A freight train is carrying goods across the country. The distance it has traveled varies directly with the number of gallons of fuel it has used. See the graph below.
Answers
Answer:
Step-by-step explanation:
The train uses
[tex]\frac{400gallons}{200miles}[/tex]
If you reduce that you get that the train uses
[tex]\frac{2gallons}{1mile}[/tex]
To find the slope of the line, we will use the 2 points on the coordinate plane where the graph goes through: (0, 0) and (400, 200)
Applying the slope formula:
[tex]m=\frac{200-0}{400-0}=\frac{1}{2}[/tex]
Answer:
6 miles per gallon
slope = 6
Step-by-step explanation:
Related Questions
Find the distance between the points (1, 5) and (1, -4).
Answers
Answer:
9
Step-by-step explanation:
[tex]\tt distance=\sqrt{(1-1)^2+(-4-5)^2}=\sqrt{0^2+9^{2}}=\sqrt{9^2} =9[/tex]
The formula for distance between two points is:
[tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} -y_{1})^{2}}[/tex]
In this case:
[tex]x_{2} =1\\x_{1} =1\\y_{2} =-4\\y_{1} =5[/tex]
^^^Plug these numbers into the formula for distance like so...
[tex]\sqrt{(1-1)^{2} + (-4-5)^{2}}[/tex]
To solve this you must use the rules of PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction)
First we have parentheses. Remember that when solving you must go from left to right
[tex]\sqrt{(1-1)^{2} + (-4-5)^{2}}[/tex]
1 - 1 = 0
[tex]\sqrt{(0)^{2} + (-4-5)^{2}}[/tex]
-4 - 5 = -9
[tex]\sqrt{(0)^{2} + (-9)^{2}}[/tex]
Next solve the exponent. Again, you must do this from left to right
[tex]\sqrt{(0)^{2} + (-9)^{2}}[/tex]
0² = 0
[tex]\sqrt{0 + (-9)^{2}}[/tex]
(-9)² = 81
[tex]\sqrt{(0 + 81)}[/tex]
Now for the addition
[tex]\sqrt{(0 + 81)}[/tex]
81 + 0 = 81
√81
^^^This can be further simplified to...
9
***Remember that the above answers are in terms of units
Hope this helped!
~Just a girl in love with Shawn Mendes
PLEASE HELP ME WITH-THIS MATH QUESTION
Answers
Answer:
146 degrees
Step-by-step explanation:
The measure of the arc is the measure of the central angle that the arc is created from.
The central angle has a measure of 146 degrees so that is the measure of the arc there.
HELPP PPLEASEEE!!!
A ship moves through the water at 30 miles/hour at an angle of 30° south of east. The water is moving 5 miles/hour at an angle of 20° east of north. Identify the ship's vector, the water current's vector, and the vector representing the ship's actual motion.
Answers
Answer:
See below in bold.
Step-by-step explanation:
Ship's vector:
Horizontal component = 30 cos 30 = 25.98.
Vertical component = 30 sin(-30) = -15.
So it is <25.98, -15).
The current's vector:
Horizontal component = 5 sin 20 = 1.71.
Vertical component = 5 cos 20 = 4.7.
So it is <1.71, 4.7>.
The ship's vector representing its actual motion is 30.73 mph east of north.
Explanation:To solve this problem, we can break down the velocities of the ship and the water current into their horizontal and vertical components. The ship's vector can be represented as:
Ship's Vector: 30 mph at an angle of 30° south of east
Breaking this down into horizontal and vertical components:
Horizontal Component = 30 mph * cos(30°) = 25.98 mph east
Vertical Component = 30 mph * sin(30°) = 15 mph south
The water current's vector can be represented as:
Water Current's Vector: 5 mph at an angle of 20° east of north
Breaking this down into horizontal and vertical components:
Horizontal Component = 5 mph * cos(20°) = 4.75 mph north
Vertical Component = 5 mph * sin(20°) = 1.71 mph east
To find the ship's actual motion, we can add the horizontal and vertical components together:
Horizontal Component = 25.98 mph east + 4.75 mph north = 30.73 mph east of north
Vertical Component = 15 mph south + 1.71 mph east = 16.71 mph south of east
Therefore, the ship's vector representing its actual motion is 30.73 mph east of north.
