The inverse demand function is P = 2400 + 5Q
The Marginal Revenue function is MR = 5QThe number of nose operations is 15The price per month is $2475Dr. Williams earns $19750 in profit each monthHow to determine the inverse demand functionGiven that
Q = 480 - 0.2P
We simply make P the subject of the formula
So, we have
0.2P = 480 - Q
Divide by 0.2
P = 2400 + 5Q
The marginal revenue functionTo find the marginal revenue function, we can use the inverse demand function P = 2400 + 5Q, and take the derivative of this function with respect to Q.
The derivative of P with respect to Q is dP/dQ = 5. This represents the change in price for a one unit change in the quantity of operations performed.
So the Marginal Revenue function is MR = dP/dQ * Q = 5Q
The number of nose operationsTo maximize profit, the doctor should equate marginal revenue to marginal cost, which is
MC = dAVC/dQ
So, we have
MC = d(2Q² - 15Q + 400)/dQ
Evaluate
MC = 4Q - 15.
So, we have
5Q = 4Q - 15
Q = -15
Take the absolute value
Q = 15
So, the number of operations is 15
The price for each operationWe have
P = 2400 + 5Q
This gives
P = 2400 + 5 * 15
Evaluate
P = 2475
The monthly profitTo find the profit, we need to subtract the total cost from the total revenue.
The total revenue is found by multiplying the price by the quantity of operations performed: TR = P * Q = 2475 * 15 = 37125
The total variable cost is found by multiplying the average variable cost by the quantity of operations performed: TVC = AVC * Q = (2Q^2 - 15Q + 400) * Q = 2Q^3 - 15Q^2 + 400Q
The total fixed cost is the fixed cost that doesn't change regardless of the level of output : TFC = $8000
The total cost is the sum of the total variable cost and total fixed cost: TC = TVC + TFC = 2Q^3 - 15Q^2 + 400Q + $8000
The profit is the difference between total revenue and total cost:
π = TR - TC = 37125 - (2Q^3 - 15Q^2 + 400Q + $8000)
When Q = 15,
profit is π = 37125 - (2(15)^3 - 15(15)^2 + 400(15) + $8000)
= 19750
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In rhombus ABCD, points E,F,G and H are the midpoints of AB, BC, CD and DA respectively. Quadrilateral EFGH has area 14 and perimeter 16. Find the side length for rhombus ABCD.
Side length of Rhombus ABCD is 8+2√2 unit
EFGH is a rectangle :
We know that ,
E, F , G , H are midpoints of AB, BC, CD , DA respectively
Since ABCD is a rhombus
AB = BC = CD = DA
AB ll CD and BC ll DA
since, E, F , G , H are midpoints of AB, BC, CD , DA respectively
from the figure below we can say that ,
1) AB ll CD ll FH and AB= CD = FH
2) BC ll DA ll GE and BC = DA = GE
Using mid point theorem we can say that ,
GH = EF = 1/2 AC and FG= EH = 1/2 BD
Since for the figure EFGH opposite sides are equal and and parallel , and the diagonals are equal in length we can say that EFGH is a rectangle.
Perimeter of a rectangle = 2(a+b) = 2( GH + EH ) = 2 (EF + GF) = 2 ( 1/2 AC + 1/2 BD )
= 2 x 1/2 ( AC + BD ) = 16
⇒ AC + BD = 16 (1)
now area of a rectangle is given by
A = ab = GH x EH = EF x GF = 1/2 AC x 1/2 BD = 1/4 (AC x BD) = 14
⇒AC x BD = 14 x 4 = 56
from equation (1)
AC ( 16 - AC) = 56
= 16 AC - AC ^2 = 56
⇒ AC^2 - 16 AC + 56 = 0
AC = 8 +/- 2√2
BD = ( 16 - AC) = 8 +/- 2 √2 = side length of rhombus ABCD
Side length of Rhombus ABCD is 8+2√2 unit EFGH is - 1
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Question 8
Find the measure of each angle indicated
47
We know the angles in a triangle add up to 180 degrees. Adding the two angles we know, ( 47 and 86) we get 133. Simply subtract 133 from 180 to get 47 degrees.
