A teacher has been given £35 to spend on pencils and rulers.
A packet of 12 pencils costs £2.15.
A pack of 30 rulers costs £6.00.
She buys 4 packs of rulers and spends the rest on packets of pencils.
How many packets of pencils can she buy?

Answer:

4/5

Step-by-step explanation:

0.8   = 8 / 10   = 4/5

Answer:

For every 3 tablespoons of cocoa Nate uses 1 tablespoon of sugar

Answer:

[tex]\cfrac{\left(x+8\right)\left(x-8\right)}{x^2+13}[/tex]

Step-by-step explanation:

[tex]\cfrac{x+8}{x+2}\cdot \cfrac{\left(x+2\right)\left(x-8\right)}{x^2+13}[/tex]

[tex]\cfrac{\left(x+8\right)\left(x+2\right)\left(x-8\right)}{\left(x+2\right)\left(x^2+13\right)}[/tex]

[tex]\cfrac{\left(x+8\right)\left(x-8\right)}{x^2+13}[/tex]

Jose and his brother each have x baseball cards

hope it really helps...!!!

Answer:The vehicle speed at the start of the skid is approximately 20.75 mph

imagine if i got it right lol funny poop right?

haha

The width of a book is 1.5 inches.

The total width of 79 books is 1.5×79

= 118.5 inches.

The cost of a 34.5 inch wide shelf is $12.95

Therefore, the cost of a 118.5 inch wide shelf will be:

(Let the cost of the 118.5 inch wide shelf be x)

[tex] \frac{34.5}{12.95} = \frac{118.5}{x} \\ cross \: multipy \\ 34.5x = 118.5 \times 12.95 \\ x = \frac{118.5 \times 12.95}{34.5} \\ x = 44.48[/tex]

x= $44.48

Answer:

21?

Step-by-step explanation:

just divide 105 by 5?

the full question wasn't here so I just guessed what u were trying to say

Answer:

2nd option

Step-by-step explanation:

[tex]\frac{x+1}{x(x-1)}[/tex] ÷ [tex]\frac{4}{3(x-1)}[/tex]

leave the first fraction, change division to multiplication, turn the second fraction upside down , that is

= [tex]\frac{x+1}{x(x-1)}[/tex] × [tex]\frac{3(x-1)}{4}[/tex] ← cancel (x - 1) on numerator / denominator

= [tex]\frac{x+1}{x}[/tex] × [tex]\frac{3}{4}[/tex]

= [tex]\frac{3(x+1)}{4x}[/tex]

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

The cylinder which would have the greater volume is that in which the two shorter sides together, you get a short, fat cylinder.

It follows from the task content that the cylinder is made from the same paper dimensions.

On this note, it follows that when the shorter sides are joined, the longer side represents the height of the cylinder formed.

Consequently, the shorter cylinder has the greater volume.

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Answer:

431.32

Step-by-step explanation:

It is just like multiplying.
  431.32

X     8.2

And you solve it.

Hooped this helped you

[tex]y = \stackrel{\stackrel{m}{\downarrow }}{5}x-3\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

well, what's the equation of a line whose slope is 5 and passes through (-2 , -13) ?

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-13})\qquad \qquad \stackrel{slope}{m}\implies 5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-13)}=\stackrel{m}{5}(x-\stackrel{x_1}{(-2)})\implies y+13=5(x+2)[/tex]

Answer: hii

✓ 12

Step-by-step explanation:

Simplify the expression.

Hopfully this helps you

-Matthew :)

Answer: 22.5 and -19.5

Step-by-step explanation:

Answer:

All of it, ad 10%

Step-by-step explanation:

100% is all of it and 10% is 1/10 of it :]

Answer:

The missing side length is 5.7

Step-by-step explanation:

Using the pythagoream theorem you can find the missing side length of a right triangle.

The formula is [tex]a^{2} + b^{2} = c^{2}[/tex] where a and b are the lengths of the triangle legs and c is the hypotenuse.

So yours would be:

[tex]7^{2} + x^{2} = 9^{2}[/tex]

Square the numbers:

[tex]49 + b^{2} = 81[/tex]

Isolate b:

[tex]b^{2} = 32[/tex]

Square root both sides:

[tex]b=\sqrt{32}[/tex]

Simplify:

[tex]\sqrt{32} = 5.7[/tex]

Answer:

shown below

Step-by-step explanation:

9 different possible tiles to choose, but there are duplicates of two types of tiles. Out of 9 tiles, two of them are S. Therefore, the probability you choose an S is 2/9 (however much percent that is).

You'd reverse the math for letters other than P:

Out of 9 tiles, two of them are P. 9 minus 2 is seven. Seven out of 9 characters are not the letter P. Therefore, the probability you choose any letter other than P is 7/9 (however much percent that is).

The correct measurements of the surveyors movement from all the options are; m∠b = 15° and h ≈ 31.28 ft

From the image attached, we see that;

A surveyor found the angle of elevation from the ground to the top from a point = 33°

Now, the surveyor moves 20 ft towards the building and the angle of elevation becomes 48°. This means that ∠A and 48° are supplementary to each other.

