Elias was given a lock for his school locker. The lock contains numbers between
O and 59 (60 different numbers). If 3 numbers are used to unlock the lock, and
the numbers can't repeat, how many codes can his lock have?

Answer: irrational number

Step-by-step explanation:

Let us write it out.

      [tex]\displaystyle \frac{23}{\sqrt{3} }[/tex]

Next, we will define ratoinal and irrational.

      A rational number is a number that can be written as a whole number, fraction, or decimal that ends / repeats.

      An irrational number is any number that cannot be turned into a fraction.

Let us see which category the number given falls into.

      [tex]\displaystyle \frac{23}{\sqrt{3} } = 13.27905619\;\;\;\;\;\;\text {it goes on...}[/tex]

This means  [tex]\frac{23}{\sqrt{3} }[/tex] is an irrational number.

Answer:

745.31

Step-by-step explanation:

20x25=500

(2(12.5)pie)/2=245.435

245.435+500=745.31

Answer:

m∠F = 45°

because

Corresponding

Parts of

Congruent

Triangles are

Congruent

Considering it's vertex, the quadratic equation that could be represented on the plane is given as follows:

f(x) = (x - 8)² - 6.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

Researching the problem on the internet, it is found that the given graph has vertex at (8,-6), hence h = 8, k = -6 and considering a = 1 the equation is given as follows:

f(x) = (x - 8)² - 6.

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Answer:

hope u understand...........

Step-by-step explanation:

I think the question should be m<-2.2 according to your number line

the answer is graphed. I hope it helps

Answer:B

Step-by-step explanation: this is because when it is greater than, it goes right, and if there is no "equal to" it is closed circle and B has a closed circle going to the right of -2.2

Answer:

that 2 out of 20 ratio you have 18 to 1 odds of getting these

The number of combinations of plays that is possible will be 2.

Let the number of combinations be represented by x.

From the information given, we are informed that the touchdown scores 7 points, a field goal scores 3 points, and a safety scores 2 points.

Therefore, this will be:

7x + 3x + 2x = 24

12x = 24

x = 24/12

x = 2

Therefore, there are 2 combinations.

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Answer:

£15.20

Step-by-step explanation:

butter : sugar : flour = 2 : 1 : 9

Total mass for 1 recipe = 30 g

2 + 1 + 9 = 12

12x = 30

x = 30/12

x = 2.5

For 1 scone:

butter = 2x = 2(2.5) g = 5 g

sugar = x = 2.5 g

flour = 9x = 9(2.5) g = 22.5 g

Cost for 1 scone:

butter: 5 g × £2.50/(500 g) = £0.025

sugar: 2.5 g × £1.60/(1000 g) = £0.004

flour: 22.5 g × £0.6/(1500 g) = £0.009

Cost for 1 recipe = £0.025 + £0.004 + £0.009 = £0.038

Cost for 400 scones = 400 × £0.038 = £15.20

Answer: £15.20

An exponential function that represents the population is y = 5 (7)ˣ. And the population after 5 days will be 84035.

The exponent denotes that the base will rise to a specific level of strength. The base is X, and the power is n.

The table is shown.

The exponential equation is given as

y = abˣ

Then at x = 1, y will be 35. Then we have

35 = ab ...1

Then at x = 2, y will be 245. Then we have

245 = ab² ...2

On solving equations 1 and 2. Then we have

a = 5 and b = 7

Then the exponential function will be

y = 5 (7)ˣ

Then the population after 5 days will be

y = 5 (7)⁵

y = 5 x 16807

y = 84035

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Using proportions, the amount that Sally can expect to receive from social security annually is given by:

c. $19,153.26.

A proportion is a fraction of a total amount, and this fraction can also represent a percentage of the total amount.

She is expected to receive 42% of her average annual salary of $45,603, hence, considering 0.42 is equivalent to 42%:

A = 0.42 x 45603 = $19,153.26.

Which means that option C is correct.

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

Explanation:

See the diagram below.

The diagram shows we have a right triangle with these side lengths:

We'll use the pythagorean theorem to find c

[tex]a^2 + b^2 = c^2\\\\c = \sqrt{a^2 + b^2}\\\\c = \sqrt{(8)^2 + (5.5)^2}\\\\c = \sqrt{94.25}\\\\c \approx 9.7082\\\\c \approx 9.7\\\\[/tex]

Mrs. Durham and Brett are about 9.7 meters apart.

