If the order of the choices is relevant ,72 times can this be done.
What is nPr in permutation formula?Suppose we want to choose 6 colors, without replacement , from 8 distinct colors. If the order of the choices is relevant
The permutation of arranging 'r' things from a collection of 'n' objects into an order or sequence is known as nPr in mathematics. Permutation is calculated using the formula nPr = (n!) / (n-r)! N permutations = nPr = n!/ (n-r)! Combination, nCr, is the selection of r items from a collection of n objects such that the order of the objects does not matter.
N permutations are as follows: 9P6 = 8!/(8-6)! = 8*7*6*5*4 = 6,720.
N combinations = nCr = n!/((n-r)!r!) is the response to b.
N combinations = = 8C6 = = 8!/((8-6)!6!) = (8*7*6)/(2*1) = 72
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In an interval whose length is z seconds, a body moves (32z + 2z^ 2 ) ft. What is the average speed v of the body in this interval?
The average speed of the body in the given interval is 32 + 2z ft/s.
The average speed v of a body in an interval of z seconds can be calculated using the formula v = d/t, where d is the distance traveled and t is the time taken.
In this case, the distance d is (32z + 2z^ 2 ) ft and the time taken is z seconds.
Therefore, the average speed v of the body in this interval is:
v = (32z + 2z^ 2 ) ft / zs
v = 32 + 2z ft/s
Therefore, the average speed of the body in the given interval is 32 + 2z ft/s.
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Is x = 6 a solution to the equation x + 13 = 18?
A. No, because 6 + 13 = 18 is not true.
B. Yes, because 6 + 13 = 18 is not true.
C. No, because 6 + 13 = 18 is true.
D. Yes, because 6 + 13 = 18 is true.
On solving the provided question, we can say that x = 6 a solution to the equation x + 13 = 18, no, because 6 + 13 = 18 is not true, as 6 + 13 = 19
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
x = 6 a solution to the equation x + 13 = 18
No, because 6 + 13 = 18 is not true, as 6 + 13 = 19
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The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a line.
a(t) = t + 4, v(0) = 3, 0 ≤ t ≤ 11(a) Find the velocity at time t. 3 m/s (b) Find the distance traveled during the given time interval.
The distance traveled during the given time interval be 2024 m.
What is meant by acceleration function?An object's rate of change in velocity is referred to as its acceleration. The rate of change in velocity is known as acceleration. Acceleration typically signals a change in speed, though this is not always the case. Because of the shifting direction of its velocity, an item moving on a circular path at a constant speed is still accelerating.
By integrating the velocity v in terms of time t, v = gt, we can determine acceleration, which is the rate of change of velocity with respect to time.
Let the function be a(t) = t + 4
time = 11
substitute the value of t in the above equation, we get
a(11) = 11 + 6 = 17 m/s²
a = v/t, so v = at
finally v = (17 m/s²) (11s)
v = 187 m/s
b) Find the distance traveled during the given time interval
[tex]$$V_{total} = V_{final} - V_{ initial[/tex]
V final = 187 m/s, Vinitial = 3 m/s
V total = 187 - 3 = 184 m/s
Let the equation of velocity be
Velocity = distance/time
distance = velocity × time
distance = 184 m/s × 11 s
distance = 2024 m
Therefore, the distance traveled during the given time interval be 2024 m.
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The polygon in the diagram is a square with center P. The length from the center to the vertex is [tex]6\sqrt{2} in[/tex]. Find the area of the square to the nearest tenth of an inch.
A) 24.0 [tex]in^{2}[/tex]
B) 72.0 [tex]in^{2}[/tex]
C) 36.0 [tex]in^{2}[/tex]
D) 144.0 [tex]in^{2}[/tex]
The area the polygon in the diagram with, a length from the center to the vertex 6√2 in is 144.0 in².
What is polygon?Any closed curve that consists entirely of connected line segments (sides) without any intersections is known as a polygon in geometry. The three simplest polygons are pentagons, triangles with three sides, and quadrilaterals with four sides (five sides). The two types are concave and convex polygons.
Convex polygons are those without any extended sides crossing over them. Equilateral refers to a polygon with equal sides. Interior angles of equiangular shapes are equal. Every equilateral and equiangular polygon is a regular polygon (e.g., an equilateral triangle or a square).