Thus;

∠A + 48° = 180°

∠A = 180 - 48

∠A = 132°

From sum of angles in a triangle;

∠B + 33° + 132° = 180°

∠B = 180 - 165°

∠B = 15°

Using sine rule, we know that;

sin 33/C = sin B/20

Thus;

sin 33/C = sin 15/20

Solving for C gives;

C = 42.22

From trigonometric ratios, h/c = sin 48

h = 42.22 sin 48

h = 31.28 ft

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Answer:

2 and 5

Step-by-step explanation:

Answer:

f(g(x)) = 5(3x + 7)

Step-by-step explanation:

Solving f(g(x))

Answer:

[tex]f(g(x)) = 3(5x + 7)[/tex]

Step-by-step explanation:

Step 1:  State the eqautions

[tex]f(x) = 5x + 11[/tex]

[tex]g(x) = 3x + 2[/tex]

Step 2:  Insert the equation and solve

[tex]f(g(x)) = 5(g(x)) + 11[/tex]

[tex]f(3x + 2) = 5(3x + 2) + 11[/tex]

[tex]f(3x + 2) = 15x + 10 + 11[/tex]

[tex]f(3x + 2) = 15x + 21[/tex]

[tex]f(g(x)) = 15x + 21[/tex]

Step 3:  Simplify completely

[tex]f(g(x)) = 15x + 21[/tex]

[tex]f(g(x)) = 3(5x + 7)[/tex]

Answer:  [tex]f(g(x)) = 3(5x + 7)[/tex]

The probability of pulling out an 7up from the ice chest that contains the different drinks is 2/13.

Probability determines the odds that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability of pulling out an 7up = number of 7ups / total number of drinks

2/(8 + 3 + 2)

2/13

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Answer:

[tex]1.003*10^{25}[/tex]

Step-by-step explanation:

We'll be using Avogadro's number which defines the amount of atoms in a mole.
To find the mole amount, we use the atomic mass to find the molar mass because the atomic mass represents how many grams are in a single mole of any element

2 Hydrogen atoms have an atomic mass of 2.016 g

1 Oxygen atom has an atomic mass of 15.999 g

Adding these two numbers gives us H2O's molar mass, which is 18.015 g/mol (grams per mole).

Now we take the supplied mass of 300g and divide it by the mm (molar mass) to find the amount of moles we have. 300/18.015 = 16.653

We have 16.653 moles in 300g of H2O.

Now we have to multiply 16.653 by Avogadro's number, [tex]6.022 * 10^{23}[/tex]

This gives us: [tex]1.003*10^{25}[/tex]

Answer:

Subtracting a negative number from a negative number – a minus sign followed by a negative sign, turns the two signs into a plus sign. So, instead of subtracting a negative, you are adding a positive. Basically, - (-4) becomes +4, and then you add the numbers. For example, say we have the problem -2 - –4.

Answer:

2635.75 or 2635 3/4

used a calculator

Answer:

 x = 5, x = 1

Step-by-step explanation:

The quadratic equation 0 = 4(x - 3)2 - 16.

Using binomial theorem, (a - b)2 = a2 - 2ab + b2 to expand (x - 3)2.

0 = 4(x2 - 6x + 9 ) - 16.

Using distributive property to multiply 4 by x2 - 6x + 9.

0 = 4x2 - 24x + 36 - 16.

Subtract 16 from 36 to get 20.

0 = 4x2 - 24x + 20.

4x2 - 24x + 20 = 0.

Divide both sides by 4.

x2 - 6x + 5 = 0.

To solve the equation, factor and rewrite as x2 + ax + bx + 5

a + b = -6, ab = 1(5) = 5.

a = -5, b = -1.

Rewriting x2 - 6x + 5 as

(x2 - 5x) + (-x + 5)

Factor x in the first and -1 in the second group.

x(x - 5) - (x - 5)

Factor out common term

(x - 5)(x - 1)

By solving the above, we get

x = 5, x = 1

Answer:

Z = 63º

Step-by-step explanation:

X = 180 - 61 - 31 = 88º Angles in a triangle add to 180º

Y = 180 - X = 180 - 88 = 92º Angles in a straight line add to 180º

Z = 180 - 25 - Y = 180 - 25 - 92 = 63º Angles in a triangle add to 180º

So Z = 63º

The table is a linear regression model, and the equation of the regression model is y = 0.24x + 0.77

See attachment for the required scatter plot

From the attached scatter plot, we can see that the points are almost on a straight line

Hence, the best model that fits the scatter plot is a linear model

Using a graphing calculator, we have the following calculation summary:

The regression equation is represented as:

y = bx + a

So, we have:

y = 0.23929x + 0.77143

Approximate

y = 0.24x + 0.77

Hence, the equation of the regression model is y = 0.24x + 0.77

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Answer:

D

Step-by-step explanation:

-9 the first option

When x = - 9, I get same value of 6.7 x 10^-18 to 1 d.p

Hope this helps!

The value of x that satisfies the given equation is -9.

The correct option is (A).

A declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the making of mathematics.

As per the given data:

We are given an equation, and we have to find the value of x that satisfies the equation.

We can use the following rule of exponents to find the result of the given equation:

(i) [tex](a^m)^n = a^{m \times n}[/tex]

(ii) [tex]a^m = a^n[/tex] then m = n

For the given equation:

[tex]3^{4x} = 27^{x - 3}\\3^{4x} = 3^{3(x - 3)}\\3^{4x} = 3^{3x - 9}[/tex]

4x = 3x - 9

4x - 3x = -9

x = -9

Hence, the value of x that satisfies the given equation is -9.

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