In a nursery class of 18 pupils, the average is
[tex]4 \frac{1}{2} [/tex]
years. What is the sum of the ages of pupils?​

Answer:

Exact Form: 27/8

Decimal Form: 3.375

Mixed Number Form: 3 3/8

Step-by-step explanation:

3 + 5/8 - 1 + 3/4

I stared by making 5/8 a decimal

which is 0.625

then  added 3 to 0.625 which is 3.625 then subtracted 1 which is 2.625

then i turned 3/4 to a decimal which is 0.75

i added 2.625 and 0.75

which is 3.375

Answer: 0

Step-by-step explanation:

3 and 5 over 8 minus 1 and 3 over 4

= 3 +5/8 - 1+3/4

= 8/8 - 4/4

=1 - 1

=0

Answer:

[tex](2x)^2 + (x^2 - 1)^2 = (x^2 + 1)^2[/tex]  PROVED

Step-by-step explanation:

The sides of the given right triangle are : [tex]2x , (x^2 -1) , (x^2 +1)[/tex]

Now here, To show:  [tex](2x)^2 + (x^2 - 1)^2 = (x^2 + 1)^2[/tex]  .... (1)

Now, by ALGEBRAIC IDENTITY: [tex](a \pm b)^2  = a ^2 +b^2 \pm 2ab[/tex]

So here, similarly

[tex](x^2-1)^2 = (x^2)^2 + (1)^2 - 2 (x^2)\\(x^2+1)^2 = (x^2)^2 + (1)^2+ 2 (x^2)[/tex]

Now, substituting the value on Left side of (1) , we get :

[tex](2x)^2 + (x^2 - 1)^2   = 4x^2 + (x^2)^2 + (1)^2 - 2 (x^2) = 4x^2 + (x^4) + 1 - 2 x^2  = x^4 + 1 + 2x^2[/tex]  ...... (a)

Also, the right side of (1) is:

[tex](x^2 + 1)^2 = (x^2)^2 + (1)^2+ 2 (x^2)  = x^4 + 1 + 2x^2[/tex]  ... (b)

from(a) and (b) we see that

[tex]x^4 + 1 + 2x^2 = x^4 + 1 + 2x^2\\\implies(2x)^2 + (x^2 - 1)^2 = (x^2 + 1)^2[/tex]

HENCE PROVED.

Answer:

a.   s = 0.9r

not very sure about b

Step-by-step explanation:

Answer:

36.10, 36, 36.01,37

Step-by-step explanatoion:

Answer:

36 , 36.01 , 36.1 , 37

Step-by-step explanation:

Answer: 24 people are in the class

I am sorry I don’t know the equation but I hope this helps.

Step-by-step explanation:

3. 18. 18

- =. —. =. —-

4. ? 24

Answer:

C

[tex]6\sqrt{x} 5-4\sqrt{x} 15[/tex]

Answer:

6√5 - 4√3

Step-by-step explanation:

The question ask us to simplify the square root of 5 times the quantity 6 minus 4 square root of 3 . The word expression can be represented mathematically as follows:

√5 × 6 - 4√3 . The expression forms a Surd.

√5 × 6 - 4√3

6√5 - 4√3

Step-by-step explanation:

denominator separately

[tex]277 \sqrt{3} [/tex]

the below 160 Number 2) Same thing with the first one Multiply the Fraquetions, then multiply the numerator and denominator separately so

[tex] \frac{590}{160} \sqrt{17} [/tex]

then change to

[tex]590 \sqrt{17} [/tex]

the below that is a 5 and above it on the top right corner out 160

Answer:

The Explanation is below with attachment.

Step-by-step explanation:

For the line  y = 2x - 5

For Drawing a line on a graph we require minimum two points, but we will plot three points.

Here you can take any random value for X so that the corresponding Y value you will get.

So, put x = 0, in the equation we will get

[tex]y = 2(0) - 5\\\therefore y = -5\\\therefore Let\ A(0,-5)[/tex]

Similarly,

Put x = 1 we will get,

[tex]y= 2(1)-5\\\therefore y =-3\\\therefore Let\ B(1,-3)[/tex]

Again,

Put x = -1 we will get,

[tex]y= 2(-1)-5\\\therefore y =-7\\\therefore Let\ C(-1,-7)[/tex]

Now we have three points say point A (0,-5)), point B (1.-3) and point C (-1,-7)

See the graph below

Answer:

10657.5

Step-by-step explanation:

We can start by finding the area of the larger triangle. Using the Pythagorean theorem, we can say that 251²-105²=the bottom side², and  251²-105²=51976, so the bottom side of the larger triangle is √51976 , or approximately 228. Then, the area of the larger triangle is √51976 * 105/2 = 11969 (approximately). Then, the area of the smallest triangle (the largest triangle - the one that we're trying to find the area of) is 105*(√51976-203)/2 = approximately 1312. Then, subtracting that from the total area, we get (√51976 * 105 -  105*(√51976-203))/2 = 105*203/2 = 10657.5

ALTERNATIVELY, upon further review, we can just see that the height is 105 and the base is 203, so we multiply those two and divide by 2, as is the formula for the area of a triangle, to get 10657.5

Answer:

10 pounds of tilapias and 36 pounds of salmon,

15 pounds of tilapias and 33 pounds of salmon,

20 pounds of tilapias and 30 pounds of salmon,

25 pounds of tilapias and 27 pounds of salmon,

30 pounds of tilapias and 24 pounds of salmon.