As all sides are equal, all diagonals are equal too, and the angle of adjacent diagonals are 90° with vertical opposite angle.
Therefore,
Each side = [tex]\sqrt{\text {diagonal}^2+ \text {diagonal}^2}[/tex]
Each side = [tex]\sqrt{(6\sqrt{2} )^2+(6\sqrt{2} )^2}[/tex]
Each side = [tex]\sqrt{(36\times 2+36\times 2}[/tex]
Each side = [tex]\sqrt{144}[/tex]
Each side = 12 inch
Area = 12 × 12
= 144.0 in²
Thus, the area the polygon in the diagram with, a length from the center to the vertex 6√2 in is 144.0 in².
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For the function given below, find a formula for the Riemann sum obtained by dividing the interval [a,b] into n equal subintervals and using the right-hand endpoint for each [tex]c_k[/tex]. Then take a limit of this sum as [tex]n[/tex]→∞ to calculate the area under the curve over [a,b].
[tex]f(x)=2x[/tex] over the interval [1,5]
The Riemann sum formula is ∫(1,5) 2x = 24
How to determine the Riemann sum formulaFrom the question, we have the following parameters that can be used in our computation:
f(x) = 2x over the interval [1, 5]
The Riemann sum for f(x) = 2x over the interval [1,5] using the right-hand endpoint for each subinterval is given by the formula:
(Δx/2) * (2c1 + 2c2 + ... + 2cn) where c1, c2, ..., cn are the right-hand endpoints of the subintervals and Δx = (b - a)/n.
As a general rule:
As n approaches infinity, the width of the subintervals approaches zero,
Also, we have the Riemann sum approaches the definite integral of f(x) = 2x over the interval [1,5], which is x² evaluated at the interval's endpoints.
So, the formula becomes
∫(1,5) 2x = x²
Substitute the intervals
∫(1,5) 2x = 5² - 1²
Evaluate
∫(1,5) 2x = 24
Hence, the formula is ∫(1,5) 2x = 24
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711
Put the measures of the angles in order from least to greatest
Answer: [tex]m\angle YOZ, m\angle VOS, m\angle UOZ, m\angle XOS, m\angle TOZ[/tex]
Step-by-step explanation:
[tex]m\angle VOS=90^{\circ}\\\\m\angle UOZ=180^{\circ}-56^{\circ}=124^{\circ}\\\\m\angle YOZ=180^{\circ}-143^{\circ}=37^{\circ}\\\\m\angle XOS=126^{\circ}\\\\m\angle TOZ=180^{\circ}-33^{\circ}=147^{\circ}[/tex]
the sums of the measures of the interior angles of a polygon is three times the sum of its exterior angles. how many sides does it have. please help
The sums of the measures of the interior angles of a polygon is three times the sum of its exterior angles then it has 8 sides .
What is Polygon?
A polygon is a two-dimensional, closed form that is flat or planar and is limited by straight sides. Its sides are not curled. A polygon's edges are another name for its sides. The vertices (or corners) of a polygon are the places where two sides converge. Here are some illustrations of polygons.
What is interior angles?
Interior angles are those that are located within the confines of two parallel lines that are intersected by a transversal.
What is exterior angles?
The angles that are created outside of a triangle are its external angles. In other terms, the angle created between one of a triangle's sides and its neighboring extended side is the triangle's external angle.
We know that sum of interior angle of regular polygon is ;
(n-2) x 180°
Where n = no. of sides
We also know that sum of exterior angle of regular polygon is 360°.
The fact that the sum of a polygon's internal angles is three times the sum of its outside angles is now a given;
Therefore;
sum of interior angles of a regular polygon = 3 x sum of exterior angle
⇒ (n-2) x 180°
⇒3 x 360°
Simplify the equation we have above by:
⇒(n-2) = 3 x 360°/180° = 6
⇒ n = 6+2 = 8
Therefore the sides of the regular polygon is 8.
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A rectangle is partitioned into 5 regions as shown. Each region is to be painted a solid color-red. orange, yellow, blue, or green-so that regions that touch are painted different colors, and colors can be used more than once. How many different colorings are possible? (A) 120 (B) 270 (C) 360 (D) 540 (E) 720
The 5 different colorings are possible.
The rectangle is partitioned into 5 regions.