In a Premier League match between Man. United and Arsenal FC, there are 22 players altogether and 3 match officials on the pitch. a. Find the probability Man. United wins the match. b. If a person is selected at random from the pitch, what is the probability that he is an official? c. If both coaches decide to play 4 defenders, 3 midfielders and 3 attackers from each side, find the probability that a player selected at random is i. a goalkeeper. ii. an attacker. iii. a defender
Answer:
a. Without any additional information provided, it is impossible to determine the probability of Manchester United winning the match. The outcome of a football match can be influenced by many factors such as player performance, tactics, and luck.
b. There are 22 players + 3 officials = 25 people on the pitch. The probability that a person selected at random from the pitch is an official is 3/25.
c. i. Since there are 2 goalkeepers on the pitch, the probability that a player selected at random is a goalkeeper is 2/22 = 1/11
ii. Since there are 3 attackers on the pitch, the probability that a player selected at random is an attacker is 3/22 = 1/7
iii. Since there are 8 defenders on the pitch, the probability that a player selected at random is a defender is 8/22 = 4/11
Shade each model. Then write each fraction as a decimal
Answer: 0.25
Step-by-step explanation:
1/4 = 0.25
The math department at a small school has 5 teachers. The ages of these teachers are 23, 34, 37, 42, and 58. Suppose you selected a random sample of 3 teachers and calculated the sample median.
(a) List all 10 possible samples of size 3. Calculate the sample median for each sample.
(b) Display the sampling distribution of the sample median.
When we select a random sample of 3 teachers and calculated the sample median from ages of 5 teachers in maths department, we get three samples of sample median 34, four samples of sample median 37 and three samples of sample median 42.
a. To list all 10 possible samples of size 3, we can use the combination formula C(5,3) = 5! / (3! * 2!) = 10.
The possible samples are:
Sample 1: (23, 34, 37) - Sample Median: 34
Sample 2: (23, 34, 42) - Sample Median: 34
Sample 3: (23, 34, 58) - Sample Median: 34
Sample 4: (23, 37, 42) - Sample Median: 37
Sample 5: (23, 37, 58) - Sample Median: 37
Sample 6: (23, 42, 58) - Sample Median: 42
Sample 7: (34, 37, 42) - Sample Median: 37
Sample 8: (34, 37, 58) - Sample Median: 37
Sample 9: (34, 42, 58) - Sample Median: 42
Sample 10: (37, 42, 58) - Sample Median: 42
b. To display the sampling distribution of the sample median, we can create a frequency table that shows how many times each sample median appears in the list of possible samples.
Sample Median Frequency
34 3
37 4
42 3
This table shows that the sample median of 34 appears in 3 out of the 10 possible samples, the sample median of 37 appears in 4 out of the 10 possible samples, and the sample median of 42 appears in 3 out of the 10 possible samples.
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leave your answer in exact form (in terms of pi, without spaces). the radius of each circle is r. if two circles are shown, r is the radius of the smaller circle and r is the radius of the larger circle. r
The small radius =5 cm; and the Long radius =5+4=9 cm.
Area (a + b) = 106 * pi cm^2 (given)
radius of a = x : radius of b = (x + 4)
Area a =[tex]pi * r^2 = pi * x^2\\[/tex]
Area b = [tex]pi * r^2 = pi * (x + 4)^2[/tex]
Area (a + b) = [tex]pi * x^2 + pi * (x + 4)^2[/tex] = 106 * pi cm^2
Area (a + b) =[tex]pi * x^2 + pi * (x^2 + 8x + 16)[/tex] = 106 * pi cm^2
Area (a + b) = pi * ([tex]2x^2[/tex]+ 8x + 16) = 106 * pi cm^2
Area (a + b) = [tex]2x^2 + 8x - 90 = 0[/tex]
2x^2 + 8x - 90 = x^2 + 4x - 45 = 0
x^2 + 4x - 45 = (x + 9)(x -5) = 0
x = 5 or x = -9
Therefore: radius a = 5 cm and radius b = 9 cm
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The question is incomplete
The sum of the areas of the two circles is 106pi cm^2 and the radius of the larger circle is 4cm longer than the radius Of the smaller circle. How could I find the length of the radii?