Step-by-step explanation:

Let's call the amount of pounds of tilapia X and the amount of pounds of salmon Y.

If each pound of tilapia costs $3 and each pound of salmon costs $5, we can write the following equation:

210 = 3X + 5Y

To find five different combinations to solve this equation, we can choose values for X and then calculate values of Y.

So, for X = 10, we have that:

210 = 30 + 5Y -> Y = 36

For X = 15, we have that:

210 = 45 + 5Y -> Y = 33

For X = 20, we have that:

210 = 60 + 5Y -> Y = 30

For X = 25, we have that:

210 = 75 + 5Y -> Y = 27

For X = 30, we have that:

210 = 90 + 5Y -> Y = 24

So the combinations are (10,36), (15,33), (20,30), (25,27) and (30,24)

Answer:Your answer is..

Step-by-step explanation:(10,36), (15,33), (20,30), (25,27) and (30,24)

Answer:

The length of the side of the square is 6 feet.

Step-by-step explanation:

Given,

Length of side of square = [tex](24 - 3x)\ feet[/tex]

According to question, x = 6

So we have to substitute x with 6 in the given expression.

Length of side of square = [tex](24-3x)= 24-3\times6=24-18=6\ feet[/tex].

Thus the length of the side of the square is 6 feet.

Final answer:

To find the length of the side of the square when x is 6, substitute 6 for x into the given expression (24 - 3x). Thus, the length of the side is calculated as 6 feet.

Explanation:

The student asked for the length of the side of the square when x = 6. To find this, we substitute x with 6 into the expression representing the side length of the square, which is (24 - 3x) feet.

Replacing x with 6, we get:

The length of the side of the square when x is equal to 6 is therefore 6 feet.

Answer:

2) The height of the sunflower plant is 210 cm when it is 60 days old.

Step-by-step explanation:

Given:

The height of the sunflower plant is given by the value of the function [tex]f(x)[/tex] for a given value of 'x' and the age of the plant is given by [tex]x[/tex].

The expression is given as:

[tex]f(60)=210[/tex]

So, the 'x' value is 60 and the function value is 210.

So, the age of the plant is 60 days old. The height of the plant is 210 cm.

Thus, the above expression [tex]f(60)=210[/tex] means that the height of the sunflower plant is 210 cm when the plant is 60 days old.

So, from among all the choices given, only choice (2) defines it correctly.

Answer:

The value of function (g o f) (2)  is 24  . option D

Step-by-step explanation:

Given function as :

f(x) = [tex]\frac{10}{x}[/tex] - 1

And g(x) = 7 x - 4

So ,

(g o f) (x) =  7 ( [tex]\frac{10}{x}[/tex] - 1 ) - 4

Or, (g o f) (x) =   [tex]\frac{70}{x}[/tex] - 7 - 4

Or,  (g o f) (x) =  [tex]\frac{70}{x}[/tex] - 11

So, For x = 2

I,e  (g o f) (2) =  [tex]\frac{70}{2}[/tex] - 11

Or,  (g o f) (2) = 35 - 11

∴ (g o f) (2) = 24

Hence The value of function (g o f) (2)  is 24  . Answer  ( option D )

Answer:

The distance is 7 (approximately).

Step-by-step explanation:

Given:

Point A, (2,3) and point B, (-4,6).

Now, to find the distance between the points using the formula:

Let A = (2,3) be [tex](x_{1}, y_{1})[/tex] and B = (-4,6) be [tex](x_{2}, y_{2})[/tex] and d = distance.

Putting the distance formula to find:

[tex]d=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2}}[/tex]

[tex]d=\sqrt{(-4-2)^{2} +(6-3)^{2}}[/tex]

[tex]d=\sqrt{(-6)^{2} +(3)^{2}}[/tex]

[tex]d=\sqrt{36 +9}[/tex]

[tex]d=\sqrt{45}[/tex]

[tex]d=6.71[/tex]

Distance = 6.71

Therefore, the distance is 7 (approximately).

Answer:

D

Step-by-step explanation:

Firstly, perpendicular line has a slope that is "negative reciprocal" of the given line's slope.

