100 people study one language at a college. Some people study French, some study Spanish. The rest of the people study German. 54 of the people in Year 10 and the rest in Year 11. 20 of 29 people who study Spanish in Year 11. 31 people study German, 15 year 11 students study French. Work out the number of Year 10's who study German.​

100 People Study One Language At A College. Some People Study French, Some Study Spanish. The Rest Of

Answers

Answer 1

Hello,

[tex]Data:\\\\\begin{array}{|c|c|c|c|c|}Year&French&Spanish&German&Total\\----&----&----&----&---\\Y10&-&-&-&54\\Y11&15&20&-&-\\----&----&----&----&---\\&-&29&31&100\\\end{array}\\\\Calculus:\\\\\begin{array}{|c|c|c|c|c|}Year&French&Spanish&German&Total\\----&----&----&----&---\\Y10&25&9&20&54\\Y11&15&20&11&46\\----&----&----&----&---\\&40&29&31&100\\\end{array}\\\\[/tex]

20 Year10's students learn German.

Answer 2
Answer:  20 students

========================================================

Explanation:

Make a table that has "Year 10", "Year 11", and "Total" as the three rows.

Then you'll have the columns "French", "Spanish", "German", "Total".

In the bottom right corner is the value 100. This is the grand total of everyone surveyed.

We're told that 54 people are in Year 10, which leaves 100-54 = 46 people in Year 11.

Along the "total" column on the far right side, we'll have 54, 46, and 100 in that order from top to bottom.

--------------------------

The info that "20 of the 29 people who study Spanish in Year 11" tells we have 20 people in year 11 who study Spanish, out of 29 people who study Spanish. That leaves 29-20 = 9 people in Year 10 who study Spanish. In the "Spanish" column, we have the values 9,20,29 in that exact order from top to bottom.

Next, we'll write 31 at the bottom of the "German" column to indicate 31 people study German.

The last bit of info is that "15 Year 11 students study French". So we'll write 15 in the "year 11" row and "french" column.

--------------------------

After all that info is sorted out and entered into the table, you should end up with what is shown in figure 1 (see attached image below). Ignore figure 2 for now as we'll work our way to getting there eventually.

The variables a,b,c,d are placeholders for positive whole numbers.  

There are probably a few approaches to take, but possibly the quickest is to notice that in the second row, we can say

15+20+c = 46

c+35 = 46

c = 46-35

c = 11

We have 11 students who study German in Year 11.

Once you determine c, it helps us find b. Focus on the German column to see that

b+11 = 31

b = 31-11

b = 20

There are 20 students in Year 10 who study German. You could stop here if you want.

--------------------------

Just two more variables to go.

Along the top row, we see that

a+9+20 = 54

a+29 = 54

a = 54-29

a = 25

and along the bottom row we see that

d+29+31 = 100

d+60 = 100

d = 100-60

d = 40

Or you could note along this first column to say

a+15 = d

d = a+15

d = 25+15

d = 40

So there are a few alternative paths to take.

--------------------------

All of the sections mentioned so far only involve filling out the table that is shown below in figure 2.

To answer the question your teacher wants to ask, which is how many Year 10 students study German, well that's simply 20 students. Refer to the conclusion of the previous two sections earlier.

By this point, we just simply copy the value from the completed table. This value being of course in the "Year 10" row and "German" column.

100 People Study One Language At A College. Some People Study French, Some Study Spanish. The Rest Of

Related Questions

Arby's age is 6 years less than 7 times Anna's age. If Anna's age is x years, which expression best shows Arby's age?
A = x
B = 7x - 6
C = x - 1
D = 6x - 7

Answers

B = 7x - 6 is the correct answer.

B=7x -6 is the right answer !

. On a test with 199 multiple choice questions, you received 149 correct answers. Estimate your results as a percentage.

Answers

567 to be a little late for a meeting and then I have a question for you and your dad to pick

Polygon ABCD is rotated 90º counterclockwise about the origin to create polygon A′B′C′D′. Match each set of coordinates to the vertices of polygon A′B′C′D′.

Answers

Answer:.

Step-by-step explanation:

The temperature is -3°C. As the day progresses, the temperature increases by 8°C, then drops by 6°C. Find the final temperature.

