Brandon is landscaping his backyard. He bought 2 7\8tons of decorative rock and 1 2\5 tons of boulders. How many total tons of rock did he buy?

Answer:

(a) 2 white & 1 red ball = 42 ways

(b) All 3 white balls =  4 ways

(c) All 3 red balls = 35 ways

Step-by-step explanation:

An urn contains 4 white balls and 7 red balls. Three balls are selected.

In how many ways can the 3 balls be drawn from a total of 11 ​balls:

​(a) If 2 balls are white and 1 is​ red?

The 2 white balls can be selected in ⁴C₂ ways

The 1 red ball can be selected in ⁷C₁ ways

2 white & 1 red ball = ⁴C₂ × ⁷C₁

2 white & 1 red ball = 6 × 7

2 white & 1 red ball = 42 ways

​(b) If all 3 balls are​ white?

The 3 white balls can be selected in ⁴C₃ ways

The 0 red ball can be selected in ⁷C₀ ways

All 3 white balls = ⁴C₃ × ⁷C₀

All 3 white balls =  4 × 1

All 3 white balls =  4 ways

​(c) If all 3 balls are​ red?

The 3 red balls can be selected in ⁷C₃ ways

The 0 white ball can be selected in ⁴C₀ ways

All 3 red balls = ⁷C₃ × ⁴C₀

All 3 red balls = 35 × 1

All 3 red balls = 35 ways

Answer:

Step-by-step explanation:

B because after having the star and the circle comes the square.

Answer:

The total number of boys and girls in the play is 48

Step-by-step explanation:

Don't ask how I know this, I just do.

The number of boys in school play will be 20 and number of girls in school play will be 28.

What do you mean by ratio ?

Ratio is the quantitative relationship between two values indicating how frequently one value contains or is contained within the other.

It is given that number of girls is 8 more than boys in a school play.

Ratio of boys to girls = 5 : 7

Let's assume the total number of boys in school play is x.

This meant the total number of girls in school play is :

= x + 8

We can write them in proportion form as :

x : x + 8 = 5 : 7

or solving it we get :

\(\frac{x}{x+8}\) = \(\frac{5}{7}\)

or

7x = 5(x+8)

7x = 5x + 40

7x - 5x = 40

2x = 40

x = 20

or number of boys in school play is 20.

So , number of girls in school play will be :

= 20 + 8

= 28

Therefore , the number of boys in school play will be 20 and number of girls in school play will be 28.

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Answer:

\(d^{2}\) - 16.

Step-by-step explanation:

To solve for the product of (d + 4) and (d - 4), we can use the FOIL method.

This means we multiply the first terms, then the outer, then the inner, and finally the last terms, then we add all the products together.

So, (d + 4) (d - 4) can be expanded like this:

Adding all of them together, we get: \(d^{2}\) - 4d + 4d - 16, which simplifies to \(d^{2}\) - 16.

Therefore, (d + 4)(d - 4) = \(d^{2}\) - 16.

Answer:

17.3

Step-by-step explanation:

area of paralellogram=base x height

height=sin(60) x 4= \(2\sqrt{3}\)

area = 5 x \(2\sqrt{3}\)

        = \(10\sqrt{3}\) = 17.3(to nearest tenth)

Answer:

I think it is $20

Step-by-step explanation:

Answer:

The graph of a function f is the set of points which satisfy the equation y = f(x). ... However, of these two answers, only x = −2 fits in the domain.

Step-by-step explanation:

The probability of getting one 6 on four rolls of a single die is 0.517

The number of rolls = 4

The probability of getting one 6 on four rolls of a single die = 1 - The probability of not getting one 6 on four rolls of a single die.

We know probability = Number of favorable outcomes / Total outcomes

In first throw,

The probability of not getting the number 6 = 5/6

Next three throws are independent events

Therefore,

The probability of not getting one 6 on four rolls of a single die = (5/6) × (5/6) × (5/6) × (5/6) = 625/1296

The probability of getting one 6 on four rolls of a single die = 1 - 625/1296

= 671/1296

= 0.517

Hence, the probability of getting one 6 on four rolls of a single die is 0.517

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Answer:

hope this helps

Step-by-step explanation:

The electrical resistance varies directly as the square of the voltage and inversely as the electric power, and the equation that relates them isR ∝ V²/PR = kV²/PR = V²/P. This relationship can be used to calculate the electrical resistance of the wire or component for any given voltage and power.

