The expression which correctly represents the number of students studying German as required is; 3y + 2x -35.
Which expression correctly represents the number of students studying German?It follows from the task content that the number of students studying German be determined from the given information.
Therefore since the total number of students is; 100.
35 students study Spanish of which y are boys, therefore, the number of girls studying Spanish is; (35 - y).
Also, since there are 3x girls in total and x of which study French, the remaining 2x study Spanish and German.
Hence, the number of girls who study German is; 2x - (35 - y).
Therefore, the total number of students (boys and girls) who study German is; 2y + 2x - (35 - y).
= 3y + 2x -35.
Ultimately, the total number of students who study German are; 3y + 2x -35.
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There is a line that includes the point (1, – 2) and has a slope of 10. What is its equation in point-slope form?
The equation of line in point - slope form will be;
⇒ y + 2 = 10 (x - 1)
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The point on the line = (1, -2)
And, The slope of the line = 10
Now,
Since, The equation of line in point-slope form is;
⇒ y - y₁ = m (x - x₁)
Where, (x₁ , y₁) is the point on the line and m is slope of the line.
Hence, The equation of line in point-slope form passing through the points (1, -2) with slope 10 is;
⇒ y - y₁ = m (x - x₁)
⇒ y - (-2) = 10 (x - 1)
⇒ y + 2 = 10x - 10
⇒ y = 10x - 10 - 2
⇒ y = 10x - 12
Thus, The equation of line in point - slope form will be;
⇒ y + 2 = 10 (x - 1)
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in a rectangle, one side is 3 times as long as the other. Now the longest side is extended by 4m. Then the area will be 96 square meters larger. How long were the original sides?
The length of the original sides of the rectangle are 72m and 24m.
What is Area of a Rectangle?The area of a rectangle formula is used to calculate the area occupied by the rectangle within its boundaries. A rectangle's area is calculated by multiplying its length and breadth.
Given:
One side is 3 times as long as the other in a rectangle.
Let the length of the rectangle be 3x and the breadth of the rectangle be x.
Area of original rectangle = length × breadth
= 3x² m²
Now, the longest side is extended by 4m.
Length of rectangle = 3x + 4
Area of rectangle = length × breadth
= x(3x + 4) m²
It is given that this area will be 96 square meters larger than the former.
So, x(3x + 4) - 3x² = 96
⇒ 3x² + 4x - 3x² = 96
⇒ 4x = 96
⇒ x = 24 m
Original length of the rectangle = 3x = 3×24 = 72m
Therefore, the original length of the rectangle is 72m and the original breadth of the rectangle is 24m.
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A car park charges £1.20 to each car entering.
The payment station only accepts £1 coins and 20p coins.
Here are the coins collected from the payment station on a particular day:
Number of £1 coins
176
Number of 20p coins
320
Assuming each driver paid the exact amount due on that day, work out the
percentage of drivers that paid with six 20p coins.
Optional working
+
Answer:
Answer: 12%
Step-by-step explanation:
12%
Explanation:
If has 176 £1 coins then 176 drivers paid £1 and 20 p coins.
The rest of the driver paid with 20 p coins.
So the number of 20 p coins is:
320 - 176 = 144
Since £1 and 20 p need 6 coins of 20 p, the number of drivers who paid only for 20 p coins is:
144 / 6 = 24
The total number of drivers is:
176 + 24 = 200
The percentage of drivers who paid only with coins id 20 p is:
24 / 200 • 100% =
0.12 • 100% = 12%
A car rental service charges an initial fee of $250 and 25$ for every hour using the car. If a customers bill totals $1,275 then how long did they rent the car for?
======================================================
Explanation:
x = number of hours
y = total cost
The equation is y = 25x+250 since 250 is the initial cost, aka y intercept, and 25 is the slope telling us how much the cost goes up per hour (aka rate of change).
I recommend making a table of values to help see how/why that equation works out.
Plug in y = 1275 and isolate x.
y = 25x+250
1275 = 25x+250
1275-250 = 25x
1025 = 25x
25x = 1025
x = 1025/25
x = 41 hours
----------------
Check:
If the customer rents the car for 41 hours, then they pay 25*41 = 1025 dollars on top of the initial fee of $250.