A study conducted at a certain college shows that 72% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that 5 randomly selected graduates all find jobs in their chosen field within a year of graduating.
Answers
Answer:
19.3%
Step-by-step explanation:
Assuming the events are independent, the probability of all five is ...
0.72^5 ≈ 0.19349 ≈ 19.3%
Answer: 19.3%
Step-by-step explanation:
If we randomly select 5 students, we know that each of them has a probability of 72% of finding a job in that year (or 0.72 in decimal form)
The joint probability in where the 5 of them have found a job, is equal to the product of the 5 probabilities:
P = 0.72*0.72*0.72*0.72*0.72 = 0.72^5 = 0.193
Where because all the students are in the same result, the number of permutations is only one.
If we want the percentage form, we must multiplicate it by 100%, and we have that P = 19.3%
Write an equation that could be used to find the value of a.
Answers
Answer:
see below
Step-by-step explanation:
The Law of Cosines tells you ...
a² = b² + c² -2bc·cos(A)
Substituting the given values gives you ...
a² = 4² +7² -2(4)(7)cos(52°)
Cathy lives in a state where speeders fined $ 10 for each mile per hour over the s speed limit cathy was given a fine for $80for speeding on a road where the speed limit is 50 miles per hour how fast was cathy driving
Answers
Answer:
58 miles per hour
Step-by-step explanation:
First you need to divide 80 by 10 to see how many miles she was over the speed limit.
80/10 = 8 miles over the speed limit.
The speed limit was 50, so 50 + 8 = 58 miles.
So Cathy was driving at 58 miles per hour
Answer:
58mph
Step-by-step explanation:
Given:
Each mph over the speed limit gets fined $10
or mathematically, rate of fine = $10/mph
also, total fine was $80.
Number of mph over the speed limit,
= total fine ÷ rate of fine
= $80 ÷ $10/mph
= 8 mph.
Given that the speed limit was 50 mph, Cathy's final speed,
= speed limit + number of mph over speed limit
= 50 + 8
= 58 mph
On a set of blueprints for a new home, the contractor has established a scale of 0.5in : 10 ft. What are the dimensions on the blueprints of a bedroom that will be 18 feet by 16 feet.
Answers
Answer:
The dimensions on the blueprints are 0.9 inches and 0.8 inches
Step-by-step explanation:
* Lets explain the relation between the drawing dimensions and
the real dimensions
- A scale drawing make a real object with accurate sizes reduced
or enlarged by a certain amount called the scale
- Ex: If the scale drawing is 1 : 10, so anything drawn with the size of
1 have a size of 10 in the real so a measurement of 15 cm on the
drawing will be 150 cm on the real
- In a scale drawing, all dimensions have been reduced by the same
proportion
* Lets solve the problem
- On a set of blueprints for a new home, the contractor has
established a scale of 0.5 in : 10 ft
∵ The drawing scale ratio must be in same unit
∴ Change the feet to inch
∵ 1 foot = 12 inches
∴ 10 feet = 10 × 12 = 120 inches
∴ The scale is 0.5 inches : 120 inches
- Simplify the scale by multiply it by 2
∴ The scale is 1 in : 240 in
- Lets find the dimensions on the blueprints
∵ The real dimensions are 18 feet and 16 feet
- Change the feet to inches
∴ 18 feet = 18 × 12 = 216 inches
∵ 16 feet = 16 × 12 = 192 inches
∵ The scale is 1 : 240
∴ 1/240 = x/216 ⇒ use cross multiplication
∴ 240 x = 216 divide both sides by 240
∴ x = 0.9 inch
∵ The scale is 1 : 240
∴ 1/240 = y/192 ⇒ use cross multiplication
∴ 240 y = 192 divide both sides by 240
∴ y = 0.8 inch
* The dimensions on the blueprints are 0.9 inches and 0.8 inches
PLS HELP ME !
