Using the arrangements formula, the number of ways to organize the plates in each case is given as follows:
ii) No brownie next to another brownie: 570,240
iii) Chocolate biscuits kept together: 8,709,120.
What is the arrangements formula?The number of possible arrangements of a set of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
In item a, if the brownies cannot be together, we have that:
In 8 of the 11 positions(combination), the arrangements will be of 4! and 4!, due to the 4 brownies and the 4 cupcakes.In the remaining 3 positions, they will be organized in 3! ways.Hence the number of ways to organize the cupcakes is:
[tex]C_{11,8} \times 4! \times 4! \times 3! = \frac{11!}{8!3!} \times 4! \times 4! \times 3! = 570,240[/tex]
In item b, the chocolate biscuits have to be kept together, hence:
The 4 biscuits can be ordered in 9 positions, from 1-4 to 9-12.In these positions, they are arranged in 4! ways.The remaining biscuits are arranged in 8! ways.Hence the number of ways that the biscuits can be arranged is:
9 x 4! x 8! = 8,709,120.
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The local grocery store is having a sale on sports drinks. For a particular brand ofsports drink, a 12-pack of 16-ounce bottles costs $10. 76. What is the unit price(per ounce) for the sports drink? Round your answer to the nearest cent.
The 12-pack contains bottles of 16 ounces each.
The total content of sports drinks is 12 × 16 = 192 ounces.
The unit price per ounce is the ratio of the total price to the total contents:
[tex]p=\frac{10.76}{192}=0.06[/tex]The unit price per ounce is $0.06
Decide
{(8,0), (5,7), (9,3), (3,8)}
if each relation is a function.
Since each input value (domain) leads to only one output value, therefore each relation classifies as a function.
An ordered pair set is known as a relation. Each ordered pair's collection of first components is known as the domain, and its set of second components is known as the range.
A function (f) is a relation that gives each value in the domain a single value from the range.
Its given that - (8,0), (5,7), (9,3), (3,8)
Mapping:
Domain Range
8 → 0
5 → 7
9 → 3
3 → 8
In other words, classify the relationship as a function if each input value (domain) results in just one output value. Do not classify the connection as a function if any domain produces two or more outputs.
As a result, the relationship given is a function.
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Find the surface area of each figure. Round your answers to the nearest hundredth. DO
NOT leave in terms of pi.
The surface area of the figure is calculated as 150.72 [tex]mi^2[/tex] and when rounded off to the nearest hundredth, it comes out as 151 [tex]mi^2[/tex].
What is Surface area?A solid object's surface area can be stated as a measurement of the overall space that the object's surface takes up. As an alternate, surface area can also be described as the area of the entire outer part, or which is said as the uppermost layer of any kind of 3D object.
Square units are used in the calculation. The total area of all the outside surfaces makes up the surface area of a three-dimensional object, which is also expressed in square units.
As an example, we can take that in order to find the exact surface area of a cuboid, we have to add the areas of all 6 faces.
In this figure, we can see that it can be stated as a cylinder.
So, as we know the formula of the surface area of a cylinder can be written as:
2[tex]\pi[/tex]rh + 2[tex]\pi r^2[/tex]
Here r = 8/2
=4 mi
h = 2 mi
Thus, putting the values, we have,
Surface area = [2 x 3.14 x 4 x 2] + [2 x 3.14 x 4 x 4]
= 50.24 + 100.48
= 150.72 [tex]mi^2[/tex]
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Temperature (°C) Number of People Day х у 1 20 280 2 24 360 3 36 450 4 32 420 5 2 28 400 ON 38 500 7 34 475 8 26 520 Question: The table shows data for the number of people using a swimming pool over 8 days in summer, and the corresponding maximum temperature (in degrees Celsius) on each day. A Find the equation of the line of best fit for the data. Round decimals to the nearest tenth. B. Can a set of data have more than one line of best fit? Why or why not?
First Step: Calculate the mean of the values in X and Y
[tex]\begin{gathered} \bar{x}=\frac{20+24+36+32+28+38+34+26}{8}=29.75 \\ \bar{y}=400.625 \end{gathered}[/tex]Second step: we have to find the sum of Squares and sum of products
Third step: find the linear equation
[tex]\begin{gathered} Y=aX+b, \\ a=\frac{SP}{SS}=\frac{3201.25}{275.5}=11.61978 \\ b=\bar{y}-a\cdot\bar{x}=54.93648 \\ Y=11.61978X+54.93648 \end{gathered}[/tex]A person takes 50 minutes average to get to work. Time may vary by 10 minutes depending on traffic. Drag and drop the correct number or equation in each box to make the sentences true. "If the time taken by the person to get to work is T minutes, the equality that models this situation is_____ the minimum time taken by the person to get to work is _____min, the maximum time taken is____min.