The objective is to find the different of color.
There are 5 rectangle and 5 colors
Each region is to be painted a solid color-red. orange, yellow, blue, or green
Need to color 5 rectangles by using given five colors.
Then, we need to use 5! colors.
The factorial of a whole number is the function that multiplies the number by every natural number below it. Symbolically, a factorial can be represented by using the symbol "!". So, "n factorial" is the product of the first n natural numbers and is represented as n!
The formula for n factorial is:
n! = n × (n - 1)!=5×4×3×2×1
=120
Therefore, the possible colorings are 5.
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Determine whether the sequence converges or diverges. If it converges, find the limit. an=(1+2/n)^n
This sequence converges to e. The sequence (1 + 2/n)^n is a geometric sequence in which each successive term is found by multiplying the previous term by a constant.
This sequence is an example of a geometric sequence where each successive term is found by multiplying the previous term by a constant. In this case, the constant is equal to (1 + 2/n).
By using the limit definition of a geometric sequence, we can see that the limit of this sequence is given by lim n→∞ (1 + 2/n)^n = e. Therefore, the sequence converges to e.
The sequence (1 + 2/n)^n converges to e.
The sequence (1 + 2/n)^n is a geometric sequence in which each successive term is found by multiplying the previous term by a constant. By using the limit definition of a geometric sequence, it can be determined that the limit of this sequence is given by lim n→∞ (1 + 2/n)^n = e. As a result, the sequence converges to e.
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LA REPRESA POZA HONDA ALMACENA 11 MILLONES DE METROS CÚBICOS DE AGUA. ¿CUÁNTOS KILÓMETROS DE AGUA ALMACENA?
Porfavor ayudenme es para Matematicas
Answer: 11/1000 o 1.1%
Step-by-step explanation:
11 ÷ 1000
0.011
11/1000 o 1.1%
Tomhas$84,076inasavingsaccountthatearns15%annually.Theinterestisnotcompounded.Tothenearestdollar,howmuchinterestwillheearnin6months?
Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
$75668.4 is the interest earned in 6 months.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Tom has $84,076 in a savings account that earns 15% annually.
The interest is not compounded.
We have to find the interest he earned in 6 months.
Use the formula i = prt,
where i is the interest earned,
p is the principal (starting amount),
r is the interest rate expressed as a decimal,
and t is the time in years.
i=84076×15/100×6
=84076×0.15×6
=$75668
Hence, $75668.4 is the interest earned in 6 months.
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You buy 4 small candles and 2 large candles for $14. Your friend buys 5 small candles and 3 large candles for $20. What is the cost of each small candle? of each large candle?
Each small candle costs $_ and each large candle costs $_.
Using simultaneous equations, each small candle costs $1.00 and each large candle costs $5.00.
What are simultaneous equations?Simultaneous equations are two or more equations solved concurrently.
Simultaneous equations are also known as a system of equations.
Small Candle Large Candle Total Cost
You buy 4 2 $14
A friend buys 5 3 $20
Let the cost of the small candle each = s and the cost of the large candle each = l
Equations:Equation 1: 4s + 2l = 14
Equation 2: 5s + 3l = 20
Multiply Equation 1 by 1.5:
Equation 3: 6s + 3l = 21
Subtract Equation 2 from Equation 3:
6s + 3l = 21
-
5s + 3l = 20
s = 1
= $1
From Equation 1:
4s + 2l = 14
4 + 2l = 14
2l = 10
l = 5
= $5
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Airline passengers get heavier In response to the increasing weight of airline passengers, the Federal Aviation Administration (FAA) in 2003 told airlines to assume that passengers average 190 pounds in the summer, including clothes and carry-on baggage. But passengers vary, and the FAA did not specify a standard deviation. A reasonable standard deviation is 35 pounds. Weights are not Normally distributed, especially when the population includes both men and women, but they are not very non-Normal. A commuter plane carries 30 passengers.
• (a) Explain why you cannot calculate the probability that a randomly selected passenger weighs more than 200 pounds.
• (b) Find the probability that the total weight of the passengers on a full flight exceeds 6000 pounds. Show your work. (Hint: To apply the central limit theorem, restate the problem in terms of the mean weight.)
The probability that the total weight of the passengers on a full flight exceeds 6000 pounds is about 0.0147 or 1.47%.