"The solid has ( a circular base, a trapezoidal base, a triangular base, or a rectangular base) in the xy-plane.
The solid has ( a circular face, a trapezoidal face, a triangular face, or a rectangular face) in the xz-plane.
The solid has ( a circular face, a trapezoidal face, a triangular face, or a rectangular face) in the yz-plane.
The solid has ( a circular face, a trapezoidal face, a triangular face, or a rectangular face) in the plane z = 1 - x.
The solid has ( a circular face, a trapezoidal face, a triangular face, or a rectangular face) in the 0plane y = 9 - 9z.
As x increases, the top of the region (decreases, increases, or remains constant).
As y increases, the top of the region (decreases, increases, or remains constant)."
The solid has a triangular face in the xy-plane.
The solid has a rectangular face in the xz-plane.
The solid has a trapezoidal face in the yz-plane.
The solid has a triangular face in the plane z = 1 - x.
The solid has a rectangular face in the plane y = 9 - 9z.
As x increases, the top of the region decreases.
As y increases, the top of the region remains constant.
The solid whose volume is given by the iterated integral, integral 0 to 1 integral 0 to (1-x) integral 0 to (9 - 9z) dy dz dx. This is a three-dimensional solid, that has been defined by three nested integrals. The outer integral is with respect to x, the second integral is with respect to y and the inner integral is with respect to z.
In the xz-plane, the solid has a rectangular face: the integral bounds for x are 0 to 1 and for z, it is 0 to (9 - 9z)
In the yz-plane, the solid has a trapezoidal face: the integral bounds for y are 0 to (1-x) and for z, it is 0 to (9 - 9z)
In the plane z = 1 - x, the solid has a triangular face: the integral bounds for x are 0 to 1 and z = 1 - x
In the plane y = 9 - 9z, the solid has a rectangular face: the integral bounds for y are 0 to (1-x) and y = 9 - 9z
As x increases, the top of the region decreases: the limit for y decreases from 9 to 0 as x increases from 0 to 1
As y increases, the top of the region remains constant: y = 9 - 9z is a constant value, as y increases, the integral bounds for z decrease from 9 to 0
This solid is a rectangular pyramid with a trapezoidal base. The rectangular face is located in the xz-plane, the trapezoidal face is located in the yz-plane, the triangular face is located in the plane z = 1
--The question is incomplete, answering to the question below
"The solid whose volume is given by the iterated integral,
∫ [0 to 1] ∫ [0 to (1-x)] ∫ [0 to (9 - 9z)] (dy dz dx)
The solid has ( a circular face, a trapezoidal face, a triangular face, or a rectangular face) in the xz-plane.
The solid has ( a circular face, a trapezoidal face, a triangular face, or a rectangular face) in the yz-plane.
The solid has ( a circular face, a trapezoidal face, a triangular face, or a rectangular face) in the plane z = 1 - x.
The solid has ( a circular face, a trapezoidal face, a triangular face, or a rectangular face) in the plane y = 9 - 9z.
As x increases, the top of the region (decreases, increases, or remains constant).
As y increases, the top of the region (decreases, increases, or remains constant)."
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An experiment is performed where a 3-color spinner is spun and then a 4-color spinner is spun. The possible outcomes for each event are red (R), blue (B), and yellow (Y) for the 3-color spinner and red (R), blue (B), yellow (Y), and green (G) for the 4-color spinner. Identify the sample space for this experiment.
The sample space for this experiment is given as follows:
{RR, RB, RY, RG, BG, BB, BY, BG, YR, YB, YY, GG}.
What is a sample space?A sample space is a set that contains all possible outcomes in the context of an experiment.
Then the sample space for this problem is composed by two letters, and the meaning of each letter is given as follows:
First letter: outcome of the 3-color spinner.Second letter: outcome of the 4-color spinner.Hence, as an example, the outcome RB means that the color of the 3-color spinner was red and the color of the 4-color spinner was blue.