The electrical resistance is the measure of the difficulty in passing electric current through a wire or an electrical component. It depends on various factors, such as the material, dimensions, and temperature of the wire.The given statement says that the electrical resistance varies directly as the square of the voltage and inversely as the electric power.

In mathematical terms, this relationship can be expressed as R ∝ V²/PR = kV²/P where R is the electrical resistance, V is the voltage, P is the electric power, and k is the constant of proportionality. The constant k depends on the material, dimensions, and temperature of the wire or component.

The given statement implies that the constant k is the same for the given wire or component, and it is not affected by the voltage or the power.To find the value of k, we can use the given values of V, P, and R.

According to the statement, if the voltage is 20 volts and the electric power is 5 watts, then the electrical resistance is 80 ohms. Therefore,R = kV²/PR = k(20²)/5R = 400k/5R = 80 ohms

Substituting the value of R in the equation, we get80 = 400k/5k = (80 x 5)/400k = 1. Therefore, the equation that relates the electrical resistance, voltage, and power isR = V²/PThe constant of proportionality k is 1 for the given wire or component.

Therefore, the electrical resistance varies directly as the square of the voltage and inversely as the electric power, and the equation that relates them isR ∝ V²/PR = kV²/PR = V²/P. This relationship can be used to calculate the electrical resistance of the wire or component for any given voltage and power.

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The equivalent expression of -14 - 6 is -14 - (+6)

Equivalent expressions are expressions that have the same value when evaluated

The expression is given as:

-14 - 6

Put the terms of the expression in brackets

-14 - (6)

Rewrite 6 as +6

-14 - (+6)

Hence, the equivalent expression of -14 - 6 is -14 - (+6)

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Answer:

wym?but thanks

Step-by-step explanation:

Based on the probability values, it will take the student 2 hours to stay outside the home

The given parameters are:

Probabilities

P(1) = 0.4

P(2) = 0.3

P(3) = 0.3

Time

Time 1 = 2 hours

Time 2 = 3 hours

Time 3 = 1 hour

When the above are represented on a table, we have the following table of values

Time (x)                    |   2        3          1

Probability (P(x))       | 0.4      0.3     0.3

The expected value of the student is then calculated as

E(x) = ∑ x * P(x)

Substitute the known values in the above equation

E(x) = 2 * 0.4 + 3 * 0.3 + 1 * 0.3

Evaluate the products

E(x) = 0.8 + 0.9 + 0.3

Evaluate the sum

E(x) = 2

Hence, the expected value is 2

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Answer:

The nth term is Tn = 2[T(n- 1) -2]

The next term is 356

Step-by-step explanation:

Given

Terms: 15,26,48,92,180

Solving (a) : The recursive n term

We have:

T1 = 15

T2 = 26 = 13 * 2 = (15 - 2) * 2

T3 = 48 = 24 * 2 = (26 - 2) * 2

T4 = 92 = 46 * 2 = (48 - 2) * 2

T5 = 180 = 90 * 2 = (92 - 2) * 2

So, the nth term can be represented as:

Tn = [T(n-1) - 2] * 2

Tn = 2[T(n-1) - 2]

The next term is the 6th term.

So, substitute 6 for n in the above formula.

T6 = 2 * [T(6 - 1) - 2]

T6 = 2 * [T5 - 2]

Substitute 180 for T5

T6 = 2 * (180 - 2)

T6 = 2 * 178

T6 = 356

Answer:

2251.86

Step-by-step explanation:

hope this works

The multiplication is gives 2400.

Significant figures are the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value.

Given number:

288.7 x 7.8

Now, rounding to 1 significant figure

288. 7 = 300

7.8 = 8

So, the multiplication is as follows:

=300* 8

= 2400

Hence, the multiplication is 2400.

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Answer:

-17/12

Step-by-step explanation:

║5/6 - 7/12║- ║5/3║

= ║10/12 - 7/12║ - ║5/3║

= ║3/12║- ║5/3║

= 3/12 - 5/3

= 3/12 - 20/12

= -17/12

The value of y' by implicit differentiation, the value of y is \(y = \sqrt{5x +c}\)

We differentiate each side of an equation with two variables by taking one as a variable and the rest are constant.

Given

The function is \(y^2 + 5 = 5x\)

where x and y are variables..