The total cost is therefore 1025+250 = 1275 dollars to confirm the answer.
----------------
Extra info:
41 hours = 24 hours + 17 hours = 1 day + 17 hours
41 hours = 41/24 = 1.70833 days approximately
What are the sum of all the factors of 50 which are between 1 and 50. A. 42B. 2550C. 92D. 15
Factors of 50 are the numbers which on dividing 50 leave no remainder. 50 is a composite number, therefore, it has more than 2 factors.
We can get the factors of 50 by Prime Factorization. We can draw a factor tree to get the prime factors of 50 as shown below:
Therefore, the prime factors are:
[tex]2,5,5[/tex]Hence, the other factors are:
[tex]\begin{gathered} 2\times5=10 \\ 5\times5=25 \end{gathered}[/tex]Therefore, the factors of 50, including 1 and 50, are:
[tex]1,2,5,10,25,50[/tex]The question asks to sum all the factors between 1 and 50. This means that 1 and 50 are not included in the sum.
Therefore, the sum will be:
[tex]\Rightarrow2+5+10+25=42[/tex]The correct option is OPTION A.
On a cold January day, Klara noticed that the temperature dropped 21 degrees over the course of the day to –9°C. Write and solve an equation to determine what the temperature was at the beginning of the day.
6+3x^4+7x^5+7x^2 it’s polynomials
The given polynomial 6+3x⁴ +7x⁵ +7x² is a quadrinomial.
What is Quadronomial?An expression that consists of variables, constants, and exponents and is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).One-term polynomials are referred to as monomials, two-term polynomials as binomials, and three-term polynomials as trinomials depending on the number of terms with nonzero coefficients. A four-term polynomial is occasionally referred to as a "quadrinomial."So, 6+3x⁴ +7x⁵ +7x²:
We can observe that the given polynomials have 4 terms, and a polynomial with 4 terms is known as a quadrinomial.Hence, the given expression is quadrinomial.Therefore, the given polynomial 6+3x⁴ +7x⁵ +7x² is a quadrinomial.
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Max is designing a hot tub for a local spa.
He wants the hot tub to have a diameter of 90 inches, what is the approximate area required for the installation of the hot tub? (Use 3.14 for.)
The area of the hot tub to be installed for local spa is 6358.5 in².
What is defined as the circle?A circle is a round figure with no corners as well as edges.A circle is defined in geometry as a closed, double curved shape.The center of the a circle is the point in a circle where all distances to the circle's points are equal. This distance is known as the circle's radius.The diameter of a circle is a line segment that passes through center of a circle and has its endpoints just on circle.Diameter = 2 × radiusFor the given question;
The diameter of the hot tub to be installed for local spa is 90 inches.
Then, radius is 90/2 = 45 inches.
The area of the circle is;
Area = πr²
Where, π = 3.14
Put the values;
Area = 3.14×45²
Area = 6358.5
Thus, the area of the hot tub to be installed for local spa is 6358.5 in².
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4. last year nina invested $6,000. she put some of it in a cd the paid 4% simple interest, and she put the rest of it in a savings account that earned 2.5% simple interest. at the end of the year she earned a total of $204 interest. how much did she invest in each account? assume there were no other deposits or withdrawals.
She invested $2,400 in the 2.5% account and $3,600 in the 4% simple interest account
Here, we want to know the amount of money invested in each account
Let the amount invested in the 4% simple interest account be $x ----> (a)
While the amount invested in the 2.5% account be $y -------->(b)
So mathematically;
Both the interests are added to get total interest
x + y = 6,000 ••••••(i)
Let’s now evaluate the interest
for the 4% account , interest = 4/100 * x = 4x/100
For the 2.5% account, interest = 2.5/100 * y= 2.5y/100
The addition of both interests gives the total simple interest;
4x/100 + 2.5y/100 = 204
Multiply through by 100
4x + 2.5y = 20,400 •••••••(ii)
From i, x = 6,000 - y
Putting this into equation ii
4(6,000-y) + 2.5y = 20,400
24,000 - 4y + 2.5y = 20,400
24,000-20,400 = 4y - 2.5y
1.5y = 3,600
y = 3,600/1.5
y = $2,400
Recalling it again,
x = 6000 - y
x = 6,000 - 2,400
x = $3,600
Therefore, Nina invested $2,400 in the 2.5% account and $3,600 in the 4% simple interest account
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line L passes through (3,5) and is parallel to y = 6x-2. Find the equation of line L
Answer:
y = 6m - 13
Step-by-step explanation:
Parallel lines have the same slope. The slope in the equation y = 6x -2 is 6.
