Bart is writing lines on a chalkboard that is initially empty. It ordinarily takes Bart 50 minutes to cover the whole board; however, today, Nelson is erasing the board while Bart is writing. Nelson can erase the board in 80 minutes by himself. If they work simultaneously, how long will it be until the whole board is covered?

The test statistic of the proportion is given as follows:

z = 4.47.

The equation that gives the test statistic for a proportion is given as follows:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

In the context of this problem, the values of these parameters are given as follows:

[tex]p = 0.06, n = 724, \overline{p} = \frac{72}{724} = 0.0994[/tex]

Hence the test statistic for the proportion is calculated as follows:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.0994 - 0.06}{\sqrt{\frac{0.06(0.94)}{724}}}[/tex]

z = 4.47.

Meaning that the first option is correct.

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Thus, the probability of the electron being in a spherical shell at distance (a) from the proton is e^(-a/a0), at distance (b) is e^(-b/a0), and at distance (c) is e^(-c/a0).

Probability is a metric for determining the possibility or chance of an event happening. It is a mathematical concept that measures the unpredictability of an occurrence and is frequently stated as a decimal or fraction. For example, if the probability of flipping a coin and obtaining heads is 0.5, there is a 50% chance of flipping heads. The number of favorable outcomes to the total number of potential outcomes is used to compute probability. In other words, it is the number of ways an event may occur divided by the total number of conceivable outcomes. Probability is used to make predictions and take wise decisions in a variety of disciplines, including mathematics, science, finance, and engineering.

How to solve?

If we assume the electron is in a hydrogen 1s orbital, the probability density function is given by the square of the 1s wavefunction, which is:

p(r) = (1/πa0^3) e^(-r/a0)

P(r, r+δr) = ∫p(r')dV = ∫p(r')4πr'^2dr'

For the given distances (a), (b), and (c), the probabilities are:

P(a) = ∫p(r')4πr'^2dr' = (1/πa0^3) ∫e^(-r'/a0)4πr'^2dr' = (1/πa0^3) * 4π * a0^3 * e^(-a/a0) = e^(-a/a0)

P(b) = e^(-b/a0)

P(c) = e^(-c/a0)

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Answer: 288

Step-by-step explanation: the number of songs downloaded this year will be x

x/12=30-6

= x/12=24

12*24= 288

x=288

Answer:

30

Step-by-step explanation:

The 45-45-90 Triangle Theorem states that in the isosceles 45-45-90 triangle, if we designate each leg as [tex]a[/tex], the base, or hypotenuse is [tex]a\sqrt{2}[/tex] . Since we know the leg is [tex]15\sqrt{2}[/tex], the hypotenuse would be:

[tex]15\sqrt{2} * \sqrt{2} =\\15 * 2=\\30[/tex]

Each shirt = $2.99, each pair of slacks = $5.99, and each sports coat = $6.99.

Total refers to a whole or full amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total. The result of adding 8 and 8 is 16.

Let shirts equal SH, Slacks equal S, and sports coats equal SC.

2SH+2S equals 17.96.

6SH+3S+2SC=49.89

5SH+1SC=21.94

We'll use them to address

6SH+3S+2SC=49.89

-6SH-6S=--53.88, multiplying by -3 to eliminate SH.

-3S+2SC=-3.99

-30SH-6SC=-131.64, multiplying the third by -6 to eliminate SH

30SH+15S+10SC=249.45,multiplying by 5 to eliminate SH.

15S + 4SC = 117.81

Now 15S + 4SC = 117.81  and -3S+2SC=-3.99

S = $5.99

As a result, we may calculate SH as $2.99 and use the value of S and SH we get SC = $6.99

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The number of small boxes and large boxes for the given linear equation condition purchased is 10 and 7 respectively.

What is a linear equation?

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

According to the question, a builder needs to purchase nails in order to construct a house.

Both small and large boxes of nails are provided. There are 50 nails in each small box and 350 in each large box.

The contractor purchased 3 more small boxes than large boxes, hence it is assumed that he purchased an 'x' number of large boxes.

He purchased (x+3) small boxes.

So, 50(x+3) + 350(x) = 2950.

50x + 150 + 350x  = 2950.

400x = 2950 - 150.

400x = 2800.

x = 7.

∴ The no. of large boxes he purchased is 7.

∴ The no. of small boxes he purchased is 10.

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a. The return on investment is $700.

b. The payment should be $20.

c. The total value is $10,680.

Calculation of the return on investment, payment and total value:

a. Since the return on investment is 7%

And, the invested amount is $10,000

So, the return on investment should be

= 7% of $10,000

= $700

b. Since the expense ratio is 0.2%

So, here the payment be like

= 0.2% of $10,000

= $20

c. The total value should be

= $10000-$20 +$700

= $10680

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Answer:

16.52

Step-by-step explanation:

hyp²= opp²+adj²

let opp =16in

hyp= 23in

adj²=23²-16²

=529 -256

= 273

adj =√273

= 16.52

Answer: nope

Step-by-step explanation:

Since the side length is three units, the specified rectangular prism's volume will be 27 units.