What is the Central Limit Theorem?
The Central Limit Theorem states that the sum of a large number of independent and identically distributed random variables is approximately Normally distributed.
(a) The reason why you cannot calculate the probability that a randomly selected passenger weighs more than 200 pounds is that the weight of passengers is not Normally distributed.
The Normal distribution is a symmetric bell-shaped distribution that is defined by its mean and standard deviation.
The weight of passengers is not symmetric and it may not follow a bell shape.
Therefore, we cannot use the Normal distribution to calculate the probability of a weight greater than 200 pounds.
(b) To calculate the probability that the total weight of the passengers on a full flight exceeds 6000 pounds, we can use the Central Limit Theorem.
Since we don't know the exact distribution of the weight of the passengers, we can use the Central Limit Theorem to approximate the total weight of the passengers on a full flight.
The mean weight of a passenger is 190 pounds, and the standard deviation is 35 pounds. Since a full flight carries 30 passengers, the mean weight of the passengers on a full flight is 19030 = 5700 pounds and the standard deviation is 35sqrt(30) = 175 pounds.
To find the probability that the total weight of the passengers on a full flight exceeds 6000 pounds, we can use the standard normal distribution table.
z = (6000 - 5700) / 175 = 2.2857
Probability P(X > 6000) = P(Z > 2.2857) = 1 - P(Z < 2.2857) = 1 - 0.9853 = 0.0147
Hence, the probability that the total weight of the passengers on a full flight exceeds 6000 pounds is about 0.0147 or 1.47%.
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A kite is flying 20 ft off the ground. It’s line is pulled taut and casts a 15 feet shadow
Answer:ts line is pulled taut and casts a 15 ft - shadow. Find the length of the line. If necessary, round your answer to the nearest tenth.
Step-by-step explanation:
Need help with this equation
4x⁴ +12x³ +15x² +9x −6 is the expression which can represent function f(g(x)). Thus, option D is correct.
What is function?A rule that transforms one number into another is called a function. However, not every rule outlines an appropriate function. In addition to introducing some of the mathematical terms related to functions, this unit explains how to determine if a given rule describes a valid function.
Given
f(x) = x² + 3x - 6
g(x) = 2x² +3x
To find expression for f(g(x))
Put the value of g(x) place of x, f(x)
f(x) = x² + 3x - 6
(2x² +3x)² + 3(2x² +3x) - 6
4x⁴ +12x³ +15x² +9x −6
Thus, 4x⁴ +12x³ +15x² +9x −6 is the expression which can represent f(g(x)).
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The article "Kids Digital Day: Almost 8 Hours" (USA Today, January 20, 2010) summarized results from a national survey of 2002 Americans age 8 to 18. The sample was selected in a way that was expected to result in a sample representative of Americans in this age group.
a. Of those surveyed, 1321 reported owning a cell phone. Use this information to construct and interpret a 90% confidence interval estimate of the proportion of all Americans age 8 to 18 who own a cell phone.
b. Of those surveyed, 1522 reported owning an MP3 music player. Use this information to construct and interpret a 90% confidence interval estimate of the proportion of all Americans age 8 to 18 who own an MP3 music player.
c. Explain why the confidence interval from Part (b) is narrower than the confidence interval from Part (a) even though the confidence level and the sample size used to compute the two intervals was the same.
The confidence interval from Part (b) is narrower than the confidence interval from Part (a) because the proportion of Americans age 8 to 18 who own an MP3 music player is higher than the proportion of Americans age 8 to 18 who own a cell phone.
a. 90% confidence interval estimate of the proportion of all Americans age 8 to 18 who own a cell phone:
(1321/2002) ± (1.645*sqrt( (1321/2002)*(1-(1321/2002)) / 2002)) = (0.6608 ± 0.0402)
Interpretation: We are 90% confident that the true proportion of all Americans age 8 to 18 who own a cell phone is between 0.6206 and 0.7010.
b. 90% confidence interval estimate of the proportion of all Americans age 8 to 18 who own an MP3 music player:
(1522/2002) ± (1.645*sqrt( (1522/2002)*(1-(1522/2002)) / 2002)) = (0.7610 ± 0.0346)
Interpretation: We are 90% confident that the true proportion of all Americans age 8 to 18 who own an MP3 music player is between 0.7264 and 0.7956.
c. The confidence interval from Part (b) is narrower than the confidence interval from Part (a) because the proportion of Americans age 8 to 18 who own an MP3 music player is higher than the proportion of Americans age 8 to 18 who own a cell phone. This means that the sample size is more likely to result in a more accurate estimation of the true population proportion for the MP3 music player than for the cell phone.
