width multiplied by its length.
So:
(real width) * (real length) = ((9) Model width) * ((9) model length)
(real width) * (real length) = * (Model width) * (model length)
(real area) = 81 * (Model area)
The proportionality constant for the area is 81.
Three times the middle integer of three consecutive integers equals four less than twice the sum of the smallest and largest. find the integers
Integers are 3, 4 and 5.
What are integers?Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The boldface Z is a common mathematical symbol for the set of integers. An integer is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043.
Given Data
Let the three consecutive integers are :
x, x+1 and x+2
According to question
3(x+1) = 4 - 2(x+x+2)
3x + 3 = 4 - 2(2x + 2)
3x + 3 = 4 - 4x - 4
3 = 4x-3x
x= 3
Integers are 3, 4 and 5.
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a. write a rule for the congruence mapping that will move a figure 5 units to the right and 3 units up. b. write a rule for congruence mapping that reflects a figure across the y-axis.c. why are these mappings called congruence mappings?
Given:
Two different congruency mapping
To find:
a) a rule for the congruence mapping that will move a figure 5 units to the right and 3 units up
b) a rule for congruence mapping that reflects a figure across the y-axis
[tex]\begin{gathered} a)\text{ Translation rule to the right:} \\ f(x\text{ -d\rparen: \lparen x, y\rparen }\rightarrow\text{ \lparen x+d, y\rparen} \\ Translation\text{ rule up:} \\ f(x)\text{ + b: \lparen x, y\rparen }\rightarrow\text{ \lparen x, y + b\rparen} \\ \\ 5\text{ units to the right and 3 units up:} \\ (x,\text{ y\rparen }\rightarrow\text{ \lparen x + 5, y + 3\rparen} \end{gathered}[/tex][tex]\begin{gathered} b)\text{ reflection across the y-axis} \\ The\text{ x coordinate will be negated while the x coordinate will remain constant} \\ (x,\text{ y\rparen }\rightarrow\text{ \lparen-x, y\rparen} \end{gathered}[/tex][tex]\begin{gathered} c)\text{ The mappings are called congruence mapping because the shapes and size remain the same } \\ \text{but the }position\text{ changes.} \\ As\text{ a result the corresponding angles and sides will be equal} \end{gathered}[/tex]If a space rover has a mass of 3900 kg, then what is its weight on Mars?
Answer:
Weight on Mars: 1,475.32 kg
Step-by-step explanation:
The formula is Weight on Mars= (Weight on Earth/9.81m/s2) * 3.711m/s2.
If a space rover has a mass of 3900 kg on Earth, the mass on Mars when it lands will be 3900kg.
What is Mass?Mass is a dimensionless quantity representing the amount of matter in a particle or object. The standard unit of mass in the International System (SI) is the kilogram.
Given,
The mass of a space rover is 3900 kg.
We need to check what is its mass in Mars.
The mass of space rover in Mars will also be same 3900 kg because the mars is same quantity it wont change according to place or time, it remains constant. Where as weight would be changed.
The mass of the object is always constant, anywhere it is on the Earth or Moon or any other planet.
Hence, If a space rover has a mass of 3900 kg on Earth, the mass on Mars when it lands will be 3900kg.
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What is an equation of the line through (0, -3) with slope of 2/5
Answer:
y = [tex]\frac{2}{5}[/tex] x - 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = [tex]\frac{2}{5}[/tex] and line crosses the y- axis at (0, - 3 ) ⇒ c = - 3
y = [tex]\frac{2}{5}[/tex] x - 3 ← equation of line
How is a line segment different from a line? How is a line segment different from a ray?
Answer:
ray:
Part of a line, containing one endpoint and extending to infinity in one direction.
line segment
Two points on a line, and all the points between those two points.
Step-by-step explanation:
HELP WITH MATH PLEASE
Answer: 5 and the power is 2
the power used is 2
Step-by-step explanation:
A bookshelf is 31 3/4 inches wide 28 inch wide, binders on the shelf side-by-side how many binders can Maria place on the shelf?
