The average rate of change of the number of miles with respect to the number of gallons is 14.5 miles per gallon
How to determine the average rate of change?The given parameters can be represented as:
M(0) = 30680
M(20) = 30970
The average rate of change is calculated as:
M'(t) = (M(20) - M(0))/(20 - 0)
This gives
M'(t) = (30970 - 30680)/(20 - 0)
M'(t) = 14.5
Hence, the average rate of change of the number of miles with respect to the number of gallons is 14.5 miles per gallon
The average rate of change of M as t changes from 8 to 16.
This is calculated using
M'(t) = (M(16) - M(8))/(16 - 8)
M'(t) = (20 - 10)/(16 - 8)
M'(t) = 1.25
The average rate of change of M as t changes from 16 to 24.
This is calculated using
M'(t) = (M(24) - M(16))/(24 - 16)
M'(t) = (25 - 20)/(24 - 16)
M'(t) = 0.625
The average rate of change of M as t changes from 24 to 32.
This is calculated using
M'(t) = (M(32) - M(24))/(32 - 24)
M'(t) = (25 - 25)/(32 - 24)
M'(t) = 0
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You deposit $4000 in an account earning 7% interest compounded continuously. How much will you have in the account in 10 years?
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$4000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years\dotfill &10 \end{cases} \\\\\\ A=4000e^{0.07\cdot 10}\implies A=4000e^{0.7}\implies A\approx 8055.01[/tex]
the graph f(x) is shown below. Which function could represent the graph of f(x)?
(1) f(x)=(x+2)(x^2+3x-4)
(2) f(x)=(x-2)(x^2+3x-4)
(3) f(x)=(x+2)(x^2+3x+4)
(4) f(x)=(x-2)(x^2+3x+4)
The function which represents the graph is f(x) = (x + 2)(x² + 3x - 4). Then the correct option is 1.
What is a function?A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.
The graph is given below.
The value of the function is zero for the values of x are -4, -2, and 1.
Let's check which function gets satisfied.
f(x) = (x + 2)(x² + 3x - 4)
The function can be written as
f(x) = (x + 2)(x + 4)(x - 1)
Then the values of x for which the value of the function is zero.
f(x) = 0
(x + 2)(x + 4)(x - 1) = 0
x = 1, -2, -4
Then the function will be f(x) = (x + 2)(x² + 3x - 4). Then the correct option is 1.
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1. In a sample of 800 students in BNHS, 160, or
20%, are Grade 7 students Based on the above
information, the school's paper reported that "20% of
all the students at BNHS are grade 7." This report is
an example ofIn a sample of 800 students in BNHS, 160, or
20%, are Grade 7 students Based on the above
information, the school's paper reported that "20% of
all the students at BNHS are grade 7." This report is
an example of
a. a sample
b. a population
c. statistical inference
d. descriptive statistics
19.. A statistics professor asked students in a class
their ages. On the basis of this information, the
professor states that the average age of all the
students in the university is 21 years. This is an
example of
a. a census
b. descriptive statistics
c. an experiment
d. statistical inference
20. A tabular summary of a set of data showing the
fraction of the total number of items in several classes
is a
a. frequency distribution
b. relative frequency distribution
c. frequency
d. cumulative frequency distribution
Answer:
1. c. statistical inference
19. d. statistical inference
20. b. relative frequency distribution
To which quadrants is tan^-1 x restricted?
A. Quadrants I and IV
B. Quadrants III and IV
C. Quadrants II and III
The quadrants is tan⁻¹x restricted is A. Quadrants I and IV
To answer the question, we need to know what tan⁻¹x is.
What is tan⁻¹x?tan⁻¹x is the inverse trigonometric function of tanx, which is the value of the angle for tanx.
Quadrant in which tan⁻¹x is restrictedTo find the quadrants in which tan⁻¹x is restricted, we know that tanx lies in the range
-∞ ≤ tanx ≤ +∞ for -90° ≤ x ≤ 90°.
