Step-by-step explanation:
=6a^3+7a^2-5a^3-9a^2-a
=a^3-2a^2-a this is the final answer.
Which is the BEST estimate of the average rate of change for the function graphed, over the interval 1 ≤ x ≤ 3?
A) 2
B) 3
C) 4
D) 6
The BEST estimate of the average rate of change for the function graphed, over the interval 1 ≤ x ≤ 3 is 2 so option A is correct.
Given:
1 ≤ x ≤ 3
we know x is between 1 and 3 so the best estimate is 2 even though the answer could also be 3 but that will be skewed.
1 ≤ 2 ≤ 3 is the best estimate.
Therefore the BEST estimate of the average rate of change for the function graphed, over the interval 1 ≤ x ≤ 3 is 2 so option A is correct.
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Pete's appliance received a bill dated July 15 for $26,000 with terms of 2/10, 1/15, n/60. On July 27 Pete sent in a partial payment of $6,000. What is the amount credited as well as the balance due?
The amount that would be credited, given the partial payments and the terms, would be $6, 060.61. The balance due would be $19, 939.39.
How to find the balance due?The terms 2/10 and 1/15 mean that if the buyer pays their bill in 10 days, they get a 2% discount. If they pay in 15 days, they get a 1% discount.
Pete paid on the:
= 27 - 15
= 12 days
This means that the 1 % discount would apply on the $6, 000. The credited amount would be:
= 6, 000 / (1 - 1%)
= $6, 060.61
The balance due would be:
= 26, 000 - 6, 060.61.
= $19,939.39
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To go to the theater you would pay $8.00 for each ticket you purchase. Which answer choice correctly represents the algebraic expression for the cost of t tickets?
A. 8t
B. 8 + t
C. 8 – t
D.
The algebraic expression that correctly represents the cost of t tickets is 8t , the correct option is (a) .
In the question ,
it is given that
the cost of 1 ticket for the theater is = $8.00
let the number of ticket be = t
so , the cost for t tickets = (cost of 1 ticket ) × ( number of tickets )
Substituting the values of number of tickets and cost of 1 ticket ,
we get ,
cost for t tickets = 8 × t
= 8t
Therefore , The algebraic expression that correctly represents the cost of t tickets is 8t .
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tan(tan^-1x)=x where?
Tan of arc tan x is equal to x when the angle x is 0 degrees
What is tan as used in math?Tangent is the ratio of the side opposite the angle we know or want to know over the side adjacent to that angle, and is sometimes abbreviated as tan.
In a right angle triangle, the formula for tan is as below
Tangent (tan) = opposite / adjacent
Arc tan (tan^(-1)) is the inverse of tan = adjacent / opposite
Arc tan is equal to tan when the angel is zero degree
therefore, tan (tan^(-1) x) = x
when x = 0
tan^(-1) 0 = 0
tan 0 = 0
tan (tan^(-1) 0)
tan (0)
0
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complete question
At what point does tan(tan^-1(x))=x
can somone help me with this will mark u brainliest
Answer:
686 cm^2
Step-by-step explanation:
First find the sides
7f = 49
4f = 28
To find a triangle area (right triangle), multiply each side like a rectangle, but divide it by two.
(49*28)/2 = 686
Answer:
67
Step-by-step explanation:
For the equation (x) = –3x2 + 2x – 1, explain if the graph will be pointing upward or downward. **20 POINTS**
Answer:
Step-by-step explanation:
the answer is "downward". If you say "why", it is because of the degree coefficient.
in the equation, the latest degree is 2 (which is quadratic equation) so from the degree its coefficient is -3. If it is negative, it should be downward like -3. But if it is positive it should be upward like 3, 1, 44.
Simplfy and solve 13+7x66
In chapters 5-8 of Frankenstein, Victor feels, for the first time in a long time, a sense of joy and calm. What causes these feelings
A. A visit from his father
B. A letter from Elizabeth
C. The arrival of Henry Clerval
D. An award for creating the monster
Answer:
C______________4_⁴________
The horsepower (hp) that a shaft can safely transmit varies jointly with its speed (in revolutions per minute (rpm))
and the cube of the diameter. If the shaft of a certain material 2 inches in diamter can transmit 16 hp at 120 rpm,
what must the diameter be in order to transmit 30 hp at 150 rpm?