The angle of depression of a point P on the ground, from the top T of the building is 23.6 degrees . If the distance from P to the foot of the building is 50m, calculate the height of the building, correct to the nearest meter.
Answers
Final answer:
To find the height of the building, we use the tangent function with the angle of depression and the horizontal distance from the point to the building's base, resulting in a building height of 22 meters when rounded to the nearest meter.
Explanation:
To calculate the height of the building when the angle of depression from the top of the building to a point P on the ground is 23.6 degrees and the distance from P to the foot of the building is 50 meters, we can use trigonometry.
Specifically, we use the tangent function which relates the angle of a right triangle to the ratio of the opposite side (height of the building in this case) over the adjacent side (distance from P to the foot of the building).
Let's denote the height of the building as H. Thus, we have:
tan(23.6°) = H / 50
From this, we can solve for H:
H = 50 × tan(23.6°)
Using a calculator, tan(23.6°) approximately equals 0.4364.Therefore, H = 50 × 0.4364 which equals 21.82 meters.Rounding to the nearest meter, the height of the building is 22 meters.
A widget company produces 25 widgets a day, 5 of which are defective. Find the probability of selecting 5 widgets from the 25 produced where none are defective.
Answers
Final answer:
To find the probability of selecting 5 non-defective widgets from 25 produced, we consider the independent probabilities of selecting a non-defective widget for each selection and multiply them together.Therefore, the probability of selecting 5 widgets where none are defective is 1024/3125 or approximately 0.327.
Explanation:
To find the probability of selecting 5 widgets where none are defective, we need to consider the probability of selecting a non-defective widget for each of the 5 selections.
The probability of selecting a non-defective widget from the 25 produced is (25-5)/25 = 20/25 = 4/5.
Since the selections are independent, we can multiply the probabilities. So the probability of selecting 5 non-defective widgets is (4/5)⁵ = 1024/3125.
Therefore, the probability of selecting 5 widgets where none are defective is 1024/3125 or approximately 0.327.
In order to estimate the mean amount of time computer users spend on the internet each month, how many computer users must be surveyed in order to be 90% confident that your sample mean is within 13 minutes of the population mean? Assume that the standard deviation of the population of monthly time spent on the internet is 228 min
Answers
Answer:
832
Step-by-step explanation:
standard deviation =228 minute
error =13 minute given
confidence level =905% =0.90
α=1-0.90=0.1
[tex]z_\frac{\alpha }{2}=z_\frac{0.1}{2}=1.645[/tex]
we know that sample size should be greater than
[tex]n\geq \left ( z_\frac{\alpha }{2}\times \frac{\sigma }{E} \right )^2[/tex]
[tex]n\geq \left ( 1.645\times \frac{228}{13} \right )^{2}[/tex]
[tex]n\geq 28.850^2[/tex]
[tex]n\geq 832.3668[/tex]
n=832
Solve the problem.
The library is to be given 3 books as a gift. The books will be selected from a list of 16 titles. If each book selected must have a different title, how many possible selections are there?
48
560
3360
4096
Answers
Answer:
560Step-by-step explanation:
You must use a combination:
[tex]_nC_k=\dfrac{n!}{k!(n-k)!}[/tex]
We have n = 16, k = 3.
Substitute:
[tex]_{16}C_3=\dfrac{16!}{3!(16-3)!}=\dfrac{13!\cdot14\cdot15\cdot16}{2\cdot3\cdot13!}\qquad\text{cancel}\ 13!\\\\=\dfrac{14\cdot15\cdot16}{2\cdot3}=\dfrac{7\cdot5\cdot16}{1}=560[/tex]
The number of possible selections is 560.
Given information:The library is to be given 3 books as a gift. The books will be selected from a list of 16 titles.
Calculation of number of selections;Here we used the combination
[tex]= nC_n\\\\= 16C_3\\\\= \frac{16!}{3!(16-3)!}\\\\ = \frac{16!}{3!13!}\\\\ = \frac{16\times 15\times 14\times 13!}{13!3!}\\\\ = \frac{16\times 15\times 14}{3\times 2\times 1}\\[/tex]
= 560
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What is 70% of 40,000.
