After 10 years students in both schools are same.
Algebra is a branch of mathematics that uses mathematical expressions to represent problems. To form a meaningful mathematical expression, variables such as x, y, and z are combined with mathematical operations such as addition, subtraction, multiplication, and division. It teaches you how to solve a problem by following a logical path. As a result, you will have a better understanding of how numbers function and interact in an equation. You will be able to do any type of math better if you have a better understanding of numbers.
There are two high schools in a small town.
High school A has currently 900 students and is projects to grow by 30 students each year
Similarly
High school B has currently 750 students and is projected to grow by 45 students each year.
To find the equation for each situation in terms of t years.
also in how many years t' the number of students in both high schools would be same?
Given
The initial strength of school A = 900
the increasing rate of students = 30 students per year
i.e students in 1 year = 30
students in t years = 30t
Total students of school A after 't' years = 900+ 30t
⇒ A = 600+ 65t
The initial strength of school B = 750
increasing rate of students = 45 per year
i.e. student in 1 year = 45
⇒ student in 't' years = 45t
Total students of school B in 't' years = 950 + 30t
=> B=950+30t
Now to find no. of years 't' when students in both schools are the same i.e. A =B
⇒ 900+ 30t = 750 + 45t
⇒ 45t-30t = 900-750
⇒ 15t = 150
⇒t= 150 /15
⇒t=10
Therefore after 10 years, students in both schools are the same.
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write an equation in STANDARD FORM of the line that passes through (-6,-10) and has the slope m=1/6
The equation of the line passing through (-6,-10) and having slope m = 1/6 in Standard From is x - 6y = 54 .
In the question ,
it is given that ,
the required line passes through the point (-6,-10) ,
and has slope(m) = 1/6 ,
So , the equation of the line that passes through the given point and slope ,
is given by ,
(y - (-10)) = 1/6(x -(-6))
(y + 10) = 1/6(x + 6)
On cross multiplication ,
we get ,
6(y + 10) = x + 6
6y + 60 = x + 6
x - 6y = 60 - 6
x - 6y = 54
Therefore , The equation of the line passing through (-6,-10) and having slope m = 1/6 in Standard From is x - 6y = 54 .
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Construct a 95% confidence interval for the number of toys that are from china in a random sample of 210 toys. It is estimated that 70% of all the world's toys come from china. Use the following Desmos Applet to help What would be the z-critical value? (two- decimal places) Answer 1 Choose... B) What is the standard error or standard deviation (Sigma value)? Answer 2 Choose... C) What is the margin of error? (Round to nearest whole number) Answer 3 Choose... D) What is the expected number of toys in random sample of 210 toys? Answer 4 Choose... E) What is the upper limit of confidence interval? Answer 5 Choose... F) What is the lower limit of confidence interval?
For the 95% confidence interval for the number of toys that are from China in a random sample of 210 toys, using the z-distribution, we have that:
a) The critical value would be of z = 1.96.
b) The standard error is of: 0.0316
c) The margin of error is of: 6%.
d) The expected number of toys in the sample is of: 147.
e) The lower limit of the interval is of: 64%.
f) The upper limit of the interval is of: 76%.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds obtained by the rule presented below as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The estimate and the sample size for this problem are given as follows:
[tex]\pi = 0.7, n = 210[/tex]
Hence the expected number of toys in random sample of 210 toys is of:
0.7 x 210 = 147.
The standard error is calculated as follows:
[tex]s = \sqrt{\frac{\pi(1-\pi)}{n}} = \sqrt{\frac{0.7(0.3)}{210}} = 0.0316[/tex]
The margin of error is the multiplication of the critical value and of the standard error, hence:
M = 1.96 x 0.0316 = 0.06 = 6%.
The bounds of the interval are the estimate plus/minus the margin of error, hence they are given as follows:
Lower bound: 70% - 6% = 64%.Upper bound: 70% + 6% = 76%.More can be learned about the z-distribution at https://brainly.com/question/25890103
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A triangular region of a community college parking lot was measured. The measure of the first angle of this triangle is double the measure of the second angle. The measure of the third angle is 117° greater than double the measure of the first angle. What are the measurements of all three angles?
The value of the first angle is 18
The value of the second angle is 9
The value of the third angle is 153
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Let the second angle be = x ____(1)
The measure of the first angle of this triangle is double the measure of the second angle.
This means,
First angle = 2x _____(1)
The measure of the third angle is 117° greater than double the measure of the first angle.
This means,
Third angle = 117 + 2(2x) = 117 + 4x _____(3)
From (1) (2) and (3) we get,
x + 2x + 117 + 4x = 180
7x + 117 = 180
7x = 180 - 117
7x = 63
x = 9
The value of first angle is 2x = 2 x 9 = 18
The value of the second angle is x = 9
The value of third angle is 117 + 4x = 117 + 4 x 9 = 117 + 36 = 153
Thus,
The value of the first angle is 18
The value of the second angle is 9
The value of the third angle is 153
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NEED ASAP PLSSSS
The arc length of this circle is 9.42 inches. Determine the length of the radius.
Complete your work in the space provided.
The length of radius of the given circle is equivalent to 6
Calculating length of an arcA circle's arc is referred to as a portion or section of its circumference. A chord of a circle is a straight line that can be formed by joining the arc's two ends.
The formula for calculating the length of an arc is expressed as:
L = rФ
where
r is the radius of the circle
Ф is the angle subtended.
Given the following parameters
L = 9.42
Ф = π/2
Determine the radius
r = L/Ф
r = 9.42/(π/2)
r = 2(9.42)/(π
r = 6
This gives the length of the radius of the circle.
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which expression includes a coefficient of 2?
A.
[tex]x {}^{2} - 5[/tex]
B. 4x + 2
C. 3(x+2)
D.
[tex]2x {}^{3} - 1[/tex]
Answer:
D
Step-by-step explanation:
The coefficient is the number before the varaible x.
How many subsets does the set S, seasons of the year, have? S={ Summer, Spring, Fall, Winter }.
The number of subsets that the set S , seasons of the year is 16 .
In the question ,
it is given that
the Set S have elements as the seasons of the year , that is
Set S [tex]=[/tex] { Summer , Spring , Fall , Winter }
So , the number of elements that are present in the set S = 4 ,
we know that the number of subsets of the set having n elements is = 2ⁿ .
So , the number of subsets of the set S having 4 elements is = 2⁴ = 16
Therefore , The number of subsets that the set S , seasons of the year is 16 .
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The shoe sizes of a group of middle school girls are shown.
5.5 6 7 8.5 6.5
6.5 8 7.5 8 5
If a shoe size of 9.5 is added to the data, how does the median change?
Answer: 7
Step-by-step explanation:
Median is the middle number of a data set.
You need to first start off with listing the shoe sizes in numerical order:
5, 5.5, 6, 6.5, 6.5, 7, 7.5, 8, 8, 8.5, 9.5
You have a total of 11 numbers in the set, so you can choose the sixth number in the set, which is 7.
So, 7 is the median number.
The median of current data is 6.5 while by adding 9.5 to the data group the median changes to 6.75.
What are the mode and median?Mode is the highest frequency number while the median is the middle value of a data set after writing in either an increasing or decreasing manner.
For example;
Set { 1,2,2,3,4,5,6} here mode is 2 and median is 3.
As per the given data,
5.5, 6, 7, 8.5 6.5,6.5, 8, 7.5, 8 5
Write the above data in increasing order,
5,5.5,6,6.5,6.5,7,7.5,8,8.5
The median is the middle value thus, 6.5 will be the median.
Now let's add 9.5 to the data group,
5,5.5,6,6.5,6.5,7,7.5,8,8.5,9.5
Now we have two middle values 6.5 and 7
Median = (6.5 + 7)/2 = 6.75
Hence "The median of current data is 6.5 while by adding 9.5 to the data group the median changes to 6.75".
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3/1 divided by 3/4 in simplest form
Answer:
4
Step-by-step explanation:
3/1=3
hence 3/(3/4 )= 3 x4/3=4
Answer:
4
Step-by-step explanation:
keep switch flip
3/1 * 4/3 = 12/3 = 4
A water skier is towed 65 m to the south of the starting point, and then is turned 40° cast of south for another 35m. What is the skier’s displacement from the starting point?
Using cosine law,
d^2 = 65^2 + 35^2 - 2(65)(35)cos140
= 8935.5022
d = sqrt(8935.5022)
= 94.5 m
Angle = inverseCos(35sin40 / 94.5) = 76.23 degrees South of East
1:
Give examples of two points that you could use to plot the graph of the function
f(x) = (3x³ + 2)/(x2-5).
The two points that could be used to plot the graph of the function (0, -0.4) and (-0.874, 0)
In this question, we have been given a function f(x) = (3x³ + 2)/(x^2-5).
We need to plot the graph of the function.
We find some coordinates of point on the graph of function.
For x = 0,
f(0) = (30³ + 2)/(0^2-5)
f(0) = 2/(-5)
f(0) = -0.4
For f(x) = 0,
0 = (3x³ + 2)/(x^2-5)
(3x³ + 2) = 0
3x³ = -2
x = -0.874
for x = 1,
f(1) = (3(1)³ + 2)/(1^2-5)
f(1) = 5/(1 - 5)
f(1) = 5/(-4)
f(1) = -1.25
The graph of function f(x) = (3x³ + 2)/(x2-5) is as shown below.
Therefore, the two points that could be used to plot the graph of the function (0, -0.4) and (-0.874, 0)
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A chemist mixes 125 milliliters of a solution that is 18% acid with 500 milliliters of pure acid.
Answer the questions below. Do not do any rounding.
(a) How many milliliters of acid are in the resulting mixture?
(b) What percentage of the resulting mixture is acid?
The amount of milliliters of acid that are in the resulting mixture is 522 ml and the percentage of the resulting mixture is 83.6%.
How to find the milliliters of acid?a. Milliliters of acid:
Milliliters of acid = ( .18 x 125ml) +500 ml
Milliliters of acid = 522.5ml
b. Percentage of the resulting mixture
Percentage of the resulting mixture = 522.5ml /(125ml + 500 ml)
Percentage of the resulting mixture = 522.5ml / 625 ml × 100
Percentage of the resulting mixture =83.6%
Therefore the milliliters of acid is 522.5ml.
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Each student in Mr. Jones's class has two standard number cubes. Each student records the number of rolls it takes until he or she rolls doubles. The results are shown on the dot plot. Based on the results, what is the probability of needing exactly 6 rolls to get doubles?
Answer:1/5
Step-by-step explanation:
it correct
Answer:
Step-by-step explanation:
Second part to the answer is 3/20
18x^5-3x^7+12x4 factor the following polynomial with the greatest common factor
Factoring the given polynomial expression with the greatest common factor gives 3x⁴(6x - x³ + 4)
Factoring a Polynomial expressionFrom the question, we are to factor the giving polynomial expression with the greatest common factor
The given polynomial expression is
18x^5-3x^7+12x4
This can be properly written as
18x⁵ - 3x⁷ + 12x⁴
First, we will determine the greatest common factor of the coefficients in the expression.
The coefficients in the expression are 18, 3, and 12.
The greatest common factor of 18, 3, and 12 is 3.
Now, we will determine the greatest common factor of x⁵, x⁷, and x⁴.
The greatest common factor of x⁵, x⁷, and x⁴ is x⁴.
Thus,
The greatest common factor of the polynomial expression is 3x⁴.
Now,
Factoring the polynomial with the greatest common factor
18x⁵ - 3x⁷ + 12x⁴
3x⁴(6x - x³ + 4)
Hence, the result of factoring the polynomial is 3x⁴(6x - x³ + 4)
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Determine the range of f(x) = |x| − 4.
The range of the function f(x) = |x| - 4 is [-4, ∞).
What do you mean by domain and range of a function?
For any function y = f(x), Domain is the set of all possible values of y that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.
We have -
f(x) = |x| - 4
According to question, we have -
f(x) = |x| - 4
We will draw the graph of the function -
f(x) = |x| + 4
Range is the set of value along the [y] - axis.
We can see that, the values of range of [y] variable is from -
[-4, ∞)
Therefore, the range of the function f(x) = |x| - 4 is [-4, ∞).
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200% of x is b min. Find the amount
Answer:
The answer is 269 in.
hope this helps!
Sorry I’m late oops
Step-by-step explanation:
A restaurant customer left $1.30 as a tip. The tax was 6 and the tip was 6% of the cost including tax.
a. What piece of information is not needed to compute the bill after tax and tip?
b. What was the total bill?
a) The piece of information not required to compute the bill after tax and tip is the cost of the item purchased by the customer.
b) The total bill paid by the restaurant customer is $22.97.
How is the total bill determined?The total bill the restaurant customer paid represents 100% of $1.30 plus the tip.
Proportionately, the amount can be computed using the percentage of the tip to equate the dollar amount.
The result is the cost of the item plus tax. Then, the total bill includes the cost, tax, and tip.
Tip left by customer = $1.30
Sales tax = 6%
Cost + tax = x
Tip = 6% of x
x = $21.67 ($1.30 ÷ 6%)
The total bill paid is $22.97 ($21.67 + $1.30).
Thus, using proportions, the restaurant customer paid $22.97, which includes the item cost, tax, and tip.
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secx - 2=0
(a) x= pi/3
Step-by-step explanation:
secx - 2=0
secx= 2
x= π/3
that's it
The x-values that satisfy the equation Sec(x) - 2 = 0 are x = π/3 and x = 5π/3.
To verify the given equation, we need to find the value(s) of x that satisfy the equation Sec(x) - 2 = 0.
Sec(x) represents the secant function, which is the reciprocal of the cosine function.
The equation can be rewritten as follows:
Sec(x) = 2
To find the solutions, we can take the reciprocal of both sides:
1 / Cos(x) = 2
Next, we can invert the equation to get the cosine function alone:
Cos(x) = 1/2
The cosine function has a value of 1/2 at two specific angles in the interval [0, 2π]: π/3 and 5π/3.
These angles correspond to the inverse cosine function (arccos), so we have:
x = arccos(1/2) = π/3 or x = arccos(1/2) + 2π = 5π/3
Therefore, the x-values that satisfy the equation Sec(x) - 2 = 0 are x = π/3 and x = 5π/3.
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Now we will calculate the actual probability that all randomly chosen student has a schedule that excludes music theory. We have found that the probability is given as
P=4C38C3
Express your answer as a fraction in simplest form.
The simplified probability that all randomly chosen student has a schedule that excludes music theory is given as follows:
p = 1/14.
How to calculate a probability?The probability of an event in an experiment is obtained as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.
In the context of this problem, these numbers of outcomes are given as follows:
Desired outcomes: [tex]C_{4,3}[/tex]Total outcomes: [tex]C_{8,3}[/tex].The symbol [tex]C_{n,x}[/tex] represents the number of combinations of x elements that can be obtained from a set of n elements, and the combination formula is presented as follows:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Considering the formula presented above, the numeric values of the combinations are obtained as follows:
Desired outcomes: 4!/(3! x 1!) = 4.Total outcomes: 8!/(3! x 5!) = 56.Hence the simplified probability is of:
p = 4/56 = 1/14.
As the quotient of 56 and 4 is of 14.
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Please help! Thanks in advance
Answer:
D
Step-by-step explanation:
You are buying some television time and the station tells you that they reach 120,000 people. They quote you $2.50 CPM (cost per thouand). How much will you have to pay for the time?
The amount that you have to pay for the time is $300.
How to calculate the cost?From the information, the person is buying some television time and the station tells you that they reach 120,000 people and they quote you $2.50 CPM
The cost will be:
= Total people × Cost per thousand
= 120000/1000 × $2.50
= 120 × $2.50
= $300
The amount is $300.
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Find the quotient of 3/5 3/7. Write your answer in the simplest form.
[tex]\cfrac{3}{5}\div\cfrac{3}{7}\implies \cfrac{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{5}\cdot \cfrac{7}{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{7}{5}\implies 1\frac{2}{5}[/tex]
There are 6 people who want to share 26 ride tickets for the carnival. Each person will get an equal number of tickets. How many tickets will each person get? How many tickets will be left over?
Answer:
4 tickets, 2 left over
Step-by-step explanation:
26/6=4.3333 round down to 4
4*6=24 so they can evenly split 24 tickets and will each get 4
26 tickets -the 24 they split evenly = 2 left over
What is tan 30°?
1
60°
90°
√3
2
30°
OA. √2
B. √3
O C. √√3
OD. √3
2
O E 1
OF.
F. 7/3
The value of the given trigonometric function tan30° is equal to ( 1/ √3).
As given in the question,
In the given right angled triangle,
Let us consider triangle be ABC,
Measure of angle A = 30°
Measure of angle B = 90°
Measure of angle C = 60°
Side length BC = 1
Side length AB = √3
Now in triangle ABC,
Value of trigonometric function tan30° is given by:
tan 30° = (opposite side) / ( adjacent side)
⇒tan 30° = BC / AB
⇒tan 30° = 1 / √3
Therefore, the value of the given trigonometric function tan30° is equal to ( 1/ √3 ).
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Angles A and B are supplementary. Determine the measure of angle A if the measure of angle B is 126.4°.
The measure of angle A is 53.6° if angle A and angle B are supplementary angles.
According to the question,
We have the following information:
Angles A and B are supplementary.
Measure of angle B = 126.4°
We know that when two angles are supplementary then it means that the sum of these angles will be 180°.
So, we have the following expression:
Angle A + angle B = 180
Angle A+126.4 = 180
Subtracting 126.4 from both the sides of the equation:
Angle A = 180-126.4
Angle A = 53.6°
Hence, the measure of angle A is 53.6° if angle A and angle B are supplementary.
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What is the domain of the function
y=³√x-1
The domain of the function is real numbers.. The value is x-1 = is a real number
What is meant by domain?The domain of a function is the set of values that we are allowed to enter into our function. This set consists of the x values for a function like f. (x). The set of values that a function can accept as input is known as its range. Once we enter an x value, the function returns this list of values.
Think about the equation y = f(x), where x and y are the independent and dependent variables. If a value for x successfully enables the creation of a single value y using another value for x, it is said to be in the domain of the function f.
A positive number has a positive cubic root.
Zero has a cubic root of zero.
A negative number has a negative cubic root.
Given ,
This implies that any real number's cubic root is also a real number.
y = ³√x-1
³√x-1 = x-1 is a cubic root
x-1 = is a real number
Therefore The value of real number is x-1 = is a real number
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Write an explicit equation for the following
sequence:
4/7,-4, 28, -196, 1372, ...
Answer:
a_n = (4/7)(-7)^(n - 1)
Step-by-step explanation:
a1 = 4/7 = 4/7 × 1 = (4/7)(-7)^0
a2 = -4 = 4/7 × (-7) = (4/7)(-7)^1
a3 = 28 = 4/7 × (-7)(-7) = (4/7) × (-7)^2
etc.
a_n = (4/7)(-7)^(n - 1)
Describe the features of the function that can be easily seen when a quadratic function is given
in the form: y=a(x − ℎ)^2 + and how they can be identified from the equation.
Please help
The function that can easily be seen when a quadratic function is given
in the form: y = a (x − ℎ)^2 + K are
the vertex of the parabolawhere the axis of symmetry of the parabola liesthe focus of the parabola the direction the curve opens toHow to get the required detailsA parabola is given in factored form when it is in the form
y = a (x − ℎ)^2 + K
the factored form can be rearranged
(y - k) = a (x − ℎ)^2
The vertex is v(h, k)
the axis of symmetry of the parabola when the parabola is written in the form as in the question is of the formula x = -b/2a.
this says that the axis of symmetry is a vertical line
the focus is given by f(h, k + 1/4a)
"a" curve opens up when a is positive and down when a is negative. when (x − ℎ) = a (y − k)^2, a opens left or right
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Which is the line x = y?
A, B, C, or D?
Answer:
The correct answer is: C
4/6 + 1/4 what's the answer pls
[tex]\boldsymbol{\sf{\dfrac{4}{6}+\dfrac{1}{4} }}[/tex]
We reduce the fraction 4/6 to its lowest expression by extracting and canceling 2.
[tex]\boldsymbol{\sf{\dfrac{4}{6}=\dfrac{4\div2}{6\div2}=\dfrac{2}{3} }}[/tex]
[tex]\boldsymbol{\sf{\dfrac{2}{3}+\dfrac{1}{4} }}[/tex]
Convert 2/3 and 1/4 to fractions with like denominators.
[tex]\boldsymbol{\sf{\dfrac{2\times4}{3\times4}+\dfrac{1\times3}{4\times3} \iff \ \dfrac{8}{12}+\dfrac{3}{12} }}[/tex]
Since 8/12 and 3/12 have the same numerator, we join numerators and add.
[tex]\boldsymbol{\sf{\dfrac{8+3}{12}= }}\boxed{\boldsymbol{\sf{\frac{11}{12} }}}[/tex]
if 4 boxes of cereal cost $16.24 how much does one box of cereal cost?
Answer: 4.06
Step-by-step explanation:
if you divided 4 into 16.24 your answer will be 4.06!!
Answer:
$4.06
Step-by-step explanation:
To find the answer, divide 16.24 by 4
This gives you the answer of how much each box costs (assuming each cereal box costs the same)
The answer is 4.06