Answer:
"If the time taken by the person to get to work is T minutes, the equality that models this situation is | t - 50 | = 10 the minimum time taken by the person to get to work is 40 min, the maximum time taken is 60 min.
Step-by-step explanation:
The difference between the time and 50 minutes is 10 minutes.
This can be expressed as:
|t - 50| = 10The minimum and maximum time can be found by solving the equation above:
t - 50 = 10 ⇒ t = 60 minutes,t - 50 = - 10 ⇒ t = 40 minutes.The blanks to be filled in as:
1) | t - 50 | = 10,2) 40,3) 60.what is the area of a triangle with a base of 9units and a height of 7units ?
The area of a triangle is given by
[tex]A=\frac{1}{2}\cdot b\cdot h[/tex]Where b is the base and h is the height of the triangle.
Let us substitute the given values of base and height into the above formula
[tex]\begin{gathered} A=\frac{1}{2}\cdot b\cdot h \\ A=\frac{1}{2}\cdot9\cdot7 \\ A=\frac{63}{2} \\ A=31.5 \end{gathered}[/tex]Therefore, the area of the triangle is 31.5 square units.
what is the value that will correctly replace the missing part? 6(2x + 4) = ? + 24
Answer:?=12x
Step-by-step explanation: 6(2x+4)=?+24, 6 x 2x= 12x. 6 x 4= 24, 24 is already in the equation, so 12x is our missing number.
Let h(x) = (fog)(x) =
f(x) =
4
(x-7) ²
Find f(x) given g(x) = x − 7.
-
F(x)= ?
Answer:
[tex]\frac{4}{x2}[/tex]
Step-by-step explanation:
h (x) = log (N) = [tex]\frac{4}{x -2} {2}[/tex]
g (x) = (x - 1)
g (x) = [tex]\frac{4}{x2}[/tex]
Aisha and her children went into a bakery and will buy cupcakes and brownies. Each cupcake costs $3 and each brownie costs $2.25. Aisha has a total of $15 to spend on cupcakes and brownies. Write an inequality that would represent the possible values for the number of cupcakes purchased, c, and the number of brownies purchased, b.
The inequality equation is 3c + 2.25b <=15 which represents the possible values of cupcakes and brownies that can be purchased by Aisha with the given amount of money.
Cost of each cupcake = $3
Cost of each brownie = $2.25
Total money available with Aisha to spend on cupcakes and brownies = $15
Let c represent the number of cupcakes purchased by Aisha and b represent the number of brownies purchased by Aisha
Formulating the inequality equation we get the following:
Cost of each cupcake*Number of cupcakes purchased + Cost of each brownie*Number of brownies purchased <= Total money available with Aisha
3c + 2.25b <=15
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Which answers choice correctly illustrates the quotient as a fraction A) 913 ÷ 29 = 31 14/29B) 852 ÷ 16 = 53 5/16C) 200 ÷ 46 = 4 8/25D) 852 ÷ 16 = 53.25
Using long division:
So:
[tex]\begin{gathered} \frac{913}{29}=_{\text{ }}Quotient\frac{remainder}{_{\text{ }}divisor} \\ so\colon \\ \frac{913}{29}=31\frac{14}{29} \end{gathered}[/tex]Answer:
A
how to solve a sequence
For the first sequence
Let a1 = 2
2, 9, 16, 23, ...
Recursive Formula
[tex]a_n=a_{n-1}+7[/tex]Explicit Formula
[tex]a_n=2+7(n-1)[/tex]For the second sequence
Let a1 = 2
2, 14, 98, 686, ...
Recursive Formula
[tex]a_n=7(a_n-1)[/tex]Explicit Formula
[tex]a_n=2\cdot7^{n-1}[/tex]Determine the equation of the line that passes through the points (0,−10) and (−8,1).