To write an equation in the slope intercept form, we need a slope and a y-intercept. We have the slope, we need to find the y-intercept.
To find the y intercept, we need a slope, and x on the line and a y on the line. The point (3,5) gives us the x and the y.
slope = 6
x = 3
y = 5
y = mx + b plug in what we know and solve for b
5 = 6(3) + b
5 = 18 + b Subtract 18 from both sides of the equation
-13 = b
y = mx + b
y = 6m - 13
Change 36 inches into feet given the fact that 1 foot = 12 inches.
===============================================
Work Shown:
1 foot = 12 inches
3*1 foot = 3*12 inches
3 feet = 36 inches
I multiplied both sides by 3 so that the "12" turns into "36".
Answer:3 feet
36/12=3
3x12=36
so 36 inches= 3 feet
hope it helps
1.2x10-8 x 4.0×10-3
Scientific Notation
Answer:
−3.11×10^2
Step-by-step explanation:
Trina wants to hang-glide at the same number of meters above sea level as she scuba-dived below sea level. Will she fly higher than Jessie did? Explain
Trina is closer to the surface of the ocean. She will not fly higher than Jessie did.
Consider the provided information.
The distance is the absolute value of a number.
Part (A) : It is given that Trina went scuba diving and reached an elevation of -85.5 meters, which is below sea level.
That means the distance she covers is: |-85.5| = 85.5 meters
Thus Trina covers 85.5 meters.
Jessie went hang gliding and reached 87.9 meters which is above sea level.
That means the distance she covers is: |87.9| = 87.9 meters
We know that 85.5 < 87.9
So, we can say that Trina is closer to the surface of the ocean as she covers less distance.
Part (B) : Trina wants to hang glide at the same number of meters above sea level as she scuba dived below sea level.
That means she will hang the glide at a height of 85.5 meters.
As we know 85.5 < 87.9
Thus, she will not fly higher than Jessie.
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can anyone help me with these questions
Answer:
Nah
Step-by-step explanation:
I keep getting the wring answer. I don’t know what I’m doing wrong.
we have the expression
[tex]y=x^2+x-4[/tex]Remember that
[tex]i^2=-1[/tex]Evaluate
For x=2i
substitute
[tex]y=(2i)^2+2i-4[/tex][tex]y=4i^2+2i-4[/tex][tex]\begin{gathered} y=4(-1)+2i-4_{} \\ y=-4+2i-4 \\ y=-8+2i \end{gathered}[/tex]“If the sum of two angles is 180 then the angles are supplementary
If the sum of two angles is 180 then the angles are supplementary.This is true.
What are supplementary angles?Supplementary angles are those that total 180 degrees. Angles 130° and 50°, for example, are supplementary angles since the sum of 130° and 50° equals 180°.
If the total of two angles is 180 degrees, they are considered to be supplementary angles since they form a linear angle when combined. If the total of two angles is 90 degrees, they are considered to be complimentary angles since they produce a right angle when combined.
If two angles add up to 180 degrees, they are considered to be supplementary angles in geometry. For example, if A + B = 180°, A and B are referred to as supplementary angles. When supplementary angles are combined, they always yield a straight angle (180 degrees).
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Describe all the x-values within or including a distance of the given value.
(Enter your answer using interval notation.)
Distance of 2 units from the number 7
The range of values, in interval notation is [-6,14] .
What is interval notation in math?