Answers

We know that the initial temperature is -3 then it rises to 8 and drops by 6 degrees then you just need to subtract six from 8                                                         [tex]\displaystyle\ 8-6=2^\circ \\\\Answer: the\ secondary\ temperature \ will \ be equal \ to \ 2^\circ[/tex]

Una bañera en forma de trapecio tiene un area de 60 metro ademas se sabe que su base mayor es 3/2 mas grande que su base menor calcule la altura cuando la base menor es 18 metros

Answers

Respuesta:

3,2 metros

Explicación paso a paso:

Área del trapecio:

A = 1/2 (a + b) h

h = altura; ayb son las bases

Área, A = 60

Sea una base más pequeña = a = 18;

b = 18 + 3/2 = 19,5

La altura se puede calcular así;

60 = 1/2 (18 + 19,5) h

60 * 2 = 37,5 horas

120 = 37,5 h

h = 120 / 37,5

h = 3,2 metros

HELP i need help on part b

Wilson is thinking about buying a house for $249,000. The table below shows the projected value of two different houses for three years.

Number of years 1 2 3
House 1 (value in dollars) 253,980 259,059.60 264,240.79
House 2 (value in dollars) 256,000 263,000 270,000

Part A: What type of function, linear or exponential, can be used to describe the value of each of the houses after a fixed number of years? Explain your answer. (2 points)

Part B: Write one function for each house to describe the value of the house f(x), in dollars, after x years. (4 points)

Part C: Wilson wants to purchase a house that would have the greatest value in 45 years. Will there be any significant difference in the value of either house after 45 years? Explain your answer, and show the value of each house after 45 years. (4 points)

Answers

Answer

Number of years 1               2            3

House 1 (value in dollars) 249,000 253,980 259,059.60

House 2 (value in dollars) 249,000 256,000 263,000

House 1: exponential function

House 2: linear function

House 1: f(x) = 249,000 * (1.02)^(x-1)

→ f(3) = 249,000 * (1.02)³⁻¹ = 249,000 * (1.02)² = 259,059.60

House 2: f(x) = 249,000 + 7,000(x-1)

→ f(3) = 249,000 + 7,000(3-1) = 249,000 + 7,000(2) = 249,000 + 14,000 = 263,000

House 1:

f(45) = 249,000 * (1.02)⁴⁵⁻¹ = 249,000 * (1.02)⁴⁴ = 249,000 * 2.39 = 595,110

House 2:

f(45) = 249,000 + 7,000(45-1) = 249,000 + 7,000(44) = 249,000 + 308,000 = 557,000

House 1 will have a greater value than House 2 after 45 years.

Step-by-step explanation:

Hope this helps, if not let me know and I will fix it.

Part A

The value for house 1 follows an exponential growth function since the value is increasing by 2% each year. This is because we multiply each value by 1.02 to get the next year's value.

249,000*1.02 = 253,980253,980*1.02 = 259,059.60259,059.60*1.02 = 264,240.792 = 264,240.79

In contrast, house 2's value increases by the same amount each year (7000 per year)

249,000 + 7,000 = 256,000256,000 + 7,000 = 263,000263,000 + 7,000 = 270,000

This fixed amount it increases directly leads to house 2 having linear growth.

-----------

Summary:House 1 = exponential functionHouse 2 = linear function

=================================================

Part B

The equation for house 1's value is y = 249000(1.02)^x

This is in the form y = ab^x, where a = 249000 is the starting value and b = 1.02 is the growth rate factor.

We can think of 1.02 as 1+0.02 to represent the 2% growth.

In other words, 1.02 = 1+r solves to r = 0.02 = 2%

-----------

The equation for the second home's value is y = 7000x+249000

The slope m = 7000 tells us how the value is going up per year.

The y intercept b = 249000 is the original home value (when x = 0).

-----------

Summary:Equation for home 1 is f(x) = 249000(1.02)^xEquation for home 2 is f(x) = 7000x+249000

=================================================

Part C

Let's plug x = 45 into each equation mentioned in part B

For home 1, we have

f(x) = 249000(1.02)^x

f(45) = 249000(1.02)^45

f(45) = 607,025.697

f(45) = 607,025.70

So that's the value of home 1 after 45 years of constant 2% growth per year

For the second home, we have,

f(x) = 7000x+249000

f(45) = 7000*45+249000

f(45) = 564,000

So there is a significant difference. This difference is 607,025.70 - 564,000 = 43,025.70 dollars.

-----------

Summary:Home 1's value = $607,025.70Home 2's value = $564,000This is a difference of $43,025.70 which is fairly significant. It's better to go with home 1.