Answers
Answer:
x = 28,000
Step-by-step explanation:
"What" is our unknown, x; "is" is an equals sign; 70% expressed as a decimal is .70; "of" means to muliply.
Our equation, then, is
x = .70(40,000) so
x = 28,000
Answer:
28000
Step-by-step explanation:
70% of 40,000 is 28000.
28,000/40,000 = 70%
40000=100%
x=70%
40000/x=100%/70%
Using the value found in the previous question, find the measure of angle R and the measure of angle Q.
Answers
Answer:
∠R = 36.06°, ∠Q = 90.81°
Step-by-step explanation:
I used the Law of Cosines to find angle R first. If you use the Law of Sines, the main angle is the same, but it differs in the decimal value. Since you started the process with the Law of Cosines, I used it again. Setting up to find angle R:
[tex]36^2=48^2+60^2-2(48)(60)cosR[/tex] and
1296 = 2304 + 3600 - 5760cosR so
-4608 = -5700cosR and
.8084210526 = cosR
Taking the inverse cosine to find the angle,
R = 36.06
That means that Q = 180 - 36.06 - 53.13 so
Q = 90.81
Three consecutive multiples of 7 have a sum of 84. What is the greatest these numbering?
A. 7
B. 21
C. 35
D. 42
Answers
Answer:
C. 35
Step-by-step explanation:
Let x represent the largest of the multiples of 7. The sum will be ...
x + (x -7) + (x -14) = 84
3x = 105 . . . . . . . . . . . . . add 21 and simplify
x = 35 . . . . . . . . . . . . . . . divide by 3
The greatest of the numbers of interest is 35.
_____
Two consecutive multiples of 7 will differ by 7. If x is the largest, the next-largest is x-7, and the one before that is x-14.
Water pressure increases 0.44 pounds per square inch (0.44 psi) with each increase of one foot in depth below sea level. Identify the independent and dependent quantity in the situation.
Answers
Answer:
Depth below sea level is the independent quantity,
Water pressure is the dependent quantity
Step-by-step explanation:
An independent quantity is a variable that can be changed in an experiment. While, dependent quantity results from the independent quantity or we can say, that depends upon the independent quantity.
Here,
The water pressure increases 0.44 pounds per square inch (0.44 psi) with each increase of one foot in depth below sea level,
So, for measuring the water pressure we took depth below sea level as a variable,
⇒ Depth below sea level is the independent quantity,
While, with increasing depth by 1 foot the pressure is also increase by 0.44 pounds per square inches ⇒ pressure depends upon the depth
⇒ Water pressure is the dependent quantity.
Answer:The best answer I think is depth, water pressure
Step-by-step explanation:
Starting at home Jessica traveled uphill to the toy store for 12 minutes at just 10 mph. She then traveled back home along the same path downhill at a speed of 30 mph. What is her average speed for the entire trip from home to the toy store and back?
Answers
Answer:
15 miles per hour
Step-by-step explanation:
Average Speed is:
Average Speed = Total Distance/Total Time
Going uphill, she took 12 minuets, that is hours is 12/60 = 0.2 hours
We know D = RT, Distance = Rate(speed) * Time
Thus,
D = 10mph * 0.2 hr = 2 miles
So, total distance (uphill and downhill) = 2 + 2 = 4 miles
Downhill the time she took is
D = RT
2miles = 30mph * T
T = 2/30 = 1/15 hours = 1/15 * 60 = 4 minutes
Hence total time is 12 + 4 = 16 minutes
Note: 16 minutes = 16/60 = 4/15 hours
Now
Average Speed = Total Distance/Total Time
Average Speed = 4 miles/ 4/15 hours = 15 mph
Answer:
The Answer is 15.00000000000000000... miles per hour
Step-by-step explanation: You do tis by doing your work and not checking for answers
Which of the following inequalities has a solution set that when graphed on the number line, is a single segment of finite length? A. x4 ≥ 1 B. x3 ≤ 27 C. x2 ≥ 16 D. 2≤ |x| ≤ 5 E. 2 ≤ 3x+4 ≤ 6
Answers
Answer:
Step-by-step explanation:
E
Answer:
B
Step-by-step explanation:
Edge
Find the value of z such that "0.9544" of the area lies between −z and z. round your answer to two decimal places.