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Consider the following data: 13,11,5,2,9,14 Step of 3 : Calculate the value of the sampe variance Round your answer to one decimal place.Refer to Exercise 3. Calculate and interpret the standard deviation of the random variable X.
The sample variance of the given data 13,11,15,2,9,14 is 356.6.
Sample variance can be defined as the expectation of the squared difference of data points from the mean of the data set. It is an absolute measure of dispersion and is used to check the deviation of data points with respect to the data's average.
we have data 13, 11, 5, 2, 9, 14, and we have to determine the sample variance of given data.
Sample variance is given by,
[tex]S^2=\frac{\sum^n_1(X_i-X')^2}{(n-1)}[/tex]
where X' is the sample mean,
the mean of given data is,
[tex]X'=\frac{(13+11+5+2+9+14)}{6} \\\\X'=\frac{54}{6} \\\\X'=9[/tex]
now the sample variance is given by,
[tex]S^2=\frac{(13+9)^2+(11+9)^2+(5+9)^2+(9+9)^2+(14+9)^2}{6-1} \\\\S^2=\frac{(484+400+289+81+529)}{5} \\\\S^2=356.6[/tex]
Hence the sample variance is 356.6.
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A dentist was making note of his upcoming appointments with different aged patients and the reasons for their visits.
The probability that an appointment is with a patient under 18 years old is 0.9, the probability that it is for a regular cleaning is 0.15, and the probability that it is with a patient under 18 years old and is for a regular cleaning is 0.14.
What is the probability that a randomly chosen appointment is with a patient under 18 years old or is for a regular cleaning?
Write your answer as a whole number, decimal, or simplified fraction.
The probability that a randomly chosen appointment is with a patient under 18 years old or is for regular cleaning is 0.95.
The probability of a random appointment being with a patient under 18 or for regular cleaning is calculated as P(Under 18 or Regular Cleaning) = P(Under 18) + P(Regular Cleaning) - P(Under 18 and Regular Cleaning).
P(Under 18) = 0.9
P(Regular Cleaning) = 0.15
P(Under 18 and Regular Cleaning) = 0.14
So, P(Under 18 or Regular Cleaning):
= 0.9 + 0.15 - 0.14
Apply the arithmetic operation, and we get
= 0.91.
Thus, the required probability is 0.91.
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A man bought one almirah for Rs 3640 and the other for Rs 4800. He sold the first almirah for a loss of 15% and the other at a profit of 13 1/3 %. How much did he gain or lose in the whole transaction.
Please tell the answer .
Answer:
Rs. 94
Step-by-step explanation:
We will denote the almirahs as A1 and A2 for ease of explanation. I am omitting currency until the final answer
For the following computations note that x% = x/100 in decimal so
15% = 15/100 = 0.15
13 1/3% = 13 1/3 ÷ 100 = 40/3 ÷ 100 = 40/300
Cost of A1 = 4800
A1 was sold for a loss of 15%
Loss = 15% of 3640 = 0.15 x 3640 = Rs 546
A2 bought at 4800 was sold at a gain of 13 1/3%
Gain from sale = 13 1/3% of 4800 = 40/300 x 4800 =Rs 640
We have to treat gain as positive and loss as negative to arrive at the answer
Net gain/loss = 640 - 546 = Rs. 94
2. If -2 is the root of a quadratic equation x²-5x+c=0, find
a: the value of c
b: the other root
The value of c according to the given equation as described is; -14.
The other root of the equation in discuss is; 7.
What is the value of c and determine the other root?As evident in the task content; if -2 is the root of a quadratic equation x²-5x+c=0, then x = -2 holds true for the equation; therefore, we have;
a). (-2)² - 5 (-2) + c = 0
4 + 10 + c = 0
c = -14
Hence, the value of c is; -14.
b). By substituting into the equation; we have;
x² - 5x - 14 = 0
(x - 7) (x + 2) = 0
x = 7 OR x = -2.