Find the solutions of the equation 3x = x4, rounded to two decimal places. (Enter your answers as a comma-separated list.)

Answers

Answer:[tex]-0.802; \ 1.517[/tex]

Step-by-step explanation:

Given

[tex]3^x=x^4[/tex]

Here, two functions are given that is [tex]y=3^x[/tex] and [tex]y=x^4[/tex]

Check for the intersection of the graph of two curves

From the graph, they cut at two different points  i.e. [tex]x=-0.802\ \text{and}\ x=1.517[/tex]

Rest two roots are negative.

If f(x) = k where k is a constant, and the
points (6, 1) and (8, 1) lie on the graph of y
= f(x), what is the value of f(0)?

Answers

Answer:

f(0) = 1

Step-by-step explanation:

Since f(x) = k, is constant the value of k is same for any x.

From the given points we see:

f(6) = 1 and f(8) = 1

It means k = 1 and the function is:

y = f(x) = 1

The value of f(0) = 1

3/4 + 5/4 with explanation and steps.... ​

Answers

Answer:

step 1

3/4+5/4

step 2

dinominator is same so we have to put 4

step 3

3+5/4

step 4

7/4

answer is 7/4

Answer:

2

Step-by-step explanation:

Given

[tex]\frac{3}{4}[/tex] + [tex]\frac{5}{4}[/tex]

Since the denominators are common, both 4 then add the numerators leaving the denominator

= [tex]\frac{3+5}{4}[/tex]

= [tex]\frac{8}{4}[/tex]

= 2

4x^2+22x factor the polynomial

Answers

Answer:

2x(2x+11)

Step-by-step explanation:

4x^2 +22x

Factor out 2x

2x*2x +2x*11

2x(2x+11)

HELP MEEE QUICK THIS MY LAST QUESTION!!!
Question 10 of 10
Is APQR- AXYZ? If so, name which similarity postulate or theorem applies.
80
Q
180°
P
5
R
х
10
A. Similar - AA
B. Similar - SSS
C. Similar - SAS
Ο Ο
D. Cannot be determined
SUBMIT

Answers

Answer:

A. Similar - AA

Step-by-step explanation:

The given parameters of ΔPQR and ΔXYZ are;

In ΔPQR, we have; PQ = 3, PR = 5, and ∠PQR = 80°

In ΔXYZ, we have; XY = 6, XZ = 10, and ∠XYZ = 80°

In ΔPQR, by sine rule, we have;

3/(sin(∠PRQ)) = 5/(sin(80°))

sin(∠PRQ) = (3/5) × sin(80°)

∴ ∠PRQ = arc sin((3/5) × sin(80°))

In ΔXYZ, by sine rule, we have;

6/(sin(∠XZY)) = 10/(sin(80°))

sin(∠XZY) = (6/10) × sin(80°) = (3/5) × sin(80°)

∴ ∠XZY = arc sin((3/5) × sin(80°))

∠PRQ = ∠XZY by transitive property of equality

Therefore in ΔPQR and ΔXYZ, we have;

∠PRQ = ∠XZY and ∠PQR = ∠XYZ

Therefore, ΔPQR is similar to ΔXYZ by Angle Angle, AA, similarity postulate.

Circle w has a radius of 20 in and central right angle. VWX find the length of VX. Leave answer in terms of pi

Answers

The arc length is 10 Pi

(I don't know for sure, but its what I got)

does anyone know how to solve this ?

Answers

Answer:

D) 144π sq. units

Step-by-step explanation:

The formula for finding the surface area of a sphere is 4π

Substitute 6 in for r.  4π = 144π

Answer:

144π sq. units

Step-by-step explanation:

The formula to determine the surface area of a sphere is: 4πr^2

But there’s no digit of pi given. Therefore we will use the formula but ignoring pi:

4πr^2

= 4r^2

= 4(6^2)

= 4(36)

= 144

Surface area is measured in square units.

Therefore the answer is 144π. The answer will be the true answer surface area once we know what π to use. For now, π will be just a variable next to 144 and will be later multiplied to it.

I hope you understand this! Hope I helped!