The Diameter of the cube would be 3 inches
What is Variation?
A variation is a relationship that exists between a set of values for one variable and a set of values for other variables.
Solution:
We know that,
Horse Power is directly proportional to RPM * Diameter
So, we can write
Horse Power = k * RPM * Diameter
here, k is any constant
From the first case given, we can find the value of k
16 = k * 2 * 120
k = 1/15
Putting the value of k in second case,
30 = 1/15 * 150 * Diameter
Diameter = 3 inches
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Solve using substitution.
x = –3
–3x − y = 2
Answer:
y=7
Step-by-step explanation:
-3(-3)-y=2
9-y=2
9-2=y
y=7
Please mark as brainliest
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Which lists the distances between towns in order from greatest to least?
(picture of problem below)
Answer:
Step-by-step explanation:
the side opposite to greater angle is greater.
72>60>48
AB>AC>BC
A=Afton
B=Badeton
C=Capeton
Determine the period.
2 y
-2
1
10
Answer:
8
Step-by-step explanation:
You want the period of a sinusoidal function that has a graph with peaks at x=1 and x=9.
PeriodThe period is the difference between x-values where the function repeats itself. Typically, we can determine the period from corresponding recognizable features of the graph.
Here, the graph has peaks at x=1 and x=9. The period is the difference between these x-values:
period = 9 - 1 = 8
The period of the function is 8 units.
__
Additional comment
In more formal terms, the period p of a function is the smallest value of p such that f(x -p) = f(p).
NO LINKS!! Explain the process of constructing a 95% confidence interval to test a null hypothesis and what a 95% confidence interval represents. (Use either proportions or means).
At 95% confidence, the z critical value is roughly z = 1.96
You would use a reference table or calculator to determine this value. Unfortunately it's not something that can be easily/quickly found by hand.
If we're trying to estimate the population mean (mu), then we'll use this margin of error formula
E = z*sigma/sqrt(n)
Or if we want to estimate the population proportion (p), then we use this formula
E = z*sqrt(phat*(1-phat)/n)
The confidence interval then spans from (pointEstimate)-E to (pointEstimate)+E. Where "pointEstimate" represents either xbar or phat depending on the context. Other point estimates are possible. We're focusing on these two for now.
xbar estimates mu
phat estimates p
--------------------------------
An example problem:
A manager at a soda bottling plant wants to know if the contents of the cans are 20 fluid ounces (fl oz) or not. Through past observations, the manager has noted the population standard deviation (sigma) is 1.72 fl oz.
The manager gathers a random sample of 50 cans to test their contents. They find the sample mean is 18 fl oz. Conduct a hypothesis test using a confidence interval at 95% confidence to see if the cans really do have 20 fl oz of drink in them or not.
--------------------------------
Solution:
Null Hypothesis: mu = 20
Alternate Hypothesis: mu ≠ 20
This is a two-tailed test.
E = margin of error
E = z*sigma/sqrt(n)
E = 1.96*1.72/sqrt(50)
E = 0.47676
L = lower boundary of confidence interval
L = xbar - E
L = 18 - 0.47676
L = 17.52324
L = 17.52
U = upper boundary of confidence interval
U = xbar + E
U = 18 + 0.47676
U = 18.47676
U = 18.48
The 95% confidence interval is approximately (17.52, 18.48)
This is equivalent to writing 17.52 < mu < 18.48 in which we are 95% confidence in saying mu is between those endpoints.
But wait, the hypothesized mu = 20 is not in the interval 17.52 < mu < 18.48, which indicates we must reject the null hypothesis and accept the alternate hypothesis.
The soda cans do not have 20 fl oz of drink. It appears they have slightly less than 20 fl oz.