Therefore, the other root of the equation is; 7.
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match the given side lengths to the correct inequality that represents the range of the 3rd side. (9 cards will be left over)
A triangle's third side must always be between (but not exactly equal to) the other two sides' total and difference in length. Take the numbers 2, 6, and 7 as an example. In light of this, the third side length must be more than 4 and lower than 8.
What is triangle?Three edges and three vertices make up a triangle, which is a polygon. It is among the fundamental shapes in geometry. Triangle ABC refers to a triangle with the vertices A, B, and C. Any three points in Euclidean geometry that are not collinear determine a singular triangle and a singular plane simultaneously. In geometry, a triangle is a three-sided polygon with three sides, three vertices, and three edges.The fact that a triangle's internal angles can be added up to equal 180 degrees is its most significant characteristic. Triangle's angle sum property is what this characteristic is known as. When three straight lines cross, a triangle is the result. There are always three sides and three corners to a triangle (angles). A triangle's vertex is the location at which two of its sides meet.To learn more about triangle, refer to:
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Divide the following and then check by multiplying.
7)84
Select the correct choice below and, if necessary, fill in the answer box to complete your choice
OA. The quotient does not have a remainder. The quotient is
B. The quotient has a remainder not equal to 0. The quotient is
OC. The quotient is undefined.
When dividing 84 by 7 then the quotient does not have a reminder and the quotient will be 12.
What is division?
A division in mathematics is the process of dividing a specific amount into equal parts. The division is the inverse of multiplication.
We can find a division fact if we know a multiplication fact: For instance, 3 5 = 15, so 15 / 5 = 3.
Also 15 / 3 = 5.
Here given that,
We have to divide 87/7,
By dividing,
we know that 8/7 gives reminder 1, and a quotient of 1.
Then divide 14 by 7,
which gives reminder 0 and quotient 2.
So by dividing 84 / 7 we get reminder 0 with a quotient of 12.
Therefore the correct option is option A. With a quotient of 12.
Hence, When dividing 84 by 7 then the quotient does not have a reminder and the quotient will be 12.
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Benjamin gets to go to festival with his friend for $120 The cost covers $45 for his lodging and 2 tickets to the festival, including all of his meals.
How much is a ticket to the festival?
Answer:
is $27.50 per each teacket
You pick a card at random. Without putting the first card back, you pick a second card at random. 1 2 3 4 What is the probability of picking a 2 and then picking a 1? Write your answer as a fraction or whole number.
The probability of picking a 2 and then picking a 1 would be = 1/2
What is probability?Probability is definitely as the expression that to represents the number of outcomes of an event.
The number of cards such as 1,2,3,4 = 4 cards.
The cards picked at random = a 1 and a 2
Therefore, the probability = 2/4 = 1/2
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the first three steps for completing the square to solve a quadratic equation are shown. x squared minus 8 x plus 2 equals 0. x squared minus 8 x equals negative 2. x squared minus 8 x plus box equals negative 2 plus box.questionwhat number goes in the boxes to complete the third step?
The number that goes in the box is 4, since 4 + (-2) = 2, which is the coefficient of x^2 in the equation. The third step is to add the same number to both sides of the equation, so the box needs to contain 4.
To complete the third step in solving a quadratic equation using the completing the square method, the number that goes in the box is 4. This is because the goal is to make the coefficient of x^2 on the left side of the equation equal to the coefficient of x^2 on the right side. The equation is x^2 - 8x + 2 = 0, so the coefficient of x^2 on the left side is 1, and the coefficient of x^2 on the right side is 2. Therefore, the number that needs to be added to the left side is 1, and the number that needs to be added to the right side is also 1. This means that 4 needs to be added to both sides of the equation, so 4 is the number that goes in the box.
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State the domain and range for the following relation. Then determine whether the relation represents a function. {( -4,6), (-4,7), (6,5), (7,9)} The domain of the relation is __. (Use a comma to separate answers as needed.) The range of the relation is ___ (Use a comma to separate answers as needed.) Does the relation represent a function? Choose the correct answer below. A. The relation is a function because there are no ordered pairs with the same second element and different first elements. B. The relation is a function because there are no ordered pairs with the same first element and different second elements. C. The relation is not a function because there are ordered pairs with 5 as the second element and different first elements. D. The relation is not a function because there are ordered pairs with - 4 as the first element and different second elements.