I need help, I can’t figure out the answer

Answers

Answer:

Step-by-step explanation:

in negative exponents you should switch both numerator and denominator so for 2 raised to -1 you should switch the numerator and denominator and it will become 1/2 in which 2 is raised to power 1

you can do the same for the remining sums

so a is 1/2 in which 2 is raised to 6 so answer is 1/64

given the nth term of geometric expression is (as in the diagram)

a) state the value of k
b) the first term of progression ​

Answers

Step-by-step explanation:

a) k = 1

b) geometric progression formula:

Tn = ar^(n-1)

first term, a = 3/2



8
6471 sq. in.
25671 sq. in.
1,02471 sq. in.

Answers

Answer:

102471 sq .in the land answer Teri ma ki bosra

Answer:

=256 pi

Step-by-step explanation:

The surface area of a sphere is

SA = 4pi r^2

SA = 4 pi (8)^2

     = 4 * pi *64

     =256 pi

A calculator requires a keystroke assembly and a logic circuit. Assume that 83% of the keystroke assemblies and 88% of the logic circuits are satisfactory. Assuming that defects in keystroke assemblies are independent of defects in logic circuits, find the probability that a finished calculator will be satisfactory. Group of answer choices

Answers

Answer:

0.7304

Step-by-step explanation:

According to the Question,

Given That,  A calculator requires a keystroke assembly and a logic circuit. Assume that 83% of the keystroke assemblies and 88% of the logic circuits are satisfactory.

We have,

P(keystroke satisfactory) =0.83 ,  P(logic satisfactory)= 0.88

Assuming that defects in keystroke assemblies are independent of defects in logic circuits

Since the events are independent. So, the probability that a finished calculator will be satisfactory

⇒ 0.83×0.88

0.7304

What is the correct expansion of (2x+3) (2x^2-5)

Answers

Answer:

4x^3 + 6x^2 -10x - 15

Step-by-step explanation:

* means multiply

4x^3 + 6x^2 -10x - 15

2x * 2x^2 = 4x^3

2x * -5 = 10x

3 * 2x^2 = 6x^2

3 * -5 = -15

Answer:

4x³ + 6x² - 10x - 15

Step-by-step explanation:

(2x+3) (2x²-5)

4x³ - 10x + 6x² - 15

4x³ + 6x² - 10x - 15

i don’t know if i got the answer wrong but help!

Answers

Answer:

skew

Step-by-step explanation:

Perpendicular lines must intersect. In fact, they intersect forming right angles.

Lines AC and RC are not in the same plane and do not intersect.

They are called "skew lines."

Skew

Because they are in different plane and do not intersect and are not parallel

find the shortest distance between the lines 3x+4y+10=0 and 3x+4y+20=0​

Answers

Answer:

the lines are parallel they are 10 units apart

Step-by-step explanation:

The shortest distance between these two parallel lines is 2.5

Given equations:

3x + 4y + 10 = 0 ----- (1)

3x + 4y + 20 = 0 ---- (20)

To find:

the shortest distance between the two lines

The slope  and y-intercept of the first equation is calculated as;

3x + 4y + 10 = 0

4y = -3x - 10

[tex]y = \frac{-3x}{4} - \frac{10}{4} \\\\y = \frac{-3x}{4} - \frac{5}{2}[/tex]

The slope = -³/₄ and the y-intercept = - ⁵/₂ = - 2.5

The slope  and y-intercept of the second equation is calculated as;

3x + 4y + 20 = 0

4y = -3x  - 20

[tex]y = \frac{-3x}{4} - \frac{20}{4} \\\\y = \frac{-3x}{4} - 5[/tex]

The slope = -³/₄ and the y-intercept = - 5

The two equations have the same slope = -³/₄

This shows that they are parallel with different y-intercepts

The shortest distance between the two lines is at their y-intercepts

The shortest distance between these two lines is calculated as;

[tex]distance = \sqrt{(-5 - (-2.5) )^2} \\\\distance = \sqrt{(-5+ 2.5)^2} \\\\distance = \sqrt{(-2.5)^2 } \\\\distance = \sqrt{6.25} \\\\distance = 2.5[/tex]

Thus, the shortest distance between these two parallel lines is 2.5

learn more here: https://brainly.com/question/11566480

Find the inverse of the function y = x2 – 12

Answers

Answer:

y=sqrt(x+12)

i hope this helped and have a nice day/night :)


The circumference of a steering wheel of a car is 20 inches. What is the radius of
the steering wheel?
40 in.
20 in
100 in.
10 in.