Since the inverse function of tanx is x.tan⁻¹x lies between -90° and 90°. That is -90° ≤ tan⁻¹x ≤ 90°.Since 90° lies in first quadrant and -90° lies in the fourth quadranttan⁻¹x lies between quadrant I and IV
So, the quadrants is tan⁻¹x restricted is A. Quadrants I and IV
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If 2^2^x = 2^3 what is the value of x
Answer:
[tex]\dfrac 32[/tex]
Step-by-step explanation:
[tex]~~~~~~~2^{2x} = 2^3\\\\\implies \ln\left(2^{2x} \right) = \ln (2^3)\\\\\implies 2x \ln(2) = 3 \ln(2) \\\\\implies 2x = 3\\\\\implies x = \dfrac 32[/tex]
Answer:
B
Step-by-step explanation:
Find the perimeter. Area=5.612x10^14
9.2x10^7
Answer:
1.962×10^8 cm
Step-by-step explanation:
The area and perimeter formulas can be use to find the perimeter of this rectangle, given its area and the length of one side.
A = LW
P = 2(L +W)
__
Solving the area formula for width, we have ...
W = A/L
Using that in the perimeter formula, we find the perimeter to be ...
P = 2(L +W) = 2(L +A/L)
Using the given values for area and length, we find the perimeter is ...
P = 2(9.2×10^7 +5.612×10^14/(9.2×10^7)) = 1.962×10^8 . . . cm
The perimeter of the rectangle is 1.962×10^8 cm, or 1962 km.
_____
Additional comment
The width is 6.1×10^6 cm, or 0.61×10^7 cm. Then the sum of length and width is (9.2 +0.61)×10^7 = 9.81×10^7 cm. The perimeter is twice that, or 19.62×10^7 cm = 1.962×10^8 cm. 1 km = 10^5 cm, so this is 1.962×10^3 km, or 1962 km.
Your scientific calculator or spreadsheet can use and present numbers in scientific notation directly. The "E" notation is used in place of "×10^". (This notation is an artifact of the earliest computer languages.)
2 cups is equivalent to___ pint.
Answer:
1 pint is equal to 2 cups
Step-by-step explanation:
2 cups is equivalent to__1_ pint.
Hope This Helped
Answer:
answer is 1
Step-by-step explanation:
A major arc will have a measure that is
O A. greater than 180°
OB. less than 180°
O C. equal to 180°
Please help on the area for 7 8 9 please all i need help is
The area of the equilateral, isosceles and right angled triangle are 12.6mm², 9.61in² and 16.81yds² respectively.
What is the area of the equilateral, isosceles and right angle triangle?Note that:
The area of an Equilateral triangle is expressed as A = ((√3)/4)a²
Where a is the dimension of the side.
The area of an Isosceles triangle is expressed as A = (ah)/2
Where a is the dimension of the base and h is the height.
The area of a Right angled triangle is expressed as A = (ab)/2
Where a and b is the dimension of the two sides other than the hypotenuse.
For the Equilateral triangle.
Given that;
a = 5.4mmArea A = ?A = ((√3)/4)(5.4mm)²
A = ((√3)/4)( 29.16mm² )
A = 12.6mm²
Area of the Equilateral triangle is 12.6mm²
For the Isosceles triangle.
Given that;
Base a = 3.4inSlant height b = 5.9inheight h = ?Area A = ?The height h is the imaginary line drawn upward from the center of a.
First, we calculate the height using Pythagorean theorem
x² = y² + z²
Where x = b = 5.9in, y = a/2 = 3.4in/2 = 1.7in, and z = h
(5.9in)² = (1.7in)² + h²
34.81in² = 2.89in² + h²
h² = 34.81in² - 2.89in²
h² = 31.92in²
h = √31.92in²
h = 5.65in
Now, the area will be;
A = (ah)/2
A = (3.4in × 5.65in )/2
A = 19.21in²/2
A = 9.61in²
Area of the Isosceles triangle is 9.61in².
For the Right angled triangle
Given that;
a = 8.2ydsb = 4.1ydsc = 9.17ydsArea A = ?A = (ab)/2
A = ( 8.2yds × 4.1yds)/2
A = ( 33.62yds²)/2
A = 16.81yds²
Area of the Right angled triangle is 16.81yds²
Therefore, the area of the equilateral, isosceles and right angled triangle are 12.6mm², 9.61in² and 16.81yds² respectively.