Since the input value of domain -4 has two different output values (7 and 6), the relation is not a function.
By definition, a relation is a function if each input value has only one output value.
Given the relation:
(-4,6)
(-4,7)
(6,5)
(7,9)
The domain is the set of the x-coordinates of each ordered pair (You do not need to write 4 twice):
domain ={-4 ,6,5}
The range is the set of the y-coordinates of each ordered pair :
range= {6,7,5,9}
Since the input value 4 has two different output values (7 and 6), the relation is not a function.
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Mariah made a cylinder out of clay that had a radius of 6 cm and a volume of 72π cm^3. She painted the entire surface of the cylinder purple. How many square centimeters of the cylinder did Mariah paint in terms of π?
Enter the correct answer in the box/blank in terms of π.
_______ cm^2 (squared)
[tex]Answer:\ \boxed{96\pi }\ cm^2[/tex]
Step-by-step explanation:
[tex]R=6\ cm \ \ \ \ V_c=72\pi \ cm^3\ \ \ \ S_c=?[/tex]
[tex]V_c=\pi R^2H\\[/tex]
[tex]72\pi =\pi 6^2H\\\\72=36H\\[/tex]
Divide both parts of the equation by 36:
[tex]2=H\\\\Thus,\ H=2\ cm[/tex]
[tex]S_c=2(\pi R^2)+2\pi R(H)\\\\S_c=2\pi (6^2)+2\pi 6(2)\\\\S_c=2\pi(36)+12\pi (2) \\\\S_c=72\pi +24\pi \\\\S_c=96\pi\ cm^2[/tex]
Examine the number line,and then choose the correct symbol to complete each statement
After examine the number line,and then the correct symbol to complete each statement is -2/4<-1/4; 3/4>2/4;-1/4<0.
What is Number line ?
A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.
What is Symbol?
A mark, sign, or term that denotes, denotes, or is taken to denote an idea, an item, or a relationship is known as a symbol. By connecting seemingly unrelated ideas and events, symbols help people look beyond the known and the visible.
In the question given some relation between the real number which are
a) -2/4 < -1/4 because negative number has the property that the those numbers which is smaller is always greater.
b) 3/4 > 2/4 both numbers are positive so clearly it 3/4 comes after 2/4 so it is greater.
c) -1/4 < 0 zero is always greater than the negative numbers
So, after examine the number line,and then the correct symbol to complete each statement is -2/4<-1/4; 3/4>2/4;-1/4<0.
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The segments GA and GB are tangent to a circle at A and B, and AGB is a 48-degree angle. Given that GA = 12 cm, find the distance from G to the nearest point on the circle.
The distance from G to the nearest point on the circle is going to be 5.61 cm.
The given figure (image attached below) has the segments GA and GB tangent to a circle at A and B, and AGB is at a 48-degree angle. We have been told that GA = 12 cm. We have to find the distance from G to the nearest point on the circle.
For this, first what we need to do is draw radii to A and B. Next draw OG which bisects the 48-angle G into two 24-angles. Let P be the point where OG intersects the circle. This becomes the distance from G to the nearest point on the circle which we need to find (image attached below).
In the right triangle AOG, radius AO is the side opposite angle AGO-
= Tangent = Perpendicular / Base
= tan(24) = r / 12
= r = 12tan(24) (i)
For OG -
= cos(24) = Base / Hypotenuse = 12 / OG
= OG = 12cos(24) (ii)
Now, we subtract (i) and (ii) -
= 12tan(24) - 12cos(24)
= 5.61 cm
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Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. sketch the region, the solid, and a typical disk or washer.
y=2−12x, y=0, x=1, x=2; rotate about the x-axis.
The Volume of the solid obtained by rotating the region bounded by the curves is 5 cm³.
Volume of a solid plain:
The volume of a solid is a measure of the space occupied by an object. It is measured by the number of unit cubes required to fill the solid.
Given in the question:
y = 2 - 1/2x
y = 0 , x = 1 and x = 2
As we know that:
We can write 19π / 12 as
(19× 22/7 )÷ 12
= 209/ 42
= 4.97 ≈ 5 cm³
Therefore, the volume is 5 cm³
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