The allowance of each person is
You: $40Friend: $32How to determine the amount of each person's allowance?From the question, the tape diagram that can be used in our computation is given as
you [][][][][]
friend[][][][]
Counting the number of boxes, we have
You = 5
Friend = 4
Next, we represent the boxes as a ratio
So, we have
You : Friend = 5 : 4
This means that
You = 5/9 * Total allowance
Friend = 4/9 * Total allowance
From the question, we have
Total allowance = $72
Substitute the known values in the above equation
So, we have the following equation
You = 5/9 * 72
Friend = 4/9 * 72
Evaluate the products
You = 40
Friend = 32
Hence, the amount of each person's allowance is $40 and $32, respectively
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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
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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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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Please Help!!!Use division to determine if the binomial is a factor. Show all work (x^3+7x^2+16x+12) ; (x+2)
Clearly, we can see that x+2 is a factor of the given polynomial.
3x^3-15x-13/x+2
Using synthetic division
The quotient when [tex]3x^{3} -15x-13[/tex] is divided by (x+2) using the synthetic division is ([tex]3x^{2} -6x-3[/tex]) and remainder is -7.
According to the question,
We have the following expressions:
[tex]3x^{3} -15x-13[/tex] is divided by (x+2)
First, we will look at some of the rules of the synthetic division:
We have to make the quotient in such a way that it is same as the term with the highest power in the dividend.
We change signs after solving using one complete term of the quotient.
We have to solve this using the synthetic division method:
x+2 )[tex]3x^{3} -15x-13[/tex]( [tex]3x^{2} -6x-3[/tex]
[tex]3x^{3} +6x^{2}[/tex]
_-___-_____
[tex]-6x^{2} -15x-13[/tex]
[tex]-6x^{2} -12x[/tex]
+ +
_________
-3x-13
-3x-6
+ +
_______
-7
Hence, the quotient when [tex]3x^{3} -15x-13[/tex] is divided by (x+2) using the synthetic division is ([tex]3x^{2} -6x-3[/tex]) and remainder is -7.
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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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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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Need help with this ASAP Ignore the top video.
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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decide if you think the method described would result in a good random sample, and explain your answer. random phone numbers are dialed in a given area code to survey people as to whether or not they've needed the services of a food pantry to feed their families.
The given situation represents a random sample because, in statistics, a simple random sampling refers to the subset of individuals chosen from a larger set called population, where the sample is chosen randomly.
In this case, the dialed number are a random event, so it can be called a simple random sample.
Using the point (-5, 4) has one endpoint, State a possible location of the other endpoint given the line segment is 7 units long. Apply the distance formula to create a possible endpoint(s) from a given location.
EXPLANATION
Since the line segment is 7 units long, we can apply the following relationship:
(x_1+ 7 , y_1) = (x_2 , y_2)
[tex](-5+7)=2[/tex]The coordinate of the endpoint is as follows:
[tex](x_{endpoint},y_{endpoint})=(2,4)[/tex]We can get to this point by applying the distance formula as follows:
[tex]distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Applying the square power to both sides:
[tex]7^2=(x_2-(-5))^2+(y_2-4)^2[/tex]Subtracting numbers:
[tex]49=(x_2+5)^2+(y_2-4)^2[/tex]Now, if the x_2 coordinate is -3, the value of y_2 will be as follows:
[tex]49=(-3+5)^2+(y_2-4)^2[/tex][tex]49=4+(y_2-4)^2[/tex]Subtracting -4 to both sides:
[tex]45=(y_2-4)^2[/tex]Applying the square root to both sides:
[tex]\sqrt{45}=y_2-4[/tex]Adding +4 to both sides:
[tex]4+\sqrt{45}=y_2[/tex]In conclusion, the equation to get the coordinate from a given point is,
[tex]49=(x_{2}+5)^{2}+(y_{2}-4)^{2}[/tex]Write each number
1. 1,000 more than 3,872
The value for a number that is 1000 more than 3,872 will be 4,872
In the given question, it is stated that we have to find out the value of the expression given. The expression states that we have to find out a number that is 1000 more than 3872.
This can easily be done. To find out the value for a number that is 1000 greater than 3872, we just need to add the value to the number i.e. we need to add 1000 to 3872. Let the new number be 'x'.
So, by solving this condition, we get
=> x = 3872 + 1000
=> x = 4872
Here we get x = 4872.
Hence, 1000 more than 3,872 will be 4,872.
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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]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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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%
Find :
1) (-50+1)÷49
Answer: The answer is -1
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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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]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
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
Liz does screen-printing. When she screen-prints a batch of T-shirts, there is an initial set-up time of 15 minutes. After that, it takes 3 minutes to print each shirt. How long does it take to screen-print a batch of 14 shirts?
The time taken to screen-print a batch of 14 shirts are 42 minutes
In the above question, it is given that,
Lizz does screen-printing and she screen-prints a batch of T-shirts
The time taken in initial set-up to screen print the first t-shirt is = 15 minutes
After that,
The time taken in screen printing further t-shirts of the batch is = 3 minutes
We need to find the time taken to screen-print a batch of 14 shirts = 3 x 14 = 42 minutes
Hence, the time taken to screen-print a batch of 14 shirts are 42 minutes
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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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Are the triangles congruent using AAS?
True
False
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.
1. Find the amount of tax owed: vacant land valued at $24,000.00; assessed at 18%; taxed at $11.00 per hundred dollars worth of property.
The amount of tax owed is $ 6,960.
It is given in the question that:-
Vacant land value = $ 24,000
Tax percentage = 18 %
Tax per hundred dollars = $ 11
We have to find the tax owed.
Tax = (18/100)*24000 = $ 4,320
Tax per hundred for $ 24000 land = 11*(24000/100) = $ 2,640
Hence, total tax owed = $ 4,320 + $ 2,640 = $ 6,960
Percentage
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.
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Write an equation in point-slope form for the line that passes through the point with the given slope.
(2, 1); m=−32
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ - 32 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies {\Large \begin{array}{llll} y-\stackrel{y_1}{1}=\stackrel{m}{- 32}(x-\stackrel{x_1}{2}) \end{array}}[/tex]
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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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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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.
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?