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1. In the figure given below, < ABC and < BDC are right angles; If AB-5cm, AD = 3cm and BD = 4cm (3 points) find BC and DC ?
In the given figure, the length of BC is 6.66 cm and the length of DC is 5.33 cm
TrigonometryFrom the question, we are to determine the length of BC and DC
Considering the diagram,
First, we will determine the measure of angle A
Using SOH CAH TOA
We can write that
[tex]sin A = \frac{4}{5}[/tex]
sin A = 0.8
∴ A = sin⁻¹(0.8)
A = 53.13°
Now, we will determine the measure of angle C
∠A + ∠ABC + ∠C = 180° (Sum of angles in a triangle)
53.13° + 90° + ∠C = 180°
∠C = 180° - 90° - 53.13°
∠C = 36.87°
Also,
Using SOH CAH TOA
[tex]tan C = \frac{BD}{DC}[/tex]
[tex]tan36.87 ^\circ=\frac{4}{DC}[/tex]
[tex]0.7500 = \frac{4}{DC}[/tex]
[tex]DC = \frac{4}{0.75}[/tex]
DC = 5.33 cm
By the Pythagorean theorem,
/BC/² = /BD/² + /DC/²
/BC/² = 4² + 5.33²
/BC/² = 16 + 28.4089
/BC/² = 44.4089
/BC/ = √44.4089
/BC/ = 6.66 cm
Hence, the length of BC is 6.66 cm and the length of DC is 5.33 cm
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Leah's family took a road trip to Mount Rushmore. Leah fell asleep 44% of the way through the trip. If Leah fell asleep after they had travelled 132 miles, what was the total length of the trip?
The total length of the trip 190.08 miles
How you do it is to add the 44% of 132 to 132
= (132 + (132×44%))
What is the length?Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived.
First, you have to find out how much 44% is. Change it into decimal form (0.44) and then multiply the two together.
132 × 0.44 is 58.08 miles.
Then you add that to the rest of the trip, 132 miles.
= (132 + 58/08
=190.08
The total length of the trip was 190.08 miles.
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Diberi 1 ½s = ⅗t² + ⅓u², hitung (ii) nilai t apabila u = -6 dan s = 28
Answer:
√2' = t
Step-by-step explanation:
1 1/2s = 3/5t^2 + 1/3u^2; substitute known values
1 1/2 • 28 = 3/5 • t^2 + 1/3 • -6^2; simplify
42 = 3 • t^2 ÷ 5 + 1/3 • 36
42 = 3 • t^2 ÷ 5 + 12; apply property of subtraction of equality
42 – 12 = 3t^2 ÷ 5 + 12 – 12; simplify
30 = 3t^2 ÷ 5; apply property of multiplication of equality
30 • 5 = 3t^2 ÷ 5 • 5; simplify
6 = 3t^2; apply property of division of equality
6 ÷ 3 = 3t^2 ÷ 3; simplify
2 = t^2
√2' = t
An account earns annual simple interest. Find the balance of
the account.
$250 at 4% for 1 year
HELP FAST
The balance of the account which earns annual simple interest of $250 at 4% for 1 year is $260
How to find simple interest?Principal, P = $250Interest rate, r = 4%Time, t = 1 yearSimple interest = principal × rate × time
= 250 × 4% × 1
= 250 × 0.04 × 1
= $10
Balance = Principal + Simple interest
= $250 + $10
= $260
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Which equation shows an example of the associative property of addition?
Answer:
(2+3)+4 = 2+(3+4) this is an example of associative property
Considering the results from part a, it follows that the volume of a cylinder can be found in the same way as the volume of a rectangular prism. use your results and what you know about volume to explain how to find the volume of a cylinder with a base radius of r units and a height of h units.
To find the volume of a cylinder we must perform a mathematical operation that is expressed in the following formula V = Π h r².