Continuous sets of real numbers can be represented by the integers that bound them using interval notation. When written, intervals resemble ordered pairs in several ways. They don't necessarily indicate a particular point, though. They are intended to serve as a shortened manner of expressing an inequality or system of inequalities.the values with a distance of 10 units from 4.
Maximum value to the right, 10 units from 4 is 4+10 = 14
Maximum value to the left, 10 units from 4 is 4 - 10 = -6
So, all the range of values, in interval notation is [-6,14]
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PLEASE SOLVE!
x+146=546
I tried but can't get it
[tex]x+146=546[/tex]
Subtract 146 from both sides:
[tex]x+146-146=546-146\\[/tex]
[tex]x=400[/tex]
Answer:
x = 400
Step-by-step explanation:
x + 146 = 546
We need to subtract 146 on both sides.
146 - 146 is equal to 0 so we cancel out. 546 - 146 is equal to 400.
So now x is alone and we have our answer.
x = 400
A custodian must move a shipment of books from the first floor to the sixth floor. The elevators weight limit is 900 pounds. If the custodian weighs 160 pounds and each box of books weighs 37 pounds , find the maximum number of boxes the custodian can move on the elevator at one time
Step-by-step explanation:
160 + 37x <= 900
37x <= 740
x <= 20
the custodian can move max. 20 boxes on the elevator at one time.
if he/she is always riding with the boxes.
if the custodian would climb the stairs and let the books ride alone, there could be
37x <= 900
x <= 900/37 = 24.32432432 ≈ 24
boxes on the elevator at one time.
a length of black steel pipe is 21'-0" long. how much if the length remains of two pieces 7'-9 5/8" are cut from the length?
A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 9 5/8, where 9 is the quotient and 5 is the remainder.
Remain length = 13.2' = 13' 2 2/5 ".
What is a mixed fraction?The quotient and remainder of a fraction are used to represent it, making it a mixed fraction. For instance, 2 1/3, where 2 is the quotient and 1 is the remainder, is a mixed fraction. A mixed fraction is a combination of a whole number and a recognized fraction.Subtract the denominator from the numerator. The quotient's whole number component should be written down. Write the leftover amount on top of the original denominator.A mixed number is said to be in its simplest form if its fractional part's highest common factor, or HCF, is 1. When mixed numbers are simplified, the fraction's value doesn't change. We can assert that the actual mixed number and the simplified mixed number are fractions of the same size.Length of black steel pipe is 21'-0".
7' 9 5/8" =7.8 '
Remain length = 13.2' = 13' 2 2/5 ".
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Write the equation of each parabola in vertex form
Answer: 9. y=[tex](x+4)^2-3[/tex]
10. y=[tex]-(x-5)^2+5[/tex]
11. y=[tex](x-2)^2+1[/tex]
12. y=[tex]x^2-3[/tex] or y=[tex](x-0)^2-3[/tex]
Step-by-step explanation:
PLEASEEEE HELPPP!!!!
The musical note e can be modeled by the function, y = asin(1320Ï€x), where a = 1 and x is the time in seconds. playing note e on your computer, you notice that it is not loud enough to be heard across the room. what change can you make to the function to make note e louder than the original? let a < 0. let a > 0. let a > 0 and a < 1. let a > 1 or a < â€"1.
The change that increases the loudness is a > 1
How to determine the change?From the question, the equation of the function that represents the musical note is given as
y = a sin(1320πx)
Where
a = 1 i.e. the amplitudex represents the timeIn sound, the sound loudness is directly proportional to the amplitude.
This means that an increment in the amplitude, would cause the note to become louder
This change is represented as a > 1
This is so because a represents the amplitude, and the initial value is 1
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Write a two-column proof
The angles ∠4 and ∠6 are found to be supplement angles.