Answers
Answer:
z = 2.00
Step-by-step explanation:
This is a number many statistics students memorize.
95.44% of the distribution lies within 2 standard deviations of the mean.
Answer:
z = 2.00
Step-by-step explanation:
The value of z such that "0.9544" of the area lies between −z and z rounded to two decimal places is z = 2.00.
Directions: Answer the questions below. Make sure to show your work and justify all your answers.
15. The city bike rental program is analyzing their growth in member rates. The number of regular members is growing by
4.7% per month. The number of VIP members is growing by 65% per year. Write a function to represent the number of
regular members after t years. Then, write an equivalent function that represents the regular members with only 1
compounding per year. What is the effective yearly rate of growth of regular members? Determine the effective rate of
growth per year for regular members. Which type of member is growing at a faster rate?
a What is the effective YEARLY rate of the growth for regular members?
b. Which type of member is growing at a faster rate?
Answers
Answer:
a) 73.52%
b) Regular membership is growing faster
Step-by-step explanation:
a) r(t) = r0·1.047^(12t) . . . . regular members after t years, where r0 is the initial value of regular members at t=0.
Equivalently, this is ...
r(t) = r0·(1.047^12)^t ≈ r0·1.7352^t
This shows the effective annual growth rate for regular members is 73.52%.
__
b) The 74% yearly growth rate of regular members is higher than the 65% yearly growth rate of VIP members. Regular membership is growing faster.
Write and equation that represents the distance traveled by a person who can bike at a rate of 8 miles per hour. Can someone help me with this?
Answers
Answer:
d = 8t
Step-by-step explanation:
A lot of math is about matching patterns. Here, the pattern you can match is given in the problem statement:
d = 6t . . . . . equation for distance traveled at 6 miles per hour
You are asked to write an equation for distance traveled at 8 miles per hour. You can see the number 6 in the above equation matches the "miles per hour" of the traveler. This should give you a clue that when the "miles per hour" changes from 6 to 8, the number in the equation will do likewise.
The equation you want is ...
d = 8t . . . . . equation for distance traveled at 8 miles per hour
The distance traveled by a person biking at 8 miles per hour is represented by the equation d = 8t, where d is the distance, and t is the time in hours. For example, if they bike for 2 hours, they will have traveled 16 miles.
Explanation:The question is about calculating the distance traveled by a person who can bike at a rate of 8 miles per hour. This can be represented by the equation d = rt, where d is the distance, r is the rate, and t is the time.
In this case, the rate (r) is 8 miles per hour. Therefore, the equation becomes: d = 8t, meaning the distance travelled is equal to 8 times the amount of time spent biking.
For example, if the person bikes for 2 hours, we would substitute 2 for t in the equation, which would look like this: d = 8 * 2. The resulting distance (d) is 16 miles.
Learn more about Distance Calculation here:https://brainly.com/question/34212393
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If the length of a diagonal of a square is "a", what is the length of its side?
Answers
[tex]b[/tex] - the side of a square
[tex]a=b\sqrt2\\b=\dfrac{a}{\sqrt2}\\\\b=\dfrac{a\sqrt2}{2}[/tex]
Answer:
a√2 / 2.
Step-by-step explanation:
Using the Pythagoras Theorem;
a^2 = s^2 + s^2 where s is the length of each side of the square.
2s^2 = a^2
s^2 = a^2 / 2
s = √(a^2 / 2)
= a / √2
= a√2 / 2 .
Subtract the second equation from the first.