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Jorge wrote the inequality −14 °F <−2 °F to compare the temperatures at 7 A.M. and 7 P.M. It was colder at 7 P.M. than at 7 A.M. What was the temperature at 7 A.M.? Complete the explanation.
The temperature at 7 A.M. is,
−2 °F.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
Jorge wrote the inequality −14 °F < −2 °F to compare the temperatures at 7 A.M. and 7 P.M.
It was colder at 7 P.M. than at 7 A.M.
That means,
−14 °F is the temperature at 7 P.M.
The temperature at 7 A.M. is,
−2 °F.
Therefore, the temperature at 7 A.M. is −2 °F.
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A certain skin cream is 80 percent effective in curing a common rash. A random sample of 100 people with the rash will use the cream. Which of the following is the best description of the shape of the sampling distribution of the sample proportion of those who will be cured? А Bimodal B Uniform
с Approximately normal D Strongly skewed to the left E) Strongly skewed to the right
The best description of the shape of the sampling distribution is Approximately normal. The correct option is C.
The sampling distribution of the sample proportion of those who will be cured with the skin cream is approximately normal. A sampling distribution is the distribution of a statistic calculated from a random sample of data. In this case, the statistic is the sample proportion of those who will be cured with the skin cream. The Central Limit Theorem states that the sampling distribution of a statistic will be approximately normal if the sample size is large enough, regardless of the shape of the underlying distribution.
Since the sample size of 100 people is large enough, the sampling distribution of the sample proportion of those who will be cured with the skin cream is approximately normal.
Hence the correct option is C.
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HELP!!!!! Brainliest!!!
Pic
The slope of the given linear relationship is 5 (A).
From the question, we have 5 different points that create a linear relationship. To determine the slope of the linear relationship, we can choose 2 random sequence points.
We might choose:
Point 1 = (0,-2)
Point 2 = (1,3)
We can find the slope of the relationship using formula of:
m = y2 - y1
x2 - x1
m = 3- (-2)
1 - 0
m = 5
1
m = 5
To ensure our finding, we can choose another pair of random points, for example:
P1 = (-2, -12)
P2 = (-1, -7)
We can use the slope formula:
m = y2 - y1
x2 - x1
m = -7 - (-12)
-1 - (-2)
m = 5
1
m = 5
Hence, the slop of the linear relationship between all the given points are 5.
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For the function v (t) = 4t² - 6t + 2, determine the value(s) of t on the closed interval [0, 3] where the value of the derivative is the same as the average rate of change.
The slope of a secant line or the average rate of change over a relatively brief period of time can be used to approximate the derivative. The closer the interval is to the actual instantaneous rate of change, slope of the tangent line, or slope of the curve, the more accurate the result is.
What is average rate?Average Rate is a single rate that applies to property at many locations and is calculated as the weighted average of the separate rates that are appropriate at each site. Examples of average rates of change include: 80 kilometers per hour is the average speed of a bus. At a pace of 100 each week, a lake's fish population grows. For every 1 volt drop in voltage, the current in an electrical circuit reduces by 0.2 amps.Divide the y-value change by the x-value change to determine the average rate of change. When analyzing changes in observable parameters like average speed or average velocity, finding the average rate of change is extremely helpful.Therefore,
[tex]& \int_0^6\left|t^2-8 t+12\right| d t \quad \quad \text { Distance traveled over }[a, b] \\[/tex]
[tex]\int_0^2 t^2-8 t+12 d t+-\int_2^6 t^2-8 t+12 d t & \text { distance }=\int_a^b\left|x^{\prime}(t)\right| d t \\[/tex]
[tex]t^2-8 t+12=0[/tex]
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For a melon selected at random from distributor j, what is the probability that the melon will have a diameter greater than 137 mm?
The probability that the melon will have a diameter greater than 137 mm is 21.19%.
What is probability?Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes. The likelihood of an event occurring might range from 0 to 1.