How to find the volume of a cylinder?To find the volume of a cylinder we must solve the following mathematical formula:
V = Πhr²let's do an exampleOur example cylinder is 10 centimeters high and 6 centimeters in diameter. What is its volume?
To find the volume we substitute the values as follows:
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use a number line to find the product.
5 x (-5)
a. -25
b. 25
c. 10
d. 0
Answer: a. -25
Step-by-step explanation:
1. Multiply the numbers
5x(−5)
Solution
−25x
There is 1/2 of a pizza left for 4 friends to share. What fraction of a pizza will each friend get to eat?
Answer:
12.5% is the answer.
Step-by-step explanation:
Faelyn grouped the terms and factored the GCF out of the groups of the polynomial 6x4 – 8x2 + 3x2 + 4. Her work is shown.
Step 1: (6x4 – 8x2) + (3x2 + 4)
Step 2: 2x2(3x2 – 4) + 1(3x2 + 4)
Faelyn noticed that she does not have a common factor. Which accurately describes what Faelyn should do next?
Faelyn should realize that her work shows that the polynomial is prime.
Faelyn should go back and regroup the terms in Step 1 as (6x4 + 3x2) – (8x2 + 4).
In Step 2, Faelyn should factor only 2x out of the first expression.
Faelyn should factor out a negative from one of the groups so the binomials will be the same.
An accurately describes what Faelyn should do next is option B. Faelyn should realize that her work shows that the polynomial is prime.
What are prime polynomials?Those polynomials with integer coefficients that cannot be factored further, with factors of lower degree and integer coefficients are called a prime polynomials.
The polynomial 6x⁴ – 8x² + 3x² + 4 needs to be factored and the steps are:
Step 1: (6x⁴ – 8x²) + (3x² + 4)
Step 2: 2x²(3x² – 4) + 1(3x² + 4)
Since they do not have any common factor.
Faelyn should realize that her work indicates that the polynomial is prime.
Prime polynomials have integer coefficients.
An accurately describes what Faelyn should do next is option B. Faelyn should realize that her work shows that the polynomial is prime.
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Jane had $5.00, then spent $2.00. How much does she have now?
Answer:
$3.00
Step-by-step explanation:
$5.00 = 5
$2.00 = 2
5
-2
_
3
3 = $3.00
Answer:
$3.00
Step-by-step explanation:
■ Write an equivalent expression.
1 (12x+
(12x + 6x − 21) =
?
x
3
?
Answer:
6x - 7
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] (12x + 6x - 21 ) ← multiply each term in the parenthesis by [tex]\frac{1}{3}[/tex]
= 4x + 2x - 7 ← collect like terms
= 6x - 7
Hey there!
ORIGINAL EQUATION:
1/3(12x + 6x - 21)
COMBINE the LIKE TERMS
= 1/3(18x - 21)
DISTRIBUTE 1/3 WITHIN the PARENTHESES:
= 1/3(18x) + 1/3(-21)
SIMPLIFY:
= 6x - 7
Therefore, the answer should be:
6x - 7
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
A jar contains five blue marbles, six red marbles, and four green marbles. What are the odds you will draw a blue marble from this jar?
Answer:
Probability=number of specific outcomes/total of all possible outcomes
There are 5 blue marbles and a total of 15 marbles.
So the probability of drawing a blue marble from the jar is:
5/15
1/3
Step-by-step explanation:
Hope this helps
A jar has 9 pennies.
3 nickels, 8 dimes, and
5 quarters. A coin is chosen
at random, not replaced
then another is chosen.
Find the probability that
a quarter was chosen
followed by a penny,
Answer:
the answer to this question is 3/40
Step-by-step explanation:
if you want my explanation you ca
Sketch a graph of each of the four angles in the same coordinate plane. Label the ordered pairs that intersect the circle. The angles given are 30°, 150°, 210°, 330°
When two straight lines or rays intersect at a shared endpoint, an angle is generated.
What is an angle?When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."
The angle can be drawn as shown below. The angle 30°, 150°, 210°, and 330° will lie in 1st, 2nd, 3rd, and 4th quadrants respectively.