6x+5y=16
(6x+2y=10)
-
------------------------
A. 12x = 26
B. 3y = 6
C. –12x = 6
D. 7y = 26
Answers
Answer:
B. 3y = 6
Step-by-step explanation:
(6x +5y) -(6x +2y) = (16) -(10)
6x +5y -6x -2y = 6 . . . eliminate parentheses
(6-6)x +(5-2)y = 6 . . . . add like terms
3y = 6 . . . . . . . . . . . simplify
Cate solved an inequality to find c, the possible number of cats that a shelter can house. She found that c < 28. Which statement best describes a possible solution to Cate's problem?
Answers
Since the number of cats has to be less than 28, a statement could be "the shelter can house no more than 28 cats.
Answer:
Possible values of c are
[tex]c=0,1,2,3,4,...,26,27[/tex]
For example: The shelter can house 17 cats because 17 < 28.
Step-by-step explanation:
Let c be the number of cats.
The given inequality is
[tex]c<28[/tex]
We need to find the possible number of cats that a shelter can house.
The number number of cats can not be
1. A fraction value
2. A Decimal value
3. A negative value
Since c<28, therefore the number of cats must be greater that or equal to 0 and less that 28.
[tex]0\leq c<28[/tex]
The possible values of c are
[tex]c=0,1,2,3,4,...,26,27[/tex]
For example: The shelter can house 17 cats because 17 < 28.
last one anyone that can help me out?
Answers
Answer:
Part a. t = 7.29 years.
Part b. t = 27.73 years.
Part c. p = $3894.00
Step-by-step explanation:
The formula for continuous compounding is: A = p*e^(rt); where A is the amount after compounding, p is the principle, e is the mathematical constant (2.718281), r is the rate of interest, and t is the time in years.
Part a. It is given that p = $2000, r = 2.5%, and A = $2400. In this part, t is unknown. Therefore: 2400 = 2000*e^(2.5t). This implies 1.2 = e^(0.025t). Taking natural logarithm on both sides yields ln(1.2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(1.2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(1.2)/0.025. This means that t = 7.29 years (rounded to the nearest 2 decimal places)!!!
Part b. It is given that p = $2000, r = 2.5%, and A = $4000. In this part, t is unknown. Therefore: 4000 = 2000*e^(2.5t). This implies 2 = e^(0.025t). Taking natural logarithm on both sides yields ln(2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(2)/0.025. This means that t = 27.73 years (rounded to the nearest 2 decimal places)!!!
Part c. It is given that A = $5000, r = 2.5%, and t = 10 years. In this part, p is unknown. Therefore 5000 = p*e^(0.025*10). This implies 5000 = p*e^(0.25). Making p the subject gives p = 5000/e^0.25. This means that p = $3894.00(rounded to the nearest 2 decimal places)!!!
Find the derivative of f(x) = 12x^2 + 8x at x = 9.
Answers
Answer:
224
Step-by-step explanation:
We will need the following rules for derivative:
[tex](f+g)'=f'+g'[/tex] Sum rule.
[tex](cf)'=cf'[/tex] Constant multiple rule.
[tex](x^n)'=nx^{n-1}[/tex] Power rule.
[tex](x)'=1[/tex] Slope of y=x is 1.
[tex]f(x)=12x^2+8x[/tex]
[tex]f'(x)=(12x^2+8x)'[/tex]
[tex]f'(x)=(12x^2)'+(8x)'[/tex] by sum rule.
[tex]f'(x)=12(x^2)+8(x)'[/tex] by constant multiple rule.
[tex]f'(x)=12(2x)+8(1)[/tex] by power rule.
[tex]f'(x)=24x+8[/tex]
Now we need to find the derivative function evaluated at x=9.
[tex]f'(9)=24(9)+8[/tex]
[tex]f'(9)=216+8[/tex]
[tex]f'(9)=224[/tex]
In case you wanted to use the formal definition of derivative:
[tex]f'(x)=\lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}[/tex]
Or the formal definition evaluated at x=a:
[tex]f'(a)=\lim_{h \rightarrow 0} \frac{f(a+h)-f(a)}{h}[/tex]
Let's use that a=9.