Solution:
Given the points below;
[tex]\left(0,−10\right)\text{ }and\text{ }(−8,1)[/tex]To find the equation of the line that passes through the points, we will apply the formula below
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]Where
[tex]\begin{gathered} (x_1,y_1)=(0,-10) \\ (x_2,y_2)=(-8,1) \end{gathered}[/tex]Substitute the values of the coordinates into the formula above
[tex]\begin{gathered} \frac{y-(-10)}{x-0}=\frac{1-(-10)}{-8-0} \\ \frac{y+10}{x}=\frac{1+10}{-8} \\ \frac{y+10}{x}=-\frac{11}{8} \\ Crossmultiply \\ 8(y+10)=-11(x) \\ 8y+80=-11x \\ 11x+8y+80=0 \end{gathered}[/tex]Hence, the equation of the line is
[tex]11x+8y+80=0[/tex]The graph is shown below with the points indicated using a graphing tool
consider the three circles, where R represents the radius of each circle which statement is true?
If two shapes are similar to each other, they have the same shape, but not necessarily the same size.
All circles are similar to each other. All points on the circumference of any circle are equidistant from its center.
The ratio of the radii of the pair of circles will give the scale factor.
The correct option is the SECOND OPTION.
If OA-OB-OC and if AOB = 9x + 20, BOC = 7x - 6 and AOC = 142 find BOC
The angle BOC has a measure of 50 degrees
How to evaluate the measure of the angle?From the question, the given parameters about the angles are:
OA-OB-OCAOB = 9x + 20BOC = 7x - 6AOC = 142The above parameters implies that
AOC = AOB + BOC
Next, we substitute the angle measurements in the above equation
So, we have
142 = 9x + 20 + 7x - 6
Evaluate the like terms
So, we have the following equation
142 = 16x + 14
Evaluate the like terms again
So, we have the following equation
16x = 128
Divide both sides by 16
x = 8
Substitute x = 8 in BOC = 7x - 6
BOC = 7 x 8 - 6
Evaluate
BOC = 50
Hence, the measure of the angle is 50 degrees
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The angle BOC has a measure of 50 degrees
What is Angle?An angle is formed when two straight lines or rays meet at a common endpoint
If OA-OB-OC and if AOB = 9x + 20, BOC = 7x - 6 and AOC = 142
We need to find BOC
We have AOC = AOB + BOC
142=9x + 20+7x-6
142=16x+14
Subtract 14 from both sides
142-14=16x
128=16x
Divide both sides by 16.
8=x
Now put x value in BOC = 7x - 6
BOC = 7x - 6
=7(8)-6
=56-6
BOC=50
Hence If OA-OB-OC and if AOB = 9x + 20, BOC = 7x - 6 and AOC = 142 then BOC=50.
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t's find profit or loss percents. C. P. = Rs 200, S. P. = Rs 220
Answer:
10% profit
Step-by-step explanation:
since the item was sold for more than it cost, this is a profit
percent profit = [tex]\frac{P}{C}[/tex] × 100%
profit P = SP - CP = Rs 220 - Rs 200 = Rs 20 , then
% profit = [tex]\frac{20}{200}[/tex] × 100% = 0.1 × 100% = 10%
Question 4 of 10 What is the scale factor from ABC to DEF? A BO 72 42 35 65 B 66 O A. 2 OB. O O D. 6 Ico
Answer:
C
Step-by-step explanation:
the scale factor is the ratio of corresponding sides, image to original, so
scale factor = [tex]\frac{EF}{BC}[/tex] = [tex]\frac{11}{66}[/tex] = [tex]\frac{1}{6}[/tex]
The total amount of candy sold at Cassandra's Candy Corner can be represented by the function C(x) = 4x3 + 16x2 + 60x + 648, where x represents the number of years since the store opened. The amount of types of candy can be modeled by the linear function T(x) = 2x + 12. Which expression represents the amount of candy sold each year per type at Cassandra's Candy Corner?
4x3 + 16x2 + 58x + 636
4x3 + 16x2 + 62x + 660
2x2 – 4x + 54
2x2 + 4x + 54
The expression which correctly represents the amount of candy sold each year per type at Cassandra's Candy corner is; 2x2 – 4x + 54.
Polynomial divisionIt follows from the task content that the expression which shows the amount of candy sold each year per type is to be determined.
Since, the function, C (x) = 4x³ + 16x² + 60x + 648 represents the total amount of candy sold while, T(x) = 2x + 12 represents the amounts of types of candy.
Therefore, the amount of candy sold each year per type is; C(x) ÷ T(x).
Hence, the result of the polynomial division as in the attached image is; 2x² - 4x + 54.
Ultimately, the amount of candy sold each year per candy is represented by the expression; 2x² - 4x + 54.
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Question
Which expression is equivalent to -40(4) +2³?
The expression equivalent to -40(4) +2³ is -152 by the concept of BODMAS Rule.