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity. The capacity of an object is measured by its volume. For instance, a cup's capacity is stated to be 100 ml if it can hold 100 ml of water in its brim. The quantity of space occupied by a three-dimensional object can also be used to describe volume.

Here,

Length of side=3 units

Volume=(side)³

=3³ unit

=27 unit³

The length of side is 3 unit, so the volume of the given rectangular prism will be 27 unit.

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The measure of an exterior angle of a triangle is equal to the measure of its neighboring interior angle if both measure 90 degrees, according to the theory of supplementary angles.

If the sums of two angles equal 180 degrees, they are said to be supplementary.

However, two angles do not need to be near one another in order to be complementary.

If two angles' measures sum up to 180 degrees, they are said to be supplementary.

A triangle's outside angle complements the neighboring inner angle.

The adjacent internal angle will therefore likewise be 90 degrees if the exterior angle is.

Therefore, the measure of an exterior angle of a triangle is equal to the measure of its neighboring interior angle if both measure 90 degrees, according to the theory of supplementary angles.

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Correct question:
Can the measure of an exterior angle of a triangle ever equal the measure of its adjacent interior angle? Explain in 2-3 sentences.

Answer:

To find the change in temperature per ice cube, you need to divide the total change in temperature by the number of ice cubes. In this case, you would divide -15F by 5 ice cubes to get -3F per ice cube. The negative sign indicates that the temperature of the tea decreased.

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to know if 5x²y²z +10x²y²z is monomial, binomial, or trinomial, and what its degree is.

The degree of a term is the sum of the degrees of the variables in the term:

  degree = 2 + 2 + 1 = 5

Two terms are shown. However, the terms are like terms, so can be combined into one term:

  15x²y²z

This tells us the expression is a monomial.

__

Additional comment

The terms of a binomial must be unlike. That is, they don't count as separate terms if they can be combined.

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Answer:

A = -5

Step-by-step explanation:

the point of intersection of the given function will be (-1,5).

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

the functions f(x) = (x+6)(x+2) and g(x) = x + 6

Equating them with each other

(x+6)(x+2) = x + 6

x+2 = 1

x = -1

f(-1) = 5

So the point of intersection of the given function will be (-1,5).

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By using the concept of function, it can be seen that the given table represents a function.

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here the values under x represents the domain and the values under y represents the Range.

From the table it can be seen that

Every point of the domain maps to unique point on the range.

So this is a function.

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Answer:

$60

Step-by-step explanation:

Let x = the original cost

x - .25x = 45

.75x = 45  Divide both sides by .75

x = 60

The line CD is the bisector line that divides the line segment AB into two equal parts that are AE = EB.

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is the m:n ratio, finding the mid-point of the line, etc.

Make an opposite bisector of the Stomach muscle and mark the convergence point of line E. To check your outcome, measure AE and EB and the points between the bisector and Stomach muscle.

The line CD is the bisector line that divides the line segment AB into two equal parts that are AE = EB.

The diagram is given below.

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Answer:

6

Step-by-step explanation:

1) Total-Amount left

112-64=48

So now we know how much money she spent on the carne asada fries. Now let's get on with the next step.

2) Amount Spent/Cost for carne asada fries

48/8=6

So they bought 6 carne asada fries

I hope this helps!!!

Step-by-step explanation:

James and Bethany Morrison are celebrating their 10th anniversary by having a reception at a local reception hall. They have budgeted $3,500 for their reception. If the reception hall charges a $50 cleanup fee plus $32 per person, find the greatest number of people that they may invite and still stay within their budget. James and Bethany can invite at most people to the reception. (Round down to the nearest whole person).

3,500 = 32p + 50

subtract 50 from both sides:

3,450 = 32p

divide both sides by 32:

p = 107.8125

because you cannot invite part of a person, round down to 107 people.

Answer:

107

Step-by-step explanation:

You have $3,450 to work with and you divide that by 32, which is the cost per person, and you come up with 107.8... You can round up to 108, but you risk(because you are) being over budget.

If its half-life is 93 minutes, then the amount left after 279 minutes will be equal to 164 grams.

In radioactivity, the half-life is the amount of time needed for half of a radioactive sample's atomic nuclei to spontaneously decay (convert into different nuclear species by emitter particles and energy) or, alternatively, the amount of time needed for the radioactive material's disintegration rate to drop by half.

As per the given information given in the question,

Initial amount, N₀ = 1312 grams

Time elapsed, t = 279 min

Half-life, [tex]t^1^/^2[/tex] = 93

Then, use the formula of half-life:

N(t) = N₀[tex](\frac{1}{2})^t^/^(^t^)^1^/^2[/tex]

Substitute the values in above equation,

N(t) = 1312[tex](\frac{1}{2})^2^7^9^/^9^3[/tex]

N(t) = 1312(1/2)³

= 1312 × 0.125

N(t) = 164 grams.