The number of binder on the bookshelf is one
How to determine the number binders on the shelf?The given parameters are:
Width of the bookshelf = 31 3/4 inches
Width of the binders = 28 inches
From the question, we understand that the binders are stacked side by side
This means that the quotient of the width of the bookshelf and the width of the binder will give the number of binders
So, we have
Number of binders = Width of the bookshelf/Width of the binders
This gives
Number of binders = (31 3/4)/28
Evaluate the quotient
Number of binders = 1.13
Approximate
Number of binders = 1
Hence, there is only one binder on the bookshelf
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Liz had 140 pens and inna had 100 pens. after inna gave some of her pens to liz,liz had 3 times the amount of pens that inna had. how many pens did inna give
Answer:
40
Step-by-step explanation:
140 + x = 3*(100-x)
140 + x = 300 - 3x
x + 3x = 300 - 140
4x = 160.
x = 40.
solve for x
pls hurry
Answer:
12
Step-by-step explanation:
Answer:
x = 19
Step-by-step explanation:
Alternate Exterior Angles Theorem
When a transversal line intersects two parallel lines, the resulting alternate exterior angles are congruent.
Therefore:
⇒ 8x + 11 = 5x + 68
⇒ 8x + 11 - 5x = 5x + 68 - 5x
⇒ 3x + 11 = 68
⇒ 3x + 11 - 11 = 68 - 11
⇒ 3x = 57
⇒ 3x ÷ 3 = 57 ÷ 3
⇒ x = 19
(6.4 × 103) ÷ (3.2 × 102)
Express your answer in scientific notation.
The required solution in scientific notation is 2 × 10¹ .
Scientific notation can be used to indicate values that are either too large or too little to be conveniently written in decimal form (typically would result in a long string of digits).
In the UK, it is also known as standard form, scientific form, and standard index form.Because it can simplify numerous mathematical operations, this base ten notation is frequently used by scientists, mathematicians, and engineers.Scientific notation for non-zero numbers takes the form m × 10n, or m times ten raised to the power of n, where n is an integer and m is a non-zero real number.The given expression is (6.4 × 10³) ÷ (3.2 × 10²)
Simplifying we get :
(6.4 × 10³) ÷ (3.2 × 10²) = 20
This can be written in the scientific notation as : 2 × 10¹
Therefore the required solution is 2 × 10¹
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Does (-7,-7) make the equation y=x true
Answer: Yes it does.
Step-by-step explanation:
Which is equivalent to
Answer:
[tex]\frac{2y^5}{x^6}[/tex]
you have chosen the correct answer
Which multiplication problem can be used to determine how many possible combinations there are for a lock consisting of 3 digits from 0–9, if the digits can be repeated?
___________________
900
___________________
Enter the values needed to find thelength CB. (Simplify your answer.)A(-3a, b)IFB(3a, b)ECB = V(4a)2 + ([?])2C(-a, -5b)Distance Formula: d = (x2 – xı)2 + (y2 - yı)2
We are asked to find the values needed for the length CB
The coordinates of points C and B are given as
C(-a, -5b)
Recall that the distance formula is given by
[tex]d=\sqrt{\left( {x_2 - x_1 } \right)^2 + \left( {y_2 - y_1 } \right)^2 }[/tex]For the given case,
[tex]\begin{gathered} (x_1,y_1)=\mleft(-a,-5b\mright) \\ (x_2,y_2)=\mleft(3a,b\mright) \end{gathered}[/tex]Let us substitute these coordinates into the above distance formula
[tex]\begin{gathered} CB=\sqrt[]{({x_2-x_1})^2+({y_2-y_1})^2} \\ CB=\sqrt[]{({3a_{}-(-a)})^2+({b_{}-(-5b)_{}})^2} \\ CB=\sqrt[]{({3a_{}+a})^2+({b_{}+5b})^2} \\ CB=\sqrt[]{({4a})^2+({6b})^2} \end{gathered}[/tex]Therefore, the required values are