Answer:

each hot dog costs $3

Step-by-step explanation:

$18÷6 hotdogs=$3 or $3×6 hotdogs=$18

Answer:

Step-by-step explanation:

1. The moment he started: 3 bacteria

1st hour: 3*2 bacteria = 3*[tex]2^{1}[/tex] bacteria

2nd hour: 3*2*2 bacteria = 3*[tex]2^{2}[/tex] bacteria

3rd hour: 3*2*2*2 bacteria = 3*[tex]2^{3}[/tex] bacteria

etc.

Each hour the number of bacteria multiplies by 2 (the power of 2 is increased by 1), therefore, [tex]B=3*(2)^{n}[/tex]

2. Exponential function has the form of [tex]f(x)=ab^{x}[/tex]

if a is greater than 0 and b is greater than 1, then it's exponential growth.

The answer is:

[tex]y=4^{x}[/tex]  (4 > 1)

3. If smth increases by 2.5% each time, that means that at first you had 100% and then it became 100%+2.5% = 102.5%. So each time we multiply the value by 1.025 (100*1.025=102.5).

4. Linear equation form: [tex]y=ax+b[/tex]

Quadratic equation form: [tex]y=ax^{2} + bx + c[/tex]

Exponential equation form: [tex]y=ab^{x}[/tex]

In this case, a = 3.8, b = -5.5, c = -4.8

5. (a) square root

(b) linear

(c) exponential

(d) quadratic

6. Each year the car's worth is multiplied by 0.82 (82%). Therefore, after n years, the value will be: V = 27 500 * [tex]0.82^{n}[/tex]

7. Neither first, nor second differences are constant in case of an exponential relation, because we do not add but multiply.

Ex. [tex]y=2^{x}[/tex]

values: 1 2 4 8 16 32...

1st diff: 1 2 4 8 16...

2nd diff: 1 2 4 8...

8. (a) [tex]7^{11} / 7^{7} = 7^{11-7} = 7^{4}[/tex]

(b) [tex](\frac{4}{9})^{12} *(\frac{4}{9})^{5} =(\frac{4}{9} )^{12+5}=(\frac{4}{9})^{17}[/tex]

(c) [tex]4^{11} / (4^{5})^{3} =4^{11} / 4^{5*3}=4^{11} /4^{15}=4^{11-15}=4^{-4}[/tex]

(d) [tex]8^{-6}*8^{3}=8^{-6+3}=8^{-3}[/tex]

The total pounds of science books that sanya carried is; 6⁷/₈ pounds

From the attached Line Plot, we can see the book weights.

Now, we are told that Sanya carried all the books weighing 2¹/₄ pounds and 2³/₈ pounds.

From the line plot we see that;

Number of books weighing 2¹/₄ pounds are 2 books

Number of books weighing 2³/₈ pounds is 1 book

Thus;

Total weight of books carried by Sanya = 2(2¹/₄) + 1(2³/₈)

Total weight = 4¹/₂ + 2³/₈

Total Weight = 6⁷/₈ pounds

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Answer:

x = 8

z = 65

Step-by-step explanation:

Through various rules, we are able to assert: (6x + 67)° = 115°.

Now, we want to solve for x:

6x + 67 = 115

6x = 48

x = 8

We know that z° is equal to the complement of (6x + 67)°, and together these must sum to 180°. Therefore, we can simply take 180° - 115° to find that z° = 65°.

a) a= 2×40 = 160°

b) b = 60/2 = 30°

c) c = 40°

d) d = 115°

Midpoint, as the word suggests, means the point which lies in the middle of something. The correct option is A.

Midpoint, as the word suggests, means the point which lies in the middle of something. The midpoint of a line segment means a point which lies in the mid of the given line segment.

There is no flaw in the steps. Hence, the correct option is A.

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Answer:

slope= (y2-y1)/x2-x1

Step-by-step explanation:

(-5-(-9))/(-9-(-1))

=-1/2

[tex]\large{\underline{\underline{\pmb{\sf{\color{yellow}{Answer:}}}}}}[/tex]

-1/2

Step-by-step explanation:

Slope

[tex] \sf let \: ( - 9, - 5) = (x_1,y_1) \\ \\ \sf ( - 1, - 9) = (x_2,y_2)[/tex]

[tex] \sf Slope(m) = \frac{y_2 - y_1}{x_2 - x_1} [/tex]

Substituting the values

[tex] \sf \implies m = \frac{ - 9 - ( - 5)}{ - 1 - ( - 9)} \\ \\ \\ \sf \implies m = \frac{ - 9 + 5}{ - 1 + 9} \\ \\ \\ \sf \implies m = \frac{ - 4}{8} \\ \\ \\ \sf \implies m = - \frac{1}{2} [/tex]

Answer: The answer is D. 72 cu ft.