A teacher covered the exterior of a rectangular prism-shaped box that measured 8 inches by 9 inches by 10 inches using one sheet of rectangular-shaped wrapping paper that measured 2 feet by 3 feet. There were no gaps or overlapping paper. How many square inches of wrapping paper were left over?
The area of left over wrapping paper is 380 square inches
How to determine the amount left?The given dimensions are:
Box = 8 inches by 9 inches by 10 inchesWrapping paper = 2 feet by 3 feet.The surface area of the box is calculated as
Surface area = 2(lw + lh + wh)
This gives
Box = 2 * (8 * 9 + 8 * 10 + 9 * 10) = 484 square inches
The surface area of the wrapping paper is calculated as
Wrapper = lw
This gives
Wrapper = 2 * 3 = 6 square feet
Express the area in square inches
Wrapper = 864 square inches
The area left is the difference between the areas calculated above
i.e. Amount left = Wrapper - Box
So, we have
Amount left = 864 square inches - 484 square inches
= 380 square inches
Hence, the amount left is 380 square inches
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8. Calculate the probability of getting red queen & probability of getting black card from a well suffled deck.
Answer:
Step-by-step explanation:
there are fifty two cards in a deck, of which 26 are black and 26 are red, in addition there are 4 queens, including two of each color.
so:
P(getting red queen) = 2/52
P(getting black card) = 26/52
If X = 32 yards, Y = 60 yards, and Z = 68 yards, what is the sine of ZA?
The sin(x) = 0.88 and sin(y) = 32/68=0.47 in the Trigonometric Functions
What is Trigonometric Functions?
Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.
The given triangle is a right-angled triangle
As Z² = X²+Y²
So sin (x) = 60/68=0.88
and sin(y) = 32/68=0.47
Hence the sin(x) = 0.88 and sin(y) = 32/68=0.47.
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Notebook paper is about 0.003 in. thick.
If you cut a sheet of paper in half, stack one piece on top of the other, cut those in half, stack all the pieces together, repeating this process 20 times, how high will the stack of paper be?
The height of the stack of paper is 3145.73 in.
How to find how high the stack of paper be?Since the Notebook paper is about 0.003 in. thick, and you cut a sheet of paper in half, stack one piece on top of the other, cut those in half, stack all the pieces together, repeating this process 20 times.
Since each piece of paper is halved, that means that the number of paper sheets doubles every time.
So, after halving n times, we would have 2 sheets of paper. Since the thickness of the Notebookpaper is 0.003 in, then the height after cuttin half n times is h = 2ⁿ × 0.003 in.
Since the paper is folded 20 times, n = 20.
So, the height h = 2ⁿ × 0.003 in.
h = 2²⁰ × 0.003 in.
h = 1048576 × 0.003 in.
h = 3145.728 in
h ≅ 3145.73 in
So, the height of the stack of paper is 3145.73 in.
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The temperature went from 13o C at 3PM to -5o C at midnight that evening.
Which statement best describes the rate of change of the temperature
during this period of time?
The rate of change of the temperature on the time interval is -2°C. This means that, in average, for each hour that passes the temperature decreases by 2 degrees Celcius.
What is the rate of change on the temperature?A rate of change is defined as the quotient between the difference in some measure (in this case it will be the difference between the final temperature and the initial temperature) and the time interval in which it happens.
Here we know that:
final temperature = -5°C
Initial temperature = 13°C
And this change goes from 3 P.M. to midnight, so the change happens on an interval of 9 hours.
Then the rate of change of the temperature is:
r = (-5°C - 13°C)/9h = -2°C/h
So for each hour, the temperature decreases by 2°C.
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On April 1, 2022 the balance in inventory is 220 units at $50 each
April 5, 2022 purchased 100 units at $60 each
Purchased 50 units at $45 each on April 10, 2022
Sold 300 units at $80 each on April 16, 2022
Sold 20 units at $95 each on April 25, 2022
Purchased 200 units at $40 each on April 30, 2022
The calculation of the ending inventory and the cost of goods sold using FIFO and LIFO methods for ABC Inc. is as follows:
FIFO LIFO
Ending inventory $10,250 $12,800
Cost of goods sold $17,000 $14,450
How does FIFO differ from LIFO?FIFO (First-in, First-out) assumes that the physical flow of goods sold depends on the chronological order of acquisition.