What are termed as the supplement angles?Supplementary angles are the ones that total 180 degrees. Angles 130° and 50°, for example, are supplementary angles since the sum of 130° and 50° equals 180°. Complementary angles, on the other hand, add up to 90 degrees. When the 2 supplementary angles are joined together, they create both a straight line and an angle.It should be noted, however, that the two supplementary angles are not required to be adjacent to each other. As a result, any two angles could be supplementary if their total amount is equal to 180°.For the given question;
∠5 ≅ ∠6 ( both are congruent means equal)
As, ∠4 and ∠5 are forming on the straight line. Thus,
∠4 + ∠5 = 180 (linear pair)
But, ∠5 ≅ ∠6 , replacing ∠5 with ∠6 .
∠4 + ∠6 = 180 supplement angles.
Thus, ∠4 and ∠6 are found to be supplement angles.
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help meeeeeeeeeeee pleaseeeeeeeeeeeeee!!
Please help , I need help thanks
these are the questions there are five , I need this today
I will give out brainlist
The solution to the inequality problem is represent by the graph attached below.
Graph of InequalitiesTo solve this problem we simply need to use a graphing a calculator to plot the graph of the two inequalities. The points of intersection represents the solution of the graph.
The broken purple line represents the first inequality and the second straight line represents the second inequality.
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an ice cream cone has a diameter of 8 cm and a slant height of 8.4 cm. find the lateral surface area of the cone. use 3.14 for π. round your answer to the nearest tenth.
an ice cream cone has a diameter of 8 cm and a slant height of 8.4 cm. find the lateral surface area of the cone then The lateral surface area of the cone is 105.2 cm².
What is lateral surface area?
The lateral surface area is the area of all the sides of a 3-dimensional object excluding its base and top.
Lateral surface area = πr√(h² + r²)
Where:
π = pi = 3.14
r = radius = 8/2 = 4cm
h = √8.4² - 4² = 7.38
3.14 x 4 x √(7.38² + 4²)
= 105.4 cm
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find the length of the arc shown in red. Leave your answer in terms of pie
EXPLANATION
Given the circle, we can see the following facts:
Diameter= 24 ft ----> radius= 12 ft
Total arc length = 360°
The arc of a semi-circle is equal to 360/2 = 180 degrees
The red labeled arc is given by the difference between 360, the other 60 degrees and the semi-circle,
360° - 180° - 60° = 120°
So, representing this as a radian form:
[tex]\text{arc length = 2}\cdot\pi\cdot r\cdot(\frac{\theta}{360})[/tex][tex]\text{arc length = 2}\cdot\pi\cdot12\cdot(\frac{120}{360})[/tex]Multiplying terms:
[tex]\text{arc length = 24}\cdot\pi\cdot\frac{1}{3}[/tex]Simplifying:
[tex]\text{arc length= 8}\cdot\pi[/tex]So, the answer is 8π ft
A study on the average minutes spent by students on internet usage is 300 with a standard deviation of 102. Answer the following questions assuming a bell-shaped distribution and using the empirical rule. What percentage of students use the internet for more than 402 minutes?.
The percentage of students that use the internet for more than 402 minutes = 16%
Percentage
Percentage, often referred to as percent, is a fraction of 100. Percentage means "per 100," and denotes part a total amount. For example, 45% represents 45 out of 100.
calculate the percentage-
The empirical rule states that
68% of the population lies within 1 standard deviation of the mean
95% of the population lies within 2 standard deviations of the mean
99.7% of the population lies within 3 standard deviations of the mean
Standard Deviation
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
The percentage will be illustrated in this:
P(X > 402) = P(X > 30 + 1 × 102)
= (1-0.68) / 2
= 0.32/2
= 16%
The percentage of students that use the internet for more than 402 minutes = 16%.
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The measure of an acute angle is represented by (3x + 12)°. Which is not a possible value for x?
A 26
B 21
C) 23
D25
a)26 is not a possible value for x as the angle becomes a right angle and doesn't remain acute
An acute angle is one whose measure is less than 90 degrees. The given acute angle in the question is represented by (3x+12)°
if x=26 then the angle is 90°
if x= 21 then the angle is 75°
if x=23 then the angle is 81°
if x=25 then the angle is 87°
∴26 cannot be a possible value for x as the angle becomes 90 degrees (right angle) and doesn't remain acute any longer.
Thus the correct answer is option a)26
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