[tex]f'(9)=\lim_{h \rightarrow 0} \frac{f(9+h)-f(9)}{h}[/tex]
We need to find f(9+h) and f(9):
[tex]f(9+h)=12(9+h)^2+8(9+h)[/tex]
[tex]f(9+h)=12(9+h)(9+h)+72+8h[/tex]
[tex]f(9+h)=12(81+18h+h^2)+72+8h[/tex]
(used foil or the formula (x+a)(x+a)=x^2+2ax+a^2)
[tex]f(9+h)=972+216h+12h^2+72+8h[/tex]
Combine like terms:
[tex]f(9+h)=1044+224h+12h^2[/tex]
[tex]f(9)=12(9)^2+8(9)[/tex]
[tex]f(9)=12(81)+72[/tex]
[tex]f(9)=972+72[/tex]
[tex]f(9)=1044[/tex]
Ok now back to our definition:
[tex]f'(9)=\lim_{h \rightarrow 0} \frac{f(9+h)-f(9)}{h}[/tex]
[tex]f'(9)=\lim_{h \rightarrow 0} \frac{1044+224h+12h^2-1044}{h}[/tex]
Simplify by doing 1044-1044:
[tex]f'(9)=\lim_{h \rightarrow 0} \frac{224h+12h^2}{h}[/tex]
Each term has a factor of h so divide top and bottom by h:
[tex]f'(9)=\lim_{h \rightarrow 0} \frac{224+12h}{1}[/tex]
[tex]f'(9)=\lim_{h \rightarrow 0}(224+12h)[/tex]
[tex]f'(9)=224+12(0)[/tex]
[tex]f'(9)=224+0[/tex]
[tex]f'(9)=224[/tex]
Five consecutive multiples of 3 yield a sum that is equal to the product of 7 and 15. What are these multiples?
Answers
Answer:
15, 18, 21, 24, 27
Step-by-step explanation:
Five multiples of 3 means we have 5 terms we are adding together to = 105.
For the sake of having something to base each one of these terms on, let's say that the first term is 3. It's not, but 3 is a multiple of 3 and we have to start somewhere. These terms go up by the next number that is divisible by 3. After 3, the next number that is divisible by 3 is 6. The next one is 9, the next is 12, the last would be 15.
Let's then say that 3 is the first term, and we are going to say that is x.
To get from 3 to 6, we add 3. Therefore, the second term is x + 3.
To get from 3 to 9, we add 6. Therefore, the third term is x + 6.
To get from 3 to 12, we add 9. Therefore, the fourth term is x + 9.
To get from 3 to 15, the last term, we add 12. Therefore, the last term is x + 12.
The sum of these terms will then be set to equal 105:
x + (x + 3) + ( x + 6) + ( x + 9) + ( x + 12) = 105
We don't need the parenthesis to simplify so we add like terms to get
5x + 30 = 105. Subtract 30 from both sides to get
5x = 75 so
x = 15
That means that 15 is the first multiple of 3.
The next one is found by adding 3 to the first: so 18
The next one is found by adding 6 to the first: so 21
The next one is found by adding 9 to the first: so 24
The last one is found by adding 12 to the first: so 27
15 + 18 + 21 + 24 + 27 = 105
Notice that all the numbers are, in fact, consecutive multiples of 3 as the instructions stated.
The five consecutive multiples of 3 that sum up to 105 are 15, 18, 21, 24, and 27.
Explanation:The question posed is regarding five consecutive multiples of 3. The sum of these multiples equals 7x15 (or 105). Let's call the first multiple of 3 as '3x'. Therefore, the five consecutive multiples can be represented as 3x, 3x+3, 3x+6, 3x+9, 3x+12.
The sum of the five consecutive multiples then is 15x + 30 (comprising 5 times 'x', plus 30 from the sum of 3, 6, 9, and 12). We know that this sum equals 105, so we can set up the following equation:
15x + 30 = 105.
Solving this equation for 'x' gives:
x = 5. This means the first multiple is 3x, or 3x5 = 15. The next multiples are therefore 15+3 (18), 18+3 (21), 21+3 (24) and 24+3 (27).