The equation of a line is  y = mx + b

Where m is the slope and b is the y-intercept

So, the given line has a slope of "-4", hence the perpendicular line would have a slope of "1/4". So immediately we can eliminate Answer Choice "A".

Now, let's see which of the other choices is our correct answer. Since we know this line has slope of "1/4", we can write:

y = (1/4)x + b

Given the point (4,5), we can replace "x" with "4" and "y" with 5 and find b:

[tex]y=\frac{1}{4}x+b\\5=\frac{1}{4}(4)+b\\5=1+b\\b=5-1\\b=4[/tex]

So, the equation is:

[tex]y=\frac{1}{4}x+4[/tex]

Correct answer is D

They need to babysit for 10 hours to have same money each day.

Step-by-step explanation:

On Thursday;

Charges = $3 per hour

Initial fee = $40

let x be the number of hours.

T(x) = 3x+40

On Friday;

Charges = $4 per hour

Initial fee = $30

F(x)= 4x+30

The cost will be same when;

T(x) = F(x)

[tex]3x+40=4x+30\\40-30=4x-3x\\10=x\\x=10[/tex]

They need to babysit for 10 hours to have same money each day.

Keywords: functions, addition

Learn more about functions at:

#LearnwithBrainly

Answer:

-0.37

Step-by-step explanation:

Answer:

could you please take a screen shot please?

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

if there are 5 tanks and 65 fish in all the tanks together, you take 65 and divide it by 5 to get 13 fish in each tank

Answer:

-1/10

Step-by-step explanation:

1/2 - 3/5

Find common denominator. in this case, it'll be 10

1/2 * 5/5 = 5/10

3/5 * 2/2 = 6/10

5/10 - 6/10 = -1/10

The molar mass of dinitrogen monoxide?

Is=N2O=(14×2)+16

=44g/mol

Final answer:

The molar mass of dinitrogen monoxide (N₂O) is 44.02 g/mol, calculated by adding the atomic masses of two nitrogen atoms (14.01 g/mol each) and one oxygen atom (16.00 g/mol).

Explanation:

The molar mass of dinitrogen monoxide, which is chemically denoted as N₂O, can be calculated by adding together the atomic mass of nitrogen with the atomic mass of oxygen. Nitrogen (N) has an atomic mass of approximately 14.01 g/mol, and since we have two nitrogen atoms, we multiply this by 2. Oxygen (O) has an atomic mass of about 16.00 g/mol. Therefore, the molar mass of dinitrogen monoxide is:

(14.01 g/mol × 2) + (16.00 g/mol × 1) = 28.02 g/mol + 16.00 g/mol = 44.02 g/mol.

This value represents the weight of one mole of dinitrogen monoxide molecules. The importance of knowing the molar mass of a compound like dinitrogen monoxide relates to the calculations involved in chemical reactions and stoichiometry, specifically when dealing with gases under various conditions of temperature and pressure.

Answer:

x=6/31, y=147/31. (6/31, 147/31).

Step-by-step explanation:

y=-22x+9

y=40x-3

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

-22x+9=40x-3

9=40x-(-22x)-3

9=40x+22x-3

9=62x-3

62x=9+3

62x=12

x=12/62

simplify,

x=6/31

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

y=40(6/31)-3=240/31-3=240/31-93/31=147/31

x=6/31, y=147/31.

Answer: The answer is B.

Step-by-step explanation:

Final answer:

The correct transformation that carries the figure onto itself is Option B: reflecting across the line y=1 and rotating 1080° clockwise about the point (-7,1), as the 1080° rotation is a multiple of 360° and does not change the figure's orientation.

Explanation:

The question is asking to identify the transformation that can be applied to a figure such that the figure maps onto itself. We're given various options that involve a reflection and a rotation. Reflection across a line like y=1 would flip the figure over this horizontal line. A rotation of 1080° clockwise about a point is equivalent to a full 360° rotation three times (since 1080° = 360° × 3), which would bring the figure back to its original position, effectively leaving it unchanged.

The correct answer is Option B, which includes a reflection across the line y=1 and a 1080° clockwise rotation about the point (-7,1). This is because the 1080° rotation, being an integer multiple of full circles, results in no net rotation, so the figure looks exactly the same after this operation. The reflection flips the figure across the line y=1 but, when combined with the rotation, it results in the figure mapping onto itself.

Options A and C suggest a 990° rotation, which is not a multiple of 360° and therefore would not result in the figure mapping onto itself. Option D suggests reflecting across the line x=-6, which is not in the given options for the reflection, and a 1080° rotation about the point (-7,1), which would rotate the figure back onto itself after the reflection, but the reflection line is incorrect.