Given A grocery store purchases melons from two distributors, J & K,
for distributor J,
mean of melons = μ = 133 mm
standard deviation = σ = 5 mm
to find the probability that the melon will have a diameter greater than 137 mm,
x = 137 mm
P(x > 137)
using z score formula
z = (x - μ)/σ
z = (137 - 133)/5
z = 0.8
P-value from Z-Table:
P(x < 137) = 0.78814
P(x > 137) = 1 - P(x < 137) = 0.21186
probability in percent = P(x > 137) = 0.21186*100 = 21.186%
P(x > 137) = 21.19%
Hence probability for melon will have a diameter greater than 137 mm is 21.19%.
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The complete question is,
A grocery store purchases melons from two distributors, J & K. Distributor J provides melons from organic farms. The distribution of the diameters of the melons from distributor J is approximately normal with mean with 133 millimeters and standard deviation 5 mm. For a melon selected at random from distributor J, what is the probability that the melon will have a diameter greater than 137mm?
There were 20 dolphins near the shore. 15 more dolphins swam in. How many dolphins are near the shore now?
Answer: 35
Step-by-step explanation: 20 +15= 35
in a large high school, 37% of the teachers believe that five minutes is not enough time for students to change classes. however, 89% of the students believe that five minutes is not enough time for students to change classes. let p hat subscript upper f and p hat subscript s be the sample proportions of teachers and students, respectively, who believe that five minutes is not enough time for students to change classes. suppose 28 teachers and 100 students are selected at random and asked their opinion on the amount of time students have to change class. which of the following is the correct calculation and interpretation of the standard deviation of the sampling distribution of p hat subscript upper f baseline minus p hat subscript s ?
The difference (faculty-student) in the sample proportions of those who think that students should have five minutes to switch classes usually varies by roughly 0.096 from the actual difference in proportions.
What is the standard deviation?A low standard deviation shows that the values tend to be close to the mean (also known as the expected value) of the set, whereas a high standard deviation suggests that the values are spread out over a broader range.
The standard deviation is a measure of variance or dispersion in statistics.
So, the sampling distribution's standard deviation is calculated as follows:
[tex]\begin{aligned}& \sigma_{\mathrm{F}}-\sigma_{\mathrm{s}}=\sqrt{\frac{0.37 \times(1-0.37)}{28}+\frac{0.89 \times(1-0.89)}{100}} \\& \sigma_{\mathrm{F}}-\sigma_{\mathrm{s}}=0.096\end{aligned}[/tex]
The actual proportional difference between those who believe five minutes is not enough time for pupils to switch courses and those who believe this is generally 0.096.
Therefore, the difference (faculty-student) in the sample proportions of those who think that students should have five minutes to switch classes usually varies by roughly 0.096 from the actual difference in proportions.
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Correct question:
n a large high school, 37% of the teachers believe that five minutes is not enough time for students to change classes. However, 89% of the students believe that five minutes is not enough time for students to change classes. Let p hat Subscript Upper F and p hat Subscript Upper S be the sample proportions of teachers and students, respectively, who believe that five minutes is not enough time for students to change classes. Suppose 28 teachers and 100 students are selected at random and asked their opinion on the amount of time students have to change class. Which of the following is the correct shape and justification of the sampling distribution of p hat Subscript Upper F Baseline minus p hat Subscript s ?
Dinesh is a mason and he takes Rs 3,250 for 5 days working everyday. If he received only Rs 7,800 in two weeks, how many days was he absent in his work?
Answer:
2 days
Step-by-step explanation:
He was paid 3,250 for 5 days that means 1 day is 3250/5 = 650
So, then 7,800/650 = 12 days(number of days he came to work) but two weeks is 14 days so the number of days he was absent was 14-12= 2
How did you find the answer to the problem?
Answer:
-4.44
because -pi means -22/7 so that means it is -3.14... and -11/3 means -3.6 and -4.123...I am a number. If you know the sum of 14 and 6 that will help you. I am that sum sqquered. I am
Answer: 4.4
Step-by-step explanation:
Answer:
400
Step-by-step explanation:
let the number be x
x= (14+6)²
x= 20²
x=400
What is the equation of the transformed function, g(x), after the transformations are applied to the graph of
the base function f(x)=√x to obtain the graph of g(x)?