So, the five multiples of 3 that yield a sum of 105 are 15, 18, 21, 24, and 27.
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Please help me with this question!
Answers
Answer:
h=2×6/8
x^2=h^2+4
x=5/2
An inlet pipe on a swimming pool can be used to fill the pool in 40 hours. The drain pipe can be used to empty the pool in 42 hours. If the pool is 23 filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?
Answers
Answer:
Pool will be filled in 280 hours
Step-by-step explanation:
Inlet pipe fills in 40 hours = 1 pool
Inlet pipe fills in 1 hours = [tex]\frac{1}{40}[/tex]
Drain pipe empty in 42 hours = 1 pool
Drain pipe empty in 1 hour = [tex]\frac{1}{42}[/tex]
If both pipes are opened together
then in pool fills in 1 hour = [tex]\frac{1}{40}[/tex] - [tex]\frac{1}{42}[/tex]
on simplifying the right side ,we get [tex]\frac{42-40}{(40)(42)}[/tex]
= [tex]\frac{2}{(40)(42)}[/tex]
= [tex]\frac{1}{840}[/tex]
[tex]\frac{1}{840}[/tex] pool fills in 1 hour
1 pool will be filled in 840 hours
[tex]\frac{2}{3}[/tex] pool is filled
empty pool = 1 - [tex]\frac{2}{3}[/tex] = [tex]\frac{1}{3}[/tex]
therfore [tex]\frac{1}{3}[/tex] pool will be filled in [tex]\frac{1}{3}[/tex]X 840 =
= 280 hours
The calculations indicate that 280 hours is the time required to fill 2/3 of the pool with both pipes open.
Inlet Pipe Rate:
The inlet pipe can fill the pool in 40 hours.
Therefore, the rate of the inlet pipe is 1/40 pool per hour.
Drain Pipe Rate:
The drain pipe can empty the pool in 42 hours.
Therefore, the rate of the drain pipe is 1/42 pool per hour.
Combined Rate when both pipes are open:
The net rate when both pipes are open is the difference between their individual rates:
Net rate = (1/40) - (1/42)
Simplify the Net Rate:
Find a common denominator for 40 and 42, which is 840:
Net rate = (42 - 40) / 840 = 2/840 = 1/420
Time to Fill 2/3 of the Pool:
Set up the equation: Net rate * Time = 2/3
Substitute the net rate: (1/420) * Time = 2/3
Cross-multiply to solve for time: Time = (2/3) * (420/1) = 280
Therefore, it takes 280 hours to fill 2/3 of the pool when both the inlet and drain pipes are open.
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Leo has b boxes of pencils. Each box contains 6 pencils. He has a total of 42 pencils. The equation that represents this situation is . The value of b that makes the equation true is .
Answers
The equation for this scenario is 6b= 42.
B= 42/6= 7
The value of b that makes the equation true is 7.
Hope this helps!
Answer:
6b = 42
b = 7 for the equation to be true.
Step-by-step explanation:
If Leo has b boxes of pencils with each containing 6 pencils, it means that the total number of pencils Leo has is dependent on the number of boxes given that the number in each box is known.
The product of the number of boxes with the number in each box gives the total number of pencils Leo has. This may be expressed mathematically as
= b × 6
= 6b
Given that Leo has 42 pencils, it means that
6b = 42
Dividing both sides by 6,
b = 42/6 = 7
It means he has 7 boxes.
Write an equation in standard form for each parabola.
Answers
Answer:
[tex]x=1/4(y-2)^{2}-1[/tex]
Step-by-step explanation:
Use Vertex form: [tex]x=a(y-k)^{2}+h[/tex]
Given: vertek (h, k)=(-1, 2)
[tex]x=a(y-2)^2 -1[/tex]
A point:(x , y) = (3, 6)
[tex]3 = a (6-2)^{2} -1[/tex]
16a=4, a=1/4
The equation is : [tex]x=1/4(y-2)^{2}-1[/tex]