LIFO (Last-in, First-out) assumes that the cost of goods sold should be based on the latest inventory purchases.
Date Description Units Unit Costs Total Cost
April 1 Beginning inventory 220 $50 $11,000
April 5 Purchases 100 $60 6,000
April 10 Purchases 50 $45 2,250
April 16 Sales -300 $80
April 25 Sales -20 $95
April 30 Purchases 200 $40 8,000
Total 570 $27,250
Units sold 320
Ending inventory 250
FIFO:
Ending Inventory = $10,250 (200 x $40 + 50 x $45)
Cost of goods sold = $17,000 ($27,250 - $10,250)
LIFO:
Ending Inventory = $12,800 (220 x $50 + 30 x $60)
Cost of goods sold = $14,450 ($27,250 - $12,800)
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Question Completion:Calculate Ending Inventory And COGS Using FIFO And LIFO Methods For ABC Inc.
AGES Pedro, Sebastian, and Manuel Martinez are each one year apart in age.
The sum of their ages is greater than the age of their father, who is 60.
a. Write an inequality to represent this situation, where x is the age of the youngest brother.
b. Solve the inequality.
c. How old can the oldest brother be? Explain your reasoning.
a) The inequality is
P + S + M > 60
b) The solution of the inequality is:
P > 19
Where P is Pedro's age.
c) The oldest brother has more than 21 years-
How to write the inequality?Let's define the variables:
p = Pedro's age.
S = Sebastian's ae
M = Manuel's age
We know that the sums of their ages is more than 60, then:
P + S + M > 60
This is the inequality.
b) We know that the brother are one year apart, then:
S = P + 1
M = P + 2
replacing that we get:
P + P + 1 + P + 2 > 60
3P + 3 > 60
3P > 60 - 3
3P > 57
P > 57/3 = 19
P > 19
So Pedro has more than 19
c) The oldest brother is 2 years older than Pedro, then:
M > 19 + 2
M > 21
Manuel is more than 21 years old.
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95 POINTS
2. Millicent's password for a website is a 5-digit number. The digits are the prime factors of 2,205 listed from least to greatest. What is Millicent's password?
33577
D 35577
B 33557
A 33357
Answer: 33577
Step-by-step explanation:
3x3x5x7x7 = 2205
Anyone can help on this one ?
Answer:
model a is more benfit the other one b/c of by hard working effort from b
The mean height of 12 men is 1.70 m, and the mean height of 8 women is 1.60 m. Find:the total height of the 12 men
Answer:
20.4 m
Step-by-step explanation:
mean is calculated as
mean = [tex]\frac{total}{count}[/tex]
given mean height of 12 men is 1.70 m , then
[tex]\frac{total}{12}[/tex] = 1.7 ( multiply both sides by 12 to clear the fraction )
total height = 12 × 1.7 = 20.4 m
What expression is equivalent to -6(t+9)
-6t -54 is the expression equivalent to-6(t+9)
How determine equivalent expressions?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s)
Given: -6(t+9)
First, clear the parenthesis by using -6 to multiply t and 9:
-6(t+9) = (-6 x t) + (-6 x 9)
= -6t + (-54)
= -6t -54
Therefore, the -6t -54 is equivalent to -6(t+9)
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Find the equation of the line tangent to the curve defined by f(x) = x^2+1 / square root x at the point (1,2). Show all your work.
Answer:
[tex]y=x+1[/tex]
Step-by-step explanation:
I am assuming that, given the nature of the curve, you know what a derivative is, and you know how to compute the derivative of the ratio of two functions.