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In the expression 67.8046 8.264 - 243.5, all of the numbers are measured quantities and have the same units. Evaluate this expression to the correct number of significant figures.
The result of evaluating 67.8046 + 8.264 - 243.5 is -167.431
How to evaluate the expression?The expression is given as:
67.8046 + 8.264 - 243.5
The highest number of significant figures in the expression is 6 (i.e. 67.8046)
This means that the result must be in 6 significant figures.
Next, we evaluate the expression as follows:
67.8046 + 8.264 - 243.5 = -167.4314
Approximate to 6 significant figures.
67.8046 + 8.264 - 243.5 = -167.431
Hence, the result of evaluating 67.8046 + 8.264 - 243.5 is -167.431
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what is this expression in simplified form?
Answer:
33.17 (A)
Step-by-step explanation:
the square root of 22 times (5x the square root of 2)
is 33.17 rounded to the nearest 10th
and 10 x the square root of 11 is 33.17
(they match)
please helb it is very hadr
Answer:
a=15.7mm2,31.4
b=18.84in2,37.68
Work out the circumference of this circle.
Give your answer in terms of pi and state its units
Answer:
14π cm
Step-by-step explanation:
Circumference of a circle given the diameter is :
πd
We simply substitute the value given in the image into our formula to find our answer:
πd = π×14 = 14π
Units will be cm as circumference is a length
This is our final answer as the question states to leave it in pi form .
Hope this helped and brainliest please
Answer:
14π cm
Step-by-step explanation:
Circumference of a circle with radius r = 2πr or 2rπ
The diameter d is twice the radius so circumference = dπ
Here d= 14 so the answer is 14π cm
Which one is the right answer
Answer:
The answer is C. Quadrant 3.
Step-by-step explanation:
Looking up a Unit Circle. We can see that 5pi/4 is in quadrant 3.
5pi/4 is also if in degree angle as 225°
These graphs depict the price and output levels of apples under perfect competition and monopoly market structures. what is the extra amount that mary would pay for apples under a monopoly instead of a perfect competition? a. $2 b. $3 c. $4 d. $5 e. $6
The extra amount that Mary would pay for apples under a monopoly instead of perfect competition is B. $3
Calculations and Parameters:From the complete information,
There are images of the prices that can be gotten under a monopoly and the ones that can be gotten in a perfect competition by Mary.
The marginal cost which is graphed against the pound of apples and the price shows Mary would pay $15 and the marginal revenue shows that Mary would pay $12.
Hence, the difference between them, which is the extra amount to be paid would be $15-$12
=$3
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Answer:
B. 3$
Hope this helps!
Step-by-step explanation:
Find the equation of the line in slope-intercept form containing the two points: (−1,5) and )(4,−3) Leave equation in fractional form.
Answer:
y = 1.6x + 3.4
Step-by-step explanation:
We have to use the equation y = m x + c to find the equation of the line.
Here,
m ⇒ slope
c ⇒ y-intercept
First, let us find the slope.
For that, we can use the given two coordinates.
( -1 , 5 ) ⇒ ( x₁ , y₁ )
( 4 , -3 ) ⇒ ( x₂ , y₂ )
The formula to find the slope of a line is :
m = ( y₁ - y₂ ) ÷ ( x₁ - x₂ )
Let us solve now.
m = ( y₁ - y₂ ) ÷ ( x₁ - x₂ )
m = ( 5 - ( -3 ) ) ÷ ( -1 - 4 )
m = ( 5 + 3 ) ÷ -5
m = 8 ÷ -5
m = -1.6
Now let us find the y-intercept (c ) of the line.
For that, let us get one of the coordinates which are given in the question.
I'll get ( -1 , 5 ) from that.
( -1 , 5 ) ⇒ ( x , y )
Let us solve now.
y = mx + c
5 = -1.6 × -1 + c
5 = 1.6 + c
5 - 1.6 = c
3.4 = c
Therefore,
m ⇒ -1.6
c ⇒ 3.4
So, the equation of the line is :
y = mx + c
y = 1.6x + 3.4