Step-by-step explanation:

The number in standard form is 632.058

The number is given as:

Six hundred thirty-one and fifty-eight thousandths

This means:

Six hundred thirty-one + fifty-eight thousandths

Express Six hundred thirty-one as 631

632  + fifty-eight thousandths

Express fifty-eight thousandths as 58/1000

632  + 58/1000

Express as decimal

632  + 0.058

Evaluate the sum

632.058

Hence, the number in standard form is 632.058

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The relationship between dollars delivered and rand received represents a function.

Corresponds to a mathematical relationship between two variables, x and y, where the set of x values ​​is associated with a y value. Being expressed by the formula:

Therefore, in the exchange rate question, x is the independent variable, that is, the value of $100, and y will correspond to the dependent variable, which is the value of rand that will be received in relation to the dollar.

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This answer does look right to me.

The number of cans the school will collect is T = 190 c.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

Given:

Each class is challenged to collect 190 cans.

If there are c classes in the school.

Then, the number of Cans can be collected is:

= Number of classes x number of cans each class collect

=  c x 190

= 190 c

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Using the given information, the radius of the sphere to the nearest meter is 13m

From the question, we are to determine the radius of the sphere

Using the formula for calculating the volume of a sphere,

[tex]V = \frac{4}{3} \pi r^{3}[/tex]

Where V is the volume

and r is the radius

From the given information,

V = 9198 m³

Then,

[tex]9198 = \frac{4}{3} \times \pi r^{3}[/tex]

[tex]9198 = \frac{4}{3} \times 3.14 \times r^{3}[/tex]

[tex]4 \times 3.14 \times r^{3} = 9198 \times 3[/tex]

[tex]4 \times 3.14 \times r^{3} = 27594[/tex]

[tex]r^{3} = \frac{27594}{4 \times 3.14}[/tex]

[tex]r = \sqrt[3]{\frac{27594}{4\times 3.14} }[/tex]

r = 12.99995 m

r ≅ 13 m

Hence, the radius of the sphere to the nearest meter is 13m.

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A cube is a three-dimensional solid object having six square faces. The measure of the length of the diagonal of the face of the cube is 12.2 cm.

A cube is a three-dimensional solid object having six square faces, facets, or sides, three of which meet at each vertex. The cube is one of the five Platonic solids and the only regular hexahedron.

Given the length of an edge of the cube is √75 cm, therefore, the length of the diagonal of the face of the cube will be √2 times the length of an edge of the cube. Thus, the measure of the length of the diagonal of the face of the cube is,

Length of the diagonal of the face = √2 × √75 = 12.2 cm

Hence, the measure of the length of the diagonal of the face of the cube is 12.2 cm.

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Answer: ITS B (12.2)

Step-by-step explanation:

I am the lizard king, I can do anything.

They are written in term of power to the base of a function. The value of n that will make both expression equal is 2/9

They are written in term of power to the base of a function. Given the expression below:

[tex]216^{n-2}=\frac{1}{36}^{3n}[/tex]

This can be further simplified as:

[tex]6^3^{n-2}=(6^{-2})^{3n}\\6^{3n-2}=6^{-6n}[/tex]

Cancel the base to have:

3n-2 = -6n
3n+6n = 2

9n = 2

n = 2/9

Hence the value of n that will make both expression equal is 2/9

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Answer:

y=½x-6

Step-by-step explanation:

m= ½

equation of the line: y-y1=m(x-x1)

y+5=½(x-2)

y=½x-6

Answer:

[tex]y =\dfrac{1}{2}x-6[/tex]

Step-by-step explanation:

Point-slope formula

[tex]y-y_1=m(x-x_1)[/tex]

where:

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}y-y_1 & =m(x-x_1)\\\\\implies y-(-5) & =\dfrac{1}{2}(x-2)\\\\y+5 & =\dfrac{1}{2}x-1\\\\y & =\dfrac{1}{2}x-1-5\\\\y & =\dfrac{1}{2}x-6\end{aligned}[/tex]

We will see that the percentage in which the price decreases is 90%, thus the age is 90 years.

How old is Andrés?

We know that the percentage in which the price decreases is equal to the age of Andrés.

We can write:

P = $4,000 = $40,000*(1 - k)

Where k is the percentage in decimal form.

Solving for k:

k = ($40,000 - $4,000)/$40,000 = 0.9

To obtain the percentage, we multiply by 100%.

0.9*100% = 90%

We conclude that Andrés is 90 years old.

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