Answer:

A=(5/2x+10)(5/2x+5)

Step-by-step explanation:

A=LW

A=(5/2x+10)(5/2x+5)

If it's Pythagorean Theorem, then use the following:

[tex]A^2 + B^2 = C^2[/tex]

You have to multiply the 2 values by themselves if you are trying to find the Hypotenuse, then you need to add those together, and then find the square root.

10 x 10 = 100

15 x 15 = 225

100 + 225 = 325.

[tex]\sqrt{325} = 18.0277564[/tex]

Answer: 18

Step-by-step explanation:

So this is referencing the Pythagorean theorem. It states that the two shorter sides squared, in your case 10 and 15, is equal to the longest side, or hypotenuse squared.

Step by step

1. Calculate both the shorter sides squared: 10*10= 100 and 15*15= 225

2. Add the 2 shorter sides: 100 + 225 = 325

3. Find the square root of 335: √(325) = 18.0277563773

4. Round to the nearest integer: 18

Answer:

$2853.5

Step-by-step explanation:

Let us assume that the interest rate of both the investments of Haley is simple interest.

So, $16820 amounts of investment in nine-year CD bearing 5.8% interest will get interest of [tex]16820 \times \frac{5.8}{100} \times 9 = 8780[/tex] dollars.

Again, $21950 amounts of investment in an online savings account giving 3% interest will give interest of [tex]21950 \times \frac{3}{100} \times 9 = 5926.5[/tex] dollars.

Therefore, the nine-year CD will give more interest by $(8780 - 5926.5) = $2853.5. (Answer)

Answer:

C. $2,853.54

Step-by-step explanation:

I just answered it correct

Answer:

The standard error of distribution for n = 4 is 5 and for n = 25 is 2.

Step-by-step explanation:

1. Let's review the information given to us for solving the question:

Population mean = 72

Standard deviation  =  10

Sample₁ = 4

Sample₂ = 25

2. For finding the standard error of the mean, we use the following formula:

Standard error = Standard deviation / √Size of the sample

Standard error for Sample₁ = 10/√4

Standard error for Sample₁ = 10/2 = 5

Now, let's find the standard error for Sample₂

Standard error for Sample₂ = 10/√25

Standard error for Sample₂ = 10/5 = 2

Answer:

The range of g(x) =  {-11,-9,-7,-5}.

Step-by-step explanation:

Given:

g(x) = x – 13 over the domain {2, 4, 6, 8).

Now, to evaluate:

Putting [tex]x=2[/tex]

[tex]g(2)=2-13=-11[/tex]

Putting [tex]x=4[/tex]

[tex]g(4)=4-13=-9[/tex]

Putting[tex]x=6[/tex]

[tex]g(6)=6-13=-7[/tex]

Putting [tex]x=8[/tex]

[tex]g(8)=8-13=-5[/tex]

So, the range is {-11,-9,-7,-5}.

Therefore, the range of g(x) =  {-11,-9,-7,-5}.

Answer:

The answer is 24/2=36/3=66/5.5=108/9=180/15.

Step-by-step explanation:

Given:

24/2=_/3=_/5.5=108/_=_/15.

Now, we need to solve this by putting [tex]x[/tex] in the place of _ and then continue:

[tex]\frac{24}{2} =\frac{x}{3}[/tex]

By cross multiplication we get:

[tex]72=2x[/tex]

By dividing with 2 we get:

[tex]36=x[/tex]

Now, we will continue like this process:

[tex]\frac{36}{3}=\frac{x}{5.5}[/tex]

[tex]198=3x[/tex]

[tex]x=66[/tex]

And, then again:

[tex]\frac{66}{5.5}=\frac{108}{x}[/tex]

[tex]66x=594[/tex]

[tex]x=9[/tex]

And, last:

[tex]\frac{108}{9}=\frac{x}{15}[/tex]

[tex]9x=1620[/tex]

[tex]x=180[/tex]

Therefore, the answer is 24/2=36/3=66/5.5=108/9=180/15.

[tex]\bf x^2+4=0\implies x^2=-4\implies x = \pm\sqrt{-4}\implies x = \pm\sqrt{-1\cdot 2^2} \\\\\\ x = \pm\sqrt{-1}\cdot \sqrt{2^2}\implies x = \pm 2i[/tex]

Answer:40100 feet

Step-by-step explanation:26400 +13700 = 40100

The total height of Mauna Loa is by summation 26400 +13700 = 40100 feet.

A summation, abbreviated as a sum, is the outcome of adding two or more numbers or quantities. Here are always an integer number of terms in a summation. There could be only two terms, but there could be one hundred, a thousand, or a million.

As per the given,

Initial height = 13700 feet

Height add on = 26400 feet

Total height = 13700 feet + 26400 feet = 40100 feet

Hence "The total height of Mauna Loa is by summation 26400 +13700 = 40100 feet".

For more information about summation

brainly.com/question/10777222

#SPJ2