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Answer: 164 grams

Step-by-step explanation: I got the answer right on my ixl

Answer:

2n + 1 = 157

2n = 157 - 1

2n = 156

n = 156/2

n = 78

Step-by-step explanation:

hope this helps

The required hours will they have ran the same number of miles is 3.

Speed distance time is the equation used to make sense of the connection between speed, distance and time. That is speed = distance ÷ time. Or on the other hand to put it one more way distance isolated by speed will give you the time. Given you know two of the sources of info you can resolve the third.

Erick distance:: 5 + 1x

Similarly for jess,

Jess distance:: 2 + 2x

To cover same number of miles, above two equations will be equate;

5 + x = 2 + 2x

x = 3 hrs

Thus, requierd number of hours is 3.

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Correct question:

Eric has already ran 5 miles and is continuing to run at a pace of 1 mile per hour. Jess has only run 2 miles and is continuing to run at a pace of 2 miles per hour. In how many hours will they have ran the same number of miles?

In linear equation,(10/21) glasses of water does she drink, in glae per hour.

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.

3/4 of hour she drinks (2/3) of a glass

So, in 1 hour she drinks (2/3)×(5/14) of a glass

So, in 1 hour she drinks (10/21) glasses of water.

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Answer:

B) 69.6

Step-by-step explanation:

Derivative of log(tanhx) = 2cossec(2x)

Let us assume y = log (tan hx)

On differentiating both sides ,

[tex] \frac{dy}{dx \: } = \frac{d \: log(tanhx)}{dx} [/tex]

[tex] \frac{dy}{dx} = \frac{d log( \tan(hx) ) }{d \tan(hx).d \tan(hx) } \times dx[/tex]

[tex] \frac{dy}{dx} = \frac{1}{ \tan(hx) \times \sec( {h}^{2x} ) } [/tex]

[tex] \frac{dy}{dx} = \frac{ \cos(hx) }{ \sin(hx) } \times \frac{1 }{ \cos(h {}^{2} ) } [/tex]

[tex] \frac{dy}{dx} = \frac{2}{2 \sin(hx). \cos(hx) } [/tex]

[tex] \frac{dy}{dx} = \frac{2}{ \sin(h)(2x) } [/tex]

dy/dx = 2 cos sec (2x)

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The slope of the line is  1/2 or 0.5

The slope of a line characterizes the direction of a line.

To find the slope of a line when the coordinates of the two points are given  you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points .

Thus if

A ( x1, y1)  and B( x2, y2)

The slope of the line is  y2 - y1 / x2-x1

Calculations

Given ;

A ( -21, -47)

B(-15, -44)

slope = 3/6

           =1/2 or 0.5

The slope of the line is 1/2 or 0.5

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Answer:

t=2/f-5

Step-by-step explanation:

The change in the temperature after 4 1/4 hour is -6.8 C.

Given :

A freezer in a lab is set so that the temperature changes at a rate of –1.6 C every hour.

Temperature :

Temperature is the degree of hotness or coldness of an object.

The degrees must contain any units like kelvin , centigrade etc .

Change in temperature after 4 1/4 hours = change rate for hour * number of hours.

= -1.6 C * 4 1/4

= -1.6 C * 4.25

= -16 / 10 C * 425 / 100

= -16 * 425 / 10 * 100 C

= -6800 / 1000 C

= -68 / 10 C

= -6.8 C

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Answer:

x = 2 , x = 5

Step-by-step explanation:

assuming you mean

[tex]\sqrt{9x-9}[/tex] = x + 1 ( square both sides to clear the radical )

([tex]\sqrt{9x-9}[/tex] )² = (x + 1)² ← expand using FOIL

9x - 9 = x² + 2x + 1 ( subtract 9x from both sides )

- 9 = x² - 7x + 1 ( add 9 to both sides )

0 = x² - 7x + 10 ← factor the quadratic

consider the factors of the constant term (+ 10) which sum to give the coefficient of the x- term (- 7)

the factors are - 2 and - 5 , since

- 2 × - 5 = + 10 and - 2 - 5 = - 7 , then

(x - 2)(x - 5) = 0

equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

x - 5 = 0 ⇒ x = 5

As a check

substitute these values into the equation and if both sides are equal then they are the solutions.

x = 2

left side = [tex]\sqrt{9(2)- 9}[/tex] = [tex]\sqrt{18-9}[/tex] = [tex]\sqrt{9}[/tex] = 3

right side = 2 + 1 = 3

left side = right side , so x = 2 is a solution

x = 5

left side = [tex]\sqrt{9(5)-9}[/tex] = [tex]\sqrt{45-9}[/tex] = [tex]\sqrt{36}[/tex] = 6

right side = 5 + 1 = 6

left side = right side, so x = 5 is a solution