A g(x) +4=√√√x+4
B g(x)=√√x+4 +5
C g(x) +5=√√x+4
D g(x)=√√x+5+4
Check the picture below, that's just a transformations template
so since we know that f(x) = √x, that means when x = 0, y = 0, so it touches the origin, so f(x) is the graph down below.
now, f(x) has moved to the left by 5 units and up by 4 units, based on the template that means C = 5 and D = 4 whilst B = 1
[tex]g(x)=\stackrel{A}{1}\sqrt{\stackrel{B}{1}x+\stackrel{C}{5}} ~~ +\stackrel{D}{4}\implies g(x)=\sqrt{x+5} ~~ +4[/tex]
x + 3x + 10 solve for x
Answer:
x = 2.5
Step-by-step explanation:
I am assuming that this is the entire equation and that it equates to 0 otherwise the answer will just be [tex]4x + 10[/tex]
[tex]x + 3x +10 = 0 \\4x + 10 = 0\\4x = 10\\x = \frac{10}{4} \\x = 2.5[/tex]
let a and b be two possible events when a random number generator is used once. suppose you are told that a and b are mutually exclusive. this implies that
It implies that the two events are mutually exclusive, meaning that they cannot occur simultaneously. This means that if event A occurs, event B cannot occur, and vice versa.
It implies that the two events are mutually exclusive, meaning that they cannot occur simultaneously. This means that if event A occurs, event B cannot occur, and vice versa.
1. Two possible events, A and B, are given when a random number generator is used once.
2. It is stated that the two events are mutually exclusive.
3. This implies that the two events cannot occur simultaneously.
4. If event A occurs, event B cannot occur and if event B occurs, event A cannot occur.
It implies that the two events are mutually exclusive, meaning that they cannot occur simultaneously. This means that if event A occurs, event B cannot occur, and vice versa.
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Suppose it takes 6.4 pounds of seed to completely plant one acre of land. Boris has 18.5 acres of land. Find the amount of seed he needs.
Answer:
1.2 Acres
Step-by-step explanation:
In the town of Tower Hill, the number of cell phones in a household is a random variable W with the following distribution:
W 0 1 2 3 4 5
P(W) 0.1 0.1 0.25 0.3 0.2 0.05
The probability that a randomly-selected household has at least two cell phones is
A. 0.20.
B. 0.25.
C. 0.55.
D. 0.70.
E. 0.80.
Answer:
the answer is alphabet c
a new real estate agent earns 5% of the cost of the sold house his first sale is a $219,000 house
Answer:
The new real state agent earns:
$10,950
Step-by-step explanation:
5% = 5/100 = 0.05
219000 * 0.05 = 10950
given the 27 blocks represented by the mccumber cube; give an example item which would fulfill any 9 of the blocks.
The McCumber Cube, which bears the name of its inventor, John McCumber, demonstrates the interdependence of the many elements of information security.
What is the McCumber Cube used for?
The McCumber Cube, which bears the name of its inventor, John McCumber, demonstrates how the many elements of information security are interconnected. You may view availability, integrity, and confidentiality on one side. All three of these include crypto in a significant way.
Information Characteristics, Information States, and Security Countermeasures are the three McCumber cube dimensions. The three CIA triangle pillars of confidentiality, integrity, and availability make up information characteristics.
The McCumber Cube, which John McCumber developed in 1991, is a reference framework for developing and assessing information security (also known as information assurance) initiatives. This security model is presented as a grid that resembles the Rubik's Cube in three dimensions.
The McCumber Cube shows three proportions. If theorized, the three dimensions of each axis become a 3 × 3 × 3 cube with 27 cells representing areas that must be addressed to secure today’s information systems. To ensure system security, each of the 27 areas must be properly addressed during the security process (McCumber, 1991).