What is equivalent expression?It is generally understood that two things are equivalent if they are the same. Similar to this, analogous mathematical expressions are those that are the same even if they appear to be different. However, when the values are plugged into the expression, both expressions provide the same outcome.
What is BODMAS rule?BODMAS is formally known as Brackets (Numbers inside the Bracket always comes first)
Priority for brackets is Orders in a bar (the power)
Division
Multiplication
Addition
Subtraction
To solve the above expression, follow the above order
-40(4) +2³ = -160+8 = -152
Therefore, the expression equivalent to -40(4) +2³ is -152.
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Please help me with this, show full work for all questions, thank you!Question 3
Answer:
0.375
Explanation:
The probability of red and purple can be calculated as the frequency for rean and purple over the total frequency
Red has a frequency of 4
Orange has a frequency of 1
Yellow has a frequency of 1
Green has a frequency of 7
Blue has a frequency of 1
Purple has a frequency of 2
The total frequency is
4 + 1 + 1 + 7 + 1 + 2 = 16
And the frequency for red and purple is
4 + 2 = 6
Then, the probability is equal to
P = 6/16 = 0.375
So, the answer for question 3 is 0.375
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The average rate of change of the function is found as 1.
What is termed as the rate of change of function?The rate of change function has been described as the rate during which one quantity changes in relation to another. The rate of change from y coordinates to x coordinates can be calculated as Δy/ Δx = (y2 - y1)/ (x2 - x1 ).For the given question;
The function is given by the equation;
g(x) = -x² - 9x + 27
The interval of the function lies as;
-9 ≤ x ≤ -1.
Let,
a = -1 ans b = -9
Then,
g(a) = g(-1), Put x = -1 in the function.
g(-1) = -(-1)² - 9(-1) + 27
g(-1) = 35
Now, g(b) = g(-9), Put x = -9 in the function.
g(-9) = -(-9)² - 9(-9) + 27
g(-9) = 27
Thus, the average rate of change of the function is-
Average rate of change = [g(a) - g(b)]/[a - b]
= [35 - 27]/[-1 + 9]
= 8/8
= 1
Thus, the average rate of change of the function is found as 1.
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Given that (3, 2, –6) and (–2, 5, 1) are solutions of two equations in a system of three linear equations, which of the following is true about the system?
The system can only be consistent and independent.
The system can be either inconsistent and independent or consistent and dependent.
The system can be either inconsistent and dependent or consistent and independent.
The system can only be inconsistent and dependent.
The statement which is true about the system of three linear equations is that: B. the system can be either inconsistent and independent or consistent and dependent.
What is a system of three linear equations?A system of three linear equations can be defined as a type of algebraic equation of the first order that has three (3) variables with each of its term having an exponent of one (1).
In Mathematics, a system of three linear equations is considered as a consistent system when it has at least one solution. However, a system of three linear equations is considered as an inconsistent system when it has no real solution.
Additionally, a system of three linear equations is considered as an independent system when it possesses exactly one solution while it is a dependent system if it has an infinite number of solutions.
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In an all boys school, the heights of the student body are normally distributed with a
mean of 67 inches and a standard deviation of 5 inches. Using the empirical rule,
determine the interval of heights that represents the middle 95% of male heights
from this school.
The interval of heights calculated by using empirical rule which represents the middle 95% of male heights from this school is between 57 inches and 77 inches.
What is Empirical rule?
Empirical rule has three rule of statement based on the normal distribution and they as as follows:
1) About 68% of the x values lie between 1 standard deviation below and above the mean.
2) About 95% of the x values lie between 2 standard deviations below and above the mean.
3) About 99.7% of the x values lie between 3 standard deviations below and above the mean.
According to the question, let us assume 'x' be a random variable representing the heights of males from this school. With the mean and standard deviation given, then the Empirical Rule number two states that the:
From the information given,
mean = 67 inches
Standard deviation = 5 inches
We want to determine where 95% of x values lies. This is 2 standard deviations from the mean Therefore,
2 standard deviations = 2 × 5 = 10 inches
The heights are
67 - 10 = 57 inches and
67 + 10 = 77 inches
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The registrars office at Acc predicts that 90% of the 6,950 spaces open on various math classes will be available during the first week of registrationA. The percent of spaces that will be filled after the first week of registration is %B. A good estimate of the number of spaces that will be filled after the first week of registration is Spaces
A: 10%
B: 6950*10%=695
parallelogram ABCD is below. m < D = 130° and m < B = (3x-1.5)° . solve for x and round to the nearest whole number.