[tex]f'(x) = \frac1{(\sqrt x)^2}[(2x+0)\sqrt x-(x^2+1)(\frac1{2\sqrt x})][/tex]
Could be rewritten in a nicer form? Probably, do we care? No, let's just evaluate it for [tex]x=1[/tex]:
[tex]f'(1)=\frac11 [(2)(1)-(1+1)\frac12]=1[2-1]=1[/tex]
We're almost done. We got the point, we have the slope, we can rewrite the tangent line as
[tex]y-y_0=f'(x_0)(x-x_0)\\y-2=1(x-1) \rightarrow y=x+1[/tex]
In Gauss elimination the given system of simultaneous equations is transformed into
Answer:
row-echelon form
Step-by-step explanation:
Matrixes are commonly used to do Gaussian elimination. By reducing the need to manually specify the parameters at each step, this strategy decreases the work required to obtain the solutions. A system of equations equations is solved using the Gauss elimination method. Let's review the definitions of these equation systems. A set of linear equations with numerous unknown components is defined as a system of linear equations. Unknown factors can be found in various equations, as we all know.
Walter bought cupcakes for his sister's birthday party. 39 out of the 52 cupcakes had sprinkles on top. What percentage of the cupcakes had sprinkles?
The percentage of the cupcakes that had sprinkles if 39 out of the 52 cupcakes had sprinkles on top is 75%.
What is percentage?A division by 100 results in a percentage, often known as a percent. A percentage denotes a component of a total sum and indicates "per 100". For example, 45% represents 45 out of 100. Calculating a percentage is the process of determining a whole's proportion in terms of 100.
Given:
The total no cupcakes = 52,
The no of sprinkled cupcakes = 39,
Percentage of sprinkled cupcakes = The no of sprinkled cupcakes / The total no cupcakes × 100
Percentage of sprinkled cupcakes = 39 / 52 × 100
Percentage of sprinkled cupcakes = 75%
Therefore, the percentage of the cupcakes that had sprinkles if 39 out of the 52 cupcakes had sprinkles on top is 75%.
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Need answer ASAP
QUESTION 16
Write an inequality of the form |x-al k so that the inequality has the given solution
set.
(-5,5)
An inequality of the form |x-al<k so that the inequality has the given solution set (-5,5) is |x|<10.
In the given question,
We have to write an inequality of the form |x-a|<k so that the inequality has the given solution set (-5,5).
We first learn about modulus,
A modulus function is a function that determines a number or variable's absolute value. It generates the size of the variable count. A function with absolute values is another name for it. No matter what input was provided to this function, the outcome is always positive.
The given set is (-5,5).
For x<(-5,5)
The mean value of x should be between -5 and 5.
-5<x<5
|x|<10
Hence, an inequality of the form |x-a l<k so that the inequality has the given solution set (-5,5) is |x|<10.
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What is the equation of this graphed line?
Answer:
y = 2x + 2
Step-by-step explanation:
(y-y1)/(y2-y1)=(x-x1)/(x2-x1)
(y-6)/(-6-6)= (x-2)/(-4-2)
(y-6)/-12 = (x-2)/-6
y-6 = 2x-4
y = 2x -4 + 6
y = 2x + 2
Calculate the height (in m) of a cliff if it takes 2.41 s for a rock to hit the ground when it is thrown straight up from the cliff with an initial velocity of 8.14 m/s. (Enter a number.)
How long (in s) would it take to reach the ground if it is thrown straight down with the same speed? (Enter a number.)
The height of the cliff is 7.57m and the time to reach the ground when thrown straight down is 0.814s
What is motion under gravity?Motion under gravity refers to the movement of an object whose vertical motion is affected by the presence of gravity. The force that attracts objects downwards is GRAVITY. In fact, gravity works towards the centre of the Earth.
When an object is moving upward,it is moving against gravity and when it is moving down it is moving with gravity.
from equation of motion
H= ut-1/2gt^2( the object is moving upward)
where h is the height of the cliff and u is the initial velocity and g is acceleration due to gravity
(g=10ms^-2).
therefore h= 8.14×2.41-(1/2×10×2.41)
= 19.62-12.05
h= 7.57m
when the object is thrown Down,
V = u + gt
u will be 0 at top before coming down
V = gt
t= 8.14/10
= 0.814s
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