On differentiating the equation, we have;

\(2yy' + 0 = 5\)

on simplifying, we have

2yy' = 5

Now solve the equation explicitly for y and differentiate to get y' in terms of x.

2yy' = 5

Separate the variables

\(y^2 = 5x + c\)

Taking square root on both the side

\(y = \sqrt{5x +c}\)

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Answer:

13.27 cm

Step-by-step explanation:

I am using (xy) to mean the length of the side xy

7^2 + (xy)^2 = 15^2

49 + (xy)^2 = 225

(xy)^2 = 225-49

(xy)^2 = 176

Side (xy) = sqrt(176) = 13.2664991614 = 13.27 cm

Answer:

A

Step-by-step explanation:

Comment

The median of a trapezoid is the line going horizontally across the midpoint values of the 12 inch and 16 inch bases.

In other words, it is the average length of the 2 bases.

Formula

(b1 + b2 ) / 2

Solution

median Length = (16 + 12) / 2

median length = 28/2

median length = 14

Answer

median length = 14 inches

The equation is incorrectly written by the student to find the third side of the triangle.

The right triangle states that if one of the angles of a triangle is a right angle - 90º, the triangle is called a right-angled triangle or a right triangle.

(Hypotenuse)² = (Base)² + (Altitude)²

If the two sides are right angle triangle is 5 units and 13 units and the equation is  5²+13²=c² then the value of c is

c=√25+169

c=13.92 and 13.92 is not an integer number.

so, the equation written by the student to find the third side is incorrect.

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Answer:

6

Step-by-step explanation:

Slope = delta y/delta x

\(slope = \frac{y_1-y_2}{x_1-x_2}\)

Slope = (-3-3)/(1-2)

Slope = -6/-1

Slope = 6

Answer:

6

Step-by-step explanation:

Given :-

And we need to find the slope of the line passing through the two points . The slope of the line passing through two points is the difference of y coordinates divided by difference of x coordinates.

Substituting the respective values :-

\(:\implies\) m = y₁ - y₂/ x₁ - x ₂

\(:\implies\) m = -3 -3 / 1 - 2

\(:\implies\) m = -6/-1

\(:\implies\) m = 6

Hence the slope of the line is 6.

Answer: 15

Step-by-step explanation:

u can multiply by 2 and get 15

Answer:

If a runner jogs at a constant speed v, then the distance d he covers in time t can be given by the equation:

d(t) = v * t

Here, v is the speed of the runner in units of distance per unit time.

Hope this helps!

( 2x + 11 ) ( 2x - 11 ) is factor of linear equation .

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

                                      A linear equation with one variable is one that contains just one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value.

= 4x² - 121

= (2x)² - ( 11 )²

= ( 2x + 11 ) ( 2x - 11 )

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We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour.

Sample Mean: = (29 + 27 + 34 + 40 + 22 + 28 + 14 + 35 + 26 + 35 + 12 + 30 + 23 + 18 + 11 + 22 + 23 + 33) / 18

= 480 / 18

≈ 26.667

Sample Standard Deviation (s):

= ✓((Σ(29 - 26.667)² + (27 - 26.667)² + ... + (33 - 26.667)²) / (18 - 1))

≈ ✓(319.778 / 17)

≈ ✓(18.81)

≈ 4.336

Confidence level = 99%

Sample Size (n) = 18

Sample Mean = 26.667

Sample Standard Deviation (s) = 4.336

Degrees of Freedom (df) = n - 1 = 18 - 1 = 17

Using a t-table or statistical software, we find that the critical value for a 99% confidence level with 17 degrees of freedom is approximately 2.898.

Margin of Error (E) = 2.898 * (4.336 / ✓18))

≈ 3.748

Confidence Interval = (26.667 - 3.748, 26.667 + 3.748)

= (22.919, 30.415)

We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour. This means that if we were to repeat the study multiple times and construct confidence intervals, approximately 99% of those intervals would contain the true mean healing rate of the population.

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Answer:

y ≥ 0

Step-by-step explanation:

The factorized expression of x = a²b² + 2a + a⁴ is x = a(ab² + 2 + a³)

The expression is given as:

x = a²b² + 2a + a⁴

Factor out a from the expression

x = a(ab² + 2 + a³)

The above expression cannot be further factorized.

Hence, the factorized expression of x = a²b² + 2a + a⁴ is x = a(ab² + 2 + a³)

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