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Express 2x=5 in the form of ax+ by+c=0 and find the value of a,b and c
Answer:
[tex]2x = 5 \\ 2x + 0y - 5 = 0 \\ a = 2 \\ b = 0 \\ c = - 5[/tex]
Determine how many two-digit numbers satisfy the following property: when the number is added to the number obtained by reversing its digits, the sum is $132.$
$\textbf{(A) }5\qquad\textbf{(B) }7\qquad\textbf{(C) }9\qquad\textbf{(D) }11\qquad \textbf{(E) }12$
132 is the total of all two-digit numbers and their reversal digits. The solution is (C) 9. Nine two-digit numbers, including 21 + 12 = 33, 32 + 23 = 55, 43 + 34 = 77, 54 + 45 = 99, 65 + 56 = 121, 76 + 67 = 143, 87 + 78 = 165, 98 + 89 = 187, and 109 + 901 = 132, meet this characteristic.
132 is the total of all two-digit numbers and their reversal digits. We must look at all potential two-digit numbers and add the number to its reversed digits in order to count the number of two-digit numbers that satisfy this property. The range of the two-digit numbers is 10 to 99. Starting with the number 11, which does not satisfy the stated criteria because 10 + 01 = 11 is not equal to 132. Then, we will look at 11 + 11, which is not equal to 132, and find that it is 22. This method will be repeated until a two-digit number is found that meets the specified attribute. As an illustration, 21 + 12 Equals 33, which is not the same as 132. This technique will be repeated until a two-digit number, such as 65 + 56 = 121, is found that satisfies the property. This operation will be repeated until nine two-digit values, such as 109 + 901 = 132, satisfy the property. As a result, the response is (C) 9.
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Write the expression in simplest form. 5/3-√2=
Answer:
[tex] \sf \: \frac{5 - 3 \sqrt{2} }{3} [/tex]
Step-by-step explanation:
Given expression,
→ (5/3) - √2
Let's simplify the expression,
→ (5/3) - √2
→ (5/3) - ((√2 × 3)/(1 × 3))
→ (5/3) - (3√2/3)
→ (5 - 3√2)/3
Hence, answer is (5 - 3√2)/3.
Answer:
[tex]\dfrac{15+5\sqrt{2}}{7}[/tex]
Step-by-step explanation:
Given rational expression:
[tex]\dfrac{5}{3-\sqrt{2}}[/tex]
To write the given rational expression in its simplest form we need to rationalise the denominator by multiplying both the numerator and denominator by the conjugate of the denominator.
The conjugate of an expression is where we change the sign in the middle of the two terms. Therefore, the conjugate of the denominator of the given expression is:
[tex]3+\sqrt{2}[/tex]Multiply the numerator and denominator by the conjugate of the denominator:
[tex]\dfrac{5}{3-\sqrt{2}} \cdot \dfrac{3+\sqrt{2}}{3+\sqrt{2}}[/tex]
Simplify:
[tex]\implies \dfrac{5(3+\sqrt{2})}{(3-\sqrt{2})(3+\sqrt{2})}[/tex]
[tex]\implies \dfrac{15+5\sqrt{2}}{9+3\sqrt{2}-3\sqrt{2}-2}[/tex]
[tex]\implies \dfrac{15+5\sqrt{2}}{9-2}[/tex]
[tex]\implies \dfrac{15+5\sqrt{2}}{7}[/tex]
A rectangular prism has a length of 10 meters, a width of 5 meters, and a height of 2 meters.
Which equations could be used to determine the volume, V, of the prism?
The volume equation of a rectangular prism is:
V = Bh orV = lwh,Where V - volume, l, w, h are dimensions, B - area of base (same as lw)
By substituting values we get:
V = 10*5*2 = 100 m³The number of solutions of (x2 + 1)2 + 2(x2 + 1) - 3 = 0 is equal to
A. 1
B. 2
C. 3
D. 4
Answer:
I'm pretty sure it's 3. I say that because I get 3 different answers.
x = -1 / 8
x = -0.125
x = -2^3
Those are the answers I got to solve the equation. There also is an answer if I were to rewrite the equation which is... 8x = -1
I hope this helps in any way <3
Step-by-step explanation:
