The institution anticipates having 2158 students who can speak three or more languages.
Describe proportion in simple terms.The two ratios given are equivalent to one another, as demonstrated by the proportional equation. The percentage expresses the equality of something like the two ratios as well as fractions.
How do you teach pupils about proportion?Comparing two integers that each stand for a component of a whole results in a percentage. In essence, a percentage declares that two fractions are equal, regardless of the difference in amount. For instance, the ratio of half of 10 marbles to half of 50 marbles is 10.
[tex]\frac{x}{32370}=\frac{12}{180}[/tex]
[tex]{x} = \frac{12}{180}\times32370\\{x}=2158[/tex]
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Write an equivalent expression in expanded form. Please help this is on a test and i am running out of time!!!!
The equivalent expression in expanded form of given function is -4x/4-4*3/4.
What is an expression?Expression in mathematics is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division. An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
We are given;
The expression of the function
=-1/4(-8x+12)
Now, to expand we take 4 common
=-1/4(-8x+12)
=-4/4(-1x+3)
=-4x/4-4*3/4
Therefore, the expression in expanded form will be -4x/4-4*3/4
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Other than itself, which angle is congruent to
WE CAN USE THE GRAPH THAG CA HELP US IN THE PROBLEM
12, x, y, 324, 972, find the sum of x and y (a) 144 (b) 52 (c) 75 (d) 109
Answer: The value of the sum of x and y is (a) 144.
Step-by-step explanation:
Given, The sequence is a Geometric Sequence.
Initially,
=> 4x3 , x , y , 324, 324x3
=> 4x3, x, y, 4x3x3x3x3, 4x3x3x3x3x3
From above,
We can deduce that,
=> x = 4 x 3 x 3
=> x = 36
Also,
=> y = 4 x 3 x 3 x 3
=> y = 108
The values of x and y are 36 and 108
Now, We can evaluate the sum of x and y,
=> x + y = 36 + 108
=> x + y = 144
Therefore, The sum of x and y is 144. Hence, option (a) is correct.
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yesterday, peter the rabbit picked 84 carrots from his garden and ate one-fourth of them. today, he ate 12 carrots. how many carrots are left?
Peter the rabbit have 51 carrots are left.
one fourth means A quarter is represented in mathematics using fractions. Mathematically, a quarter fraction is a whole divided into four equal parts. where 1 indicates the part being referenced and 4 indicates the number of parts the whole is divided into. In numeric format, it is written as ¼.
so total carrot is 84
and he ate one fourth on that day
so remaining are
84*1/4= 21
21 he eat on that the then remaining =
84 - 21 = 63
63 carrots are remain for next day and
he eat 12 carrot on next day
so remaining = 63 - 12 = 51
so 51 carrot left .
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in 2012, the national average for students graduating within six years from a private, nonprofit institution was around 66%. write this percent as a fraction and do not simplify.
The 66 percent in the form of fraction representing the national average of the students graduating within six years from a private and non profit institution is given by 33 / 50.
Percent of students graduating from private nonprofit institution within six years is equal to 66 percent
Value of one percent is equal to one part of 100
Percent in the form of fraction is given by :
⇒ 1 percent = one part of hundred
⇒ 1 percent = ( 1 / 100 )
⇒ 66 percent = ( 66 / 100 ) in fraction form
Simplify the fraction in more reduced form we get,
⇒ 66 percent = ( 33 / 50 ) in fraction form
Therefore, the fraction form of the 66 percent students who have graduate within six years from private non-profit institution is equal to ( 33 / 50 ).
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which of the following points lies on the line 2x - y =12
a. (2,4)
b. (4,4)
c. (5,-2)
d. (0,12)
Answer:
C
Step-by-step explanation:
Plug (5, -2) into the equation
2(5) - (-2) =
10 + 2 =
12
C is the answer
(5, -2) is the answer
risol buys a souvenir cup for $14.97
d a book of postcards for $4.32. How
ch does Marisol spend?
Answer:
$19.29
Step-by-step explanation:
We know
Marisol buys a souvenir cup for $14.97 and a book of postcards for $4.32.
How much does Marisol spend?
14.97 + 4.32 = $19.29
So. Marisol spend $19.29
14 units up of f(x)= – 2x–4.
Answer:
-2x + 10
Step-by-step explanation:
When you add units you affect the y axis.
Knowing this you can translate it 14 units up by adding 14 + (-4).
given: jg/hg=kg/ig, 1=2
prove: ef || hi
The triangles ΔIGH and ΔGFE are similar triangles. So, GJ / GE = HG / FG, then the side FE is parallel to the side HI.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the corresponding sides will be constant then the triangles will be similar triangles and the third sides of the triangles will be parallel.
GJ / GH = GK / GI, then the side KJ is parallel to the side HI.
In triangles ΔIGH and ΔGFE, then we have
∠IGH = ∠FGE (Vertival angle)
∠1 = ∠2 (Given)
Then the triangles ΔIGH and ΔGFE are similar triangles. Then we have
GJ / GE = HG / FG, then the side FE is parallel to the side HI.
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1. there are 15 boys and 17 girls in a math class. what is the ratio of boys to girls? (6.rp.1) * 15:17 15:32 17:15 32:15
If there are 15 boys and 17 girls in a math class then, the ratio of boys to girls is Option A. 15:17
The ratio of boys to girls in the math class is 15:17. This can be found by dividing the number of boys by the number of girls, which gives:
15/17
This ratio cannot be simplified because 15 and 17 do not have any common factors other than 1. Therefore, the ratio of boys to girls is 15:17.
The ratio of boys to girls in a math class is the relationship between the number of boys and the number of girls. The ratio is a way of expressing the comparison between two quantities. In this case, there are 15 boys and 17 girls in the class. To find the ratio of boys to girls, we divide the number of boys by the number of girls, which gives 15/17. This ratio cannot be simplified further because 15 and 17 do not have any common factors other than 1. Therefore, the ratio of boys to girls in the math class is 15:17. This means that for every 15 boys in the class, there are 17 girls.
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In the previous problem, how does the angle of depression from the top of the taller building relate to the angle of elevation from the top of the shorter building? a. they are congruentb. they are complementaryc. they are supplementaryd. they are alternate interior anglese. they are alternate exterior anglesf. they are corresponding angles
The angle of depression from the top of the taller building and the angle of elevation from the top of the shorter building are alternate interior angles.
Alternate interior angles are the angles formed when a transversal intersects two coplanar lines. They lie on the inner side of the parallel lines but on the opposite sides of the transversal. The transversal crosses through the two lines which are Coplanar at separate points.
The angles of elevation and depression are formed by the line of sight and the horizontal line. When the line of vision is above the horizontal line, the angle is of elevation, and if the line of sight is below the horizontal, the angle is of depression.
If the angle of depression of the taller building is 15° the angle of elevation of the shorter building is 15° too.
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A colored spinner with eight equal sections is given.
spinner divided evenly into eight sections with three colored blue, one red, two purple, and two yellow
Using the fair spinner, determine P(less than 4) when the spinner is spun once.
0.125
0.25
0.375
0.5
The probability using the fair spinner to get P less than 4 is 3/8.
What is probability?Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
The total sections = 8.
The probability of less than 4 is:
P(less than 4) = Number of outcomes less than 4/ Total sections
P(less than 4) = 3/8
Hence, the probability using the fair spinner to get P less than 4 is 3/8.
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Answer: ITS 0.25!
Step-by-step explanation: i took the test
PLEASE HELP 20 POINTS
Turning 180° counterclockwise is essentially the same thing as a horizontal flip about the y axis.
That means C will find itself on the opposite side of the x axis, with negative inputs. However, it is still above the x axis, so it will have a positive y coordinate.
Your answer should be (-3,1)
Create a function table of the function y=−2x−3 for the values listed
All the values of y are calculated, the function table is complete. In this case, the final table looks like this
| x | -2x | -2x-3 | y |
| -2 | 4 | 1 | -3 |
| -1 | 2 | -1 | -5 |
| 0 | 0 | -3 | -3 |
| 1 | -2 | -5 | -7 |
| 2 | -4 | -7 | -9 |
The function y=-2x-3 is a linear equation. This means that the graph of the equation is a line with a constant slope. The slope of this line is -2 and the y-intercept is -3. The table above shows the output of the function for different values of x. To calculate the value of y for a given x, the first step is to calculate -2x. Then subtract 3 from the result to get the value of y. For example, for x=-2, -2*(-2)=-4 and -4-3=-3, so y=-3. For x=1, -2*(1)=-2 and -2-3=-5, so y=-5. In this way, the output of the function can be calculated for any given value of x.
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Hassan deposits $325 into an account that pays 4.7% annual interest compounded monthly. Write an equation to represent Hassanʼs account balance A after t years.
Use a system of equations to determine how many years it will take for the account reach $200. Round to the nearest year.
It will take 10 years for the account to reach $200, as determined by solving the equation A = [tex]325(1 + 0.047/12)^(12t)[/tex] for t.
[tex]A = 325(1+0.047/12)^(12t)[/tex]
[tex]200 = 325(1+0.047/12)^(12t)[/tex]
[tex]200/325 = (1+0.047/12)^(12t)[/tex]
[tex]log_((1+0.047/12))(200/325) = 12t[/tex]
[tex]t = log_((1+0.047/12))(200/325) / 12[/tex]
t = 8.75 years
It will take 9 years for the account to reach $200.
Hassan deposited $325 into an account that pays 4.7% annual interest compounded monthly. We can use a system of equations to determine how many years it will take for the account to reach $200. To do this, we first write an equation to represent Hassan's account balance A after t years. This equation is[tex]A = 325(1+0.047/12)^(12t)[/tex]. We then solve for t by taking the logarithm of both sides, which gives us means that it will take 8.75 years for the account to reach $200, which we round up to 9 years.
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Pls help me fast fast
The sum of the measures of angles A, D, and F is:
A + D + F = 360°
How to find the sum of the 3 angles?First, we know that the sum of the interior angles of any triangle is always equal to 180°, then we can write:
B + C + E = 180°
We also can see that:
A + B = 180°
C + D = 180°
E + F = 180°
Then we can rewrite:
E = 180° - F
C = 180° - D
B = 180° - A
And replace that on the equation above:
B + C + E = 180°
( 180° - F) + (180° - D) + (180° - A) = 180°
Moving the variables to the right side we will get:
3*180° = 180° + A + D + F
3*180° - 180° = A + D + F
360° = A + D + F
That is the sum of the 3 measures.
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help me please i actually cant do this
Answer:
a: Angle 1 and Angle 3
b: Angle 8 and Angle 5
c: Angle 2 and Angle 9
d: Angle 5 and Angle 3
e: none of the above
What number would correctly replace the G?
Write a real-world situation and an algebraic expression that is represented by the bar diagram:
The expression is there are 2 chocolates and 5 lollypops having a total cost of $5. The expression is 2C + 5L = $5.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.
Suppose the real-time situation is if there are 2 chocolates and 5 lollypops having a total cost of $5.
The mathematical form of the expression can be written as:-
2C + 5L = 5
Here, C is the cost per chocolate and L is the cost of per Lollypop.
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The complete question is given below.
Write the expression if there are 2 chocolates and 5 lollypops having a total cost of $5.
Danny cycled a total of 9 kilometers by making 3 trips to work. After 4 trips to work, how
many kilometers will Danny have cycled in total? Assume the relationship is directly
proportional.
The distance Danny travelled in 4 trips is 12 kilometres.
How to find the distance he travelled?Danny cycled a total of 9 kilometres by making 3 trips to work. After 4 trips to work, the number of kilometres Danny would have cycled in total can be calculated as follows:
Using the proportional relationship,
3 trips = 9 kilometres
4 trips = ?
cross multiply
Distance cycled by Danny = 4 × 9 / 3
Distance cycled by Danny = 36 / 3
Distance cycled by Danny = 12 kilometres
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(b) a telemarketing supervisor tells a new worker that the odds of making a sale on a single call are 6 to 13. what is the probability of a successful call? (round your answer to two decimal places.)
Probability of a successful call 0.3157 = 31.57%
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will learn the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
A probability is the number of desired outcomes divided by the number of total outcomes.
The odds of making a sale on a single call are 6 to 13.
This means that in 6+13 = 19 calls, 6 are successful.
What is the probability of a successful call?
p = 6/19 =
0.3157 = 31.57% probability of a successful call.
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The Grade 8 learners decided to start living more healthily.They will either jog or cycle.there are 125 Grade 8 learners and they jog and cycle in the ratio 3:2.calculate how many learners participate in each sport
Answer:
We can start by finding the total number of learners who participate in jogging and cycling by multiplying the ratio by the total number of learners. Let's say x is the number of learners who jog. Then, the number of learners who cycle is 2x.
The total number of learners who jog and cycle is 125, so:
x + 2x = 125
3x = 125
x = 125 / 3
x = 41.67
Since x represents the number of learners who jog, there are 41.67 learners who jog. Since the number of learners who cycle is 2x, there are 2 * 41.67 = 83.33 learners who cycle.
Since these are whole numbers of learners, we round up to the nearest whole number to get 42 joggers and 83 cyclists.
The number of students participating in each of the sports will be 75 for jogging and 50 for cycling.
Solution:
Let's assume that the number of students who participated in jogging will be 3x and those in cycling will be 2x
Given,
3x + 2x = 125
5x = 125
So, x = 25
Therefore, the number of students in jogging will be 3*25 = 75 and in cycling will be 2*25 = 50
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How much will $10,000 deposited in an account earning 2.5% interest compounded annually be worth in 20 years?
Answer:
Step-by-step explanation:
The formula to calculate the future value of an investment with compounded interest is:
Future value = Principal * (1 + rate/compoundings per year)^(number of years * compoundings per year)
In this case, the principal is $10,000, the interest rate is 2.5%, compounded annually, and the number of years is 20. So, the future value can be calculated as follows:
Future value = $10,000 * (1 + 2.5%/1)^(20 * 1)
Future value = $10,000 * (1.025)^20
Future value = $10,000 * 1.62897526
Future value = $16,289.75
Therefore, $10,000 deposited in an account earning 2.5% interest compounded annually would be worth $16,289.75 in 20 years.
Calculate the value of , assuming 4 is in radians and that the sin function available in python accepts radians. Store the result in a variable sin4
By using Python to calculate the value of sin4 is a simple process that involves understanding the concept of radians and using the sine function available in Python's math module.
A radian is a unit of measurement for angles. It is defined as the angle formed when the arc length of a circle is equal to the radius of that circle. This means that an angle of 1 radian is equal to the angle formed by an arc length of 1 radius on a circle.
The sine function, denoted as sin(x), is a mathematical function that takes an angle x as input and returns the ratio of the opposite side to the hypotenuse in a right-angled triangle with an angle x.
Now, we can proceed to calculate the value of sin4 using Python. In Python, the sine function is available in the math module, so we will need to import this module at the beginning of our code. We will then use the sin() function to calculate the sine of 4 radians as follows:
import math
sin4 = math.sin(4)
Here, we are calling the sin() function and passing it the value of 4 as an argument. Since the sine function in Python accepts radians, we do not need to convert 4 to degrees.
Finally, we store the result of this calculation in a variable called sin4. This variable will now hold the value of the sine of 4 radians, which we can use in our program as needed.
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can ypu please answer this question
Answer: A=71°
Step-by-step explanation:
A+B+C=180°
A+38°+C=180°
A+C=180°-38°
A+C=142°
142°/2=71°
∴A=71°
∴C=71°
Please help, its due today, ill give brainliest
Answer: bro just look it up fr fr
Step-by-step explanation:
Use a graphing calculator to find an equation of the line of best fit for the data. Round the slope to the nearest tenth and the y
-intercept to the nearest integer.
The equation of the line of the best fit for the data will be, y=2.07x-7.5.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
The equation of the line is;
y=mx+c
y=2.07x-7.5
Hence, the equation of the line of the best fit will be, y=2.07x-7.5
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Use substitution to solve
3x-2y=3
y=6+4x
Please explain how you got the answer
substitute y
3x - 2(6 + 4x) = 3
3x - 12 -8x = 3
-5x - 12 = 3
- 5x = 15
x = -3
Mr. Kazoo is planning to build a fence
gate 40 inches wide. He plans to use
boards 7 inches wide. How many
1
2
boards should he buy?
The number of boards Mr.Kazoo should buy is given by the equation A = 6
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the number of boards Mr.Kazoo should buy be A
The total length of the board = 40 inches
The length of each board = 7 inches
So , the number of boards = total length / length of each board
Substituting the values in the equation , we get
The number of boards A = 40 / 7
The number of boards A = 5.71
The number of boards A = 6 boards
Hence , the number of boards is 6
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Whitney prepared 16 kilograms of dough after working 4 hours. How much dough did
Whitney prepare if she worked for 5 hours? Assume the relationship is directly proportional.
Answer:
Step-by-step explanation:
time take for 1 dough = 16kg/4hours= 4kg/hour
Dough in 5 hours = 4 x 5 = 20
She prepared 20kilograms of dough in 5 hours