Answers

Answer: 10π or 3.18


Step 1: Write equation

To solve for the radius, we must first find the equation. We will use the formula for a circumference. The circumference is equal to 2 times pi (π) times the radius. Let’s write the equation now.

C=2πr

Step 2: Substitute information

Before we find the radius, we must first substitute the information provided to us. In this case, we can substitute c for 20, as that is the circumference.

C=2πr
20= 2πr

Step 3: Solve for the radius

Now that we have steps one and two done, we can solve for the radius. Let’s start by rewriting the equation.

20= 2πr

Great! Now let’s get rid of the constant on the right side. Let’s divide each term by 2.

20= 2πr
10= πr

Now let’s move the pi side to the left. Divide each term by pi to do so.

10= πr
10π= r

This is your answer! If desired, you could divide the term by pi to get the proper answer of 3.18. Since this is not an option provided, I will leave the answer as 10π, assuming that the teacher would like you to leave the pi symbol.

The radius of the steering wheel is 10 inches.

What is a circle?

A circle is the defined as a closed, two-dimensional curved shape in the geometry. Every point on the circle is equal distance from a certain point known as the centre of circle. A circle is a two-dimensional form that is measured in terms of radius.

What is the circumference of a circle?

Circumference of a circle is defined as perimeter of circle is defined as the enclosing boundary of a curved geometrical figure called a circle. It is the product of π and its diameter.

Circumference (C) = π × d , where d is the diameter of a circle.

Given data as :

Circumference of a steering wheel of a car = 20π inches

Circumference(C) =  20π inches

Substitute the value of c in formula of Circumference :

20π = π × d      [ diameter(d) = 2 radius(r) ]

20π = π × 2 r

Divided by 2π both the sides

10 =  r

r = 10

r = 10 inches

Hence, the radius of the steering wheel is 10 inches.

Learn more about Circumference of a circle here :

https://brainly.com/question/17357009

#SPJ5

Question seems to be incomplete the correct question would be

The circumference of a steering wheel of a car is 20π  inches. What is the radius of

the steering wheel?

A bag of raisins contains 20 oz. If you want to give 25 people equal servings how many ounces should you
give each person? (It says leave your answer as a mixed number) I don’t understand how to do that.

Answers

.8 oz. is the correct answer. Find this by dividing the amount of raisins by the number of people.

product of -2/3 and 5 2/4?​

Answers

Answer: [tex]-\frac{11}{3}[/tex]

Step-by-step explanation:

[tex]-\frac{2}{3} *5\frac{2}{4} \\\\\\=-\frac{2}{3} *5\frac{1}{2} (5\frac{1}{2} =\frac{5*2}{2} +\frac{1}{2} =\frac{10+1}{2} =\frac{11}{2})\\\\\\=-\frac{2}{3} *\frac{11}{2} =-\frac{11}{3}[/tex]

PLEASE ANSWER ASAPPP

Answers

Answer:

the answer is 2035.75 cm³

Step-by-step explanation:

comment if you want explanation

QUICK PLEASE
42% of £719.24 Give your answer rounded to 2 DP.​

Answers

Answer:

719.24 is the correct answer

719.24/100 x 42 = 302.0808

Answer rounded to 2 DP = 302.08

could someone help me with this ASAP?

Answers

Answer:

just draw a circle that connects all of the 10's on the graph.

a circle is NOT a function

Step-by-step explanation:

expand the following:

a) 8(×-2y)​

Answers

Answer:

8x-16y

Step-by-step explanation:

8*x-8*2y

8x-16y

Answer.

8x - 16y

Explained in the picture atteached:

Which of the following graphs represents the equation y=3x+2? A.Graph B. Graph B C. Graph C D. Graph D

Answers

from process of elimination, it’s graph c

Mike was in charge of collecting contributions for the Food Bank. He received
contributions of:
$40, $80, $60, $40, and $100
Find the mean, median, and mode of the contributions.

Answers

What is mean: A mean is the simple mathematical average of a set of two or more numbers. To solve for it add all numbers together then divide by how many numbers are there. (Its best to put them in order)

$40 + $40 $60 + $80 + $100= $320/5= $64 is the mean

what is median: The median is the value separating the higher half of a data sample

40,40,60,80,100 (i like to cross it out so 40 and 100 cancle each other, another 40 and 80 cancel each other) now that you are left with only 1 number which is 60 that is the median.

What is Mode: the number that repeats the most

Mode is 40 because 40 repeats twice

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