Given:
m∠D = 130 degrees
m∠B = (3x - 1.5) degrees
Let's solve for the value of x.
A parallelogram is a quadilateral that has equal opposite angles and equal opposite sides.
Since a parallelogram has equal opposite angles, measure of angle D and measure of angle B are equal.
Thus, we have the equation:
m∠B = m∠D
(3x - 1.5) = 130
Solve for x.
Remove the parentheses:
3x - 1.5 = 130
Add 1.5 to both sides:
3x - 1.5 + 1.5 = 130 + 1.5
3x + 0 = 131.5
3x = 131.5
Divide both sides by 3:
[tex]\begin{gathered} \frac{3x}{3}=\frac{131.5}{3} \\ \\ x=43.83\approx44 \end{gathered}[/tex]Therefore, the value of x rounded to the nearest whole number 44
ANSWER:
44
Which number is enquivalent to 6/10
We have the fraction 6/10
For finding the equivalent number, we divide 6 by 10:
6 / 10 = 0.6
0.6 is the equivalent number
We have 6 in the numerator and 10 in the denominator, if we calculate any mathematical operation to both, we will find the equivalent fractions.
Let's see two examples:
1. Let's divide by 2:
6 divided by 2 is 3; and 10 divided by 2 is 5. Then our new equivalent fraction is
[tex]\frac{3}{5}[/tex]2. Let's multiply by 3:
6 multiplied by 3 is 18; 10 multiplied by 3 is 30. Then a second equivalent fraction is:
[tex]\frac{18}{30}[/tex]We can calculate additional equivalent fractions, using the same operation for both: numerator and denominator.
For calculating the equivalent fraction in hundreds, we will use the initial decimal equivalent we calculated at the beginning: 0.6
0.6 = 6/10 and we multiply it by 10 numerator and denominator
6 * 10 = 60 and 10 * 10 = 100. Then the fraction is 60/100
20 divided by 10 is 2 and 100 divided by 10 is 10, so the equivalent fraction is 2/10
This case is exactly the same than the previous we solved:
?/10 = 120/100
As you can see the first fraction is notated in tens and the second is notated in hundreds. Therefore, if you divide 120 between 10, what is the result?
The midpoint of segment AB is (2,4). If the coordinates of point B are (5,7), find the coordinates of point A.
A (1, 1)
B (-1, 1)
C (1, -1)
D (-1, -1)
Answer:
I don't know why you asking me??
Answer:-1,1
Step-by-step explanation:
-1,1
What is a(b(x)) if a(x) = 3x 2 and g(x) = -3x + 1?
The equivalent composite function of the given one is expressed as; -9x + 5
What is a function?Function is a type of relation, or rule, that maps one input to specific single output. Composite functions are also known as function of a function.
Given the following functions as;
a(x) = 3x+2 and
b(x) = -3x + 1
To determine the value of a(b(x));
a(b(x)) = a(-3x+1)
a(b(x)) = 3(-3x+1) + 2
a(b(x)) = -9x + 3 + 2
a(b(x)) = -9x + 5
Therefore, This gives the equivalent composite function of the given one.
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Describe a series of transformations Matt can perform to device if the two windows are congruent
A transformative sequence is a particular arrangement of transforming events. This suggests that a series of transformations may manage more than one transition, and that the order in which they occur is crucial. A and B are similar in this case.
Congruent is what?When two figures or objects in geometry have the same shapes, sizes, or are mirror images of one another, they are said to be congruent.
Formally, two sets of points are said to be congruent if, and only if, an isometry, which is a collection of rigid motions including translation, rotation, and reflection, can transform them into one another.
This shows that resizing an object will not allow it to be properly aligned with another object, only by moving and reflecting it. Therefore, two independent plane figures on a piece of paper are congruent if we can cut them out and then precisely line them up. The paper might be distributed.
Each box is the same size in terms of length and width. The only change is where the figure is located.
Transformations can be divided into four categories: translation, rotation, reflection, and dilation.
Two figures are said to be "congruent" if they can be positioned perfectly over one another. Congruent refers to things that are exactly the same size and shape.
Hence, A and B are congruent.
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A scientist mixes water (containing no salt) with a solution that contains 15% salt. She wants to obtain 105 ounces of a mixture that is 5% salt. How many ounces of water and how many ounces of the 15% salt solution should she use?
Let's call X the ounces of water and Y the ounces of the salt solution.
Of she
Are the triangles congruent using AAS?
True
False