[tex]CB=\sqrt[]{({4a})^2+({6b})^2}[/tex]Simplify. (a²b) ³.(b²c²)
Answer:
(a²b)³(b²c²)=a⁶b⁵c²
Given: A = [ 1 -1 -2 3] B = [ 1 5 8 -8 ] C = [ 1 2 3 4 ]
Solve: AX + B = C
Given in the question the matrix
A = [ 1 -1 B = [ 1 5 C = [ 1 2
-2 3 ] 8 -8 ] 3 4]
after solving AX + B = C, we get the value of x
x = [ 1 -21/5
-1 8/5] ..........(ii)
Given A = [ 1 -1 B = [ 1 5 C = [ 1 2
-2 3 ] 8 -8 ] 3 4]
find x, if AX + B = C
AX + B = C
AX = C -B = [ 1 2 [ 1 5
-
3 4] 8 -8 ]
AX = [ 1-1 2-5 = [ 0 -3
3-8 4+8 ] -5 12]
X = A -1 [ 0 -3
-5 12] .........(i)
A = [1 1 |A| = {3*1 - 1 *(-2)}
-2 3] = 5
A-1 = [tex]\frac{adj A}{|A|}[/tex]
Adj A = [cofactor A]^1 = [ [tex]a_{11}[/tex] = 3 [tex]a_{12}[/tex] = 2
[tex]a_{21}[/tex] = -1 [tex]a_{22}[/tex] = 1 ] ^1
adj A = [ 3 -1 A -1 = 1/5 [ 3 -1
2 1] 2 1]
x = 1/5 [3 -1 [ 0 -3
2 1] -5 12]
= 1/5 [ 5 -21 = [ 1 -21/5
-5 8] -1 8/5] ..........(ii)
Hence, required solution of the given matrix is equation (ii)
Therefore, Given the matrix A = [ 1 -1 B = [ 1 5 C = [ 1 2
-2 3 ] 8 -8 ] 3 4]
after solving AX + B = C, we get the value of x
x = [ 1 -21/5
-1 8/5] ..........(ii)
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An airline company wants to provide service to San Francisco, Los Angeles, Chicago, Dallas, Washington D.C., and New York City. The company's president draws lines between each pair of cities in the list on a map. No three of the cities are collinear How many lines did the president draw?
The president draw 15 lines on map.
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
here, it is given that :
there are 6 cities
No three of the cities are collinear that is are not in a straight line.
Now, to find the lines did the president draw use the formulae :
n(n-1)/2
where, n = number of cities
lines did the president draw = 6 x 5/ 2
= 15
Therefore, The president draw 15 lines on map.
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I need the answer asapplease and thank you!!!
In mathematics, a line's slope, also known as its gradient, is numerical representation of line's steepness and direction. The equation will be [tex]y= \frac{-1}{3}x +5[/tex].
What is a slope?In mathematics, a line's slope, also known as its gradient, is numerical representation of line's steepness and direction. The letter m is the frequently used to represent slope; the reason for this usage is unclear, although it can be found in O'Brien's (1844) and Todhunter's (1888) formulations of the equation for the straight line as "[tex]y = mx + b[/tex]" and "[tex]y = mx + c[/tex]," respectively.
The ratio of "vertical change" to "horizontal change" between the (any) two unique points on a line is used to compute slope. The ratio can also be written as a quotient ("rise over run"), which produces the same number for every two distinct points on the same line. A declining line has a negative "rise." The line might be useful, as determined by a road surveyor, or it might appear in a diagram that represents a road or a roof as a description or design.
Let, x= -3, x1= -2, y= 5, y1= 2
Then,
slope= [tex]\frac{x-x1}{y-y1} = \frac{-3-(-2)}{5-2} =\frac{-1}{3}[/tex]
now,
y= mx+c
y= [tex]\frac{-1}{3}[/tex]x+ 5
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–3d = 5.7
ANSWER ASAP!!!!!!!!!!
Answer:
D = 1.9
You can find for d by using the associative property of division (divide instead of multiply):
5.7 divided -3 = 1.9
Step-by-step explanation:
Hope it helps! =D