write the equation of the line that crosses the y-axis at "-2" and has a slope of 2/3

30%  is the probability that a student surveyed plans to attend the school.

What does a probability simple definition entail?

The likelihood or chance that a specific event will occur is represented by a probability. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%. Probability is the chance that something will happen, or how likely it is that an event will occur. When we toss a coin in the air, we use the word probability to refer to how likely it is that the coin will land with the heads side up.

  P(Boys) = 50%

  P(Girls) = 50%

 P(Boy attending) = 30%

  p = P(B)/P(Total)  = 30%/100  = 0.3  = 30%

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Considering the given linear function, it is found that:

a)

b) The discrete domain of the function is: {0, 1, 2, 3, 4, 5, 6, 7}.

c) The graph of the function is given at the end of the answer.

A linear function, in slope-intercept format, is modeled according to the rule given below:

y = mx + b

In which:

The amount of money you have remaining after printing p photographs is  modeled by the following function:

M(p) = 10 - 1.44p.

Hence the coefficients are as follows:

The number of photos printed is a discrete number, as this number cannot assume decimal values, hence the domain is also discrete.

You cannot print a negative value of numbers, neither can M(p) be negative, hence the domain, which is the number of photos you can print, is:

{0, 1, 2, 3, 4, 5, 6, 7}.

Considering the above domain, the graph of the function is given by the image at the end of the answer.

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Answer:

Yo wassup. To your question it will be 360 degrees.

Step-by-step explanation:

Now bro can you mark as brainlest?

Answer:

x = 6y

x + y = 14

where x & y are the number of hours Valerie and Diana watched television respectively.

Step-by-step explanation:

:)

Answer:b because it has three sides.

Step-by-step explanation:

Answer:

1 pound 3.4 ounces

Step-by-step explanation:

Answer: I hope this helps.

Step-by-step explanation:

The state spelled out with letter tiles depends on the probability of picking the letter O, and the possible states are Ohio,  Colorado and  Oregon respectively.

To solve this problem, we need to consider the frequency of the letter O in each state's name.

If the probability of picking the letter O is 1/2, then the state must have two O's in its name. The only state that meets this criteria is OHIO.

If the probability of picking the letter O is 3/8, then the state must have three O's in its name. The only state that meets this criteria is COLORADO.

If the probability of picking the letter O is 1/3, then the state must have at least three O's in its name. The only state that meets this criteria is OREGON.

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Answer:

Probability of getting a green ball is more than that of getting a white ball.

Step-by-step explanation:

There are in all (5+3= 8) outcomes of the experiment. There are 5 outcomes in favour of the event of getting a green ball as there are 5 identical green balls in the bag.

Therefore, P(a green ball) = 5/8

In the same way,P(a white ball) = 3/8

Thus, clearly the probability of getting a green ball is more than that of getting a white ball.

Answer:

15

Step-by-step explanation:

Let the small boxes = x

Let the large boxes = y

x + y = 30

6x + 8y = 210

6(30 - y) + 8y = 210

180 - 6y + 8y = 210

180 + 2y = 210

2y = 210 - 180

2y = 30

y = 15

x = 30 - 15

x = 15

Answer:

15

Step-by-step explanation:

Call the number of small boxes  and the number of large boxes . We can use the following system of equations to represent the information given: Multiplying the first equation by 6 and subtracting the result from the second equation yields Solving for  gives , or . Thus,  large boxes were sent.

Answer: 156.38 m

Step-by-step explanation:

Using the arc length formula, the answer is \(2\pi(8^2) \cdot \frac{140}{360} \approx 156.38\)

Based on the volume of the solid, the value of K is 8960.

The volume of the solid = volume of the cone + volume of the hemisphere

The volume of the cone = ¹/₃hπr²

The volume of the hemisphere = ²/₃πr³

where;

r is radius = 20 cm

h is the height of the cone = ?

The curved surface area of the cone = πrl

The curved surface area of the cone = 580π cm²

πrl =  580π

l = 580/20

l = 29 cm

h = √(29² - 10²)

h = 27.2 cm

The volume of cone = ¹/₃ * 27.2 * 20² * π

The volume of the cone = 3626.7π cm³

The volume of the hemisphere = ²/₃ * π * 20³

The volume of the hemisphere = 5333.3 cm³

The volume of the solid = 5333.3π cm³ + 3626.7π cm³

The volume of the solid = 8960π cm³

The volume of the solid is kπcm³ = 8960π cm³

K =  8960

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So you know that Natalie won 97 bouncy balls but after she gave them away, she had 10 remaining. So she gave away 87 balls

Then we just have to do a simple operation:

So this means that Natalie has 29 friends!

Answer:

p^5

Step-by-step explanation:

p^10/2=p^5

Answer: x=12

Step-by-step explanation:

The two angles provided are on a straight line

A straight line is 180 degrees, so we can add the two angles to make 180 and solve for x

\(10x-20+6x+8=180\)

Simplify

\(10x-20+6x+8=180\\10x+6x-20+8=180\\16x-12=180\)

Add 12 on both sides

\(16x-12=180\\16x-12+12=180+12\\16x=192\)

Divide both sides by 16 to isolate x

\(16x=192\\\frac{16x}{16} =\frac{192}{16} \\x=12\)

Answer:

Step-by-step explanation:

First, 90 - 18 = 72

2nd,  72 divided by 6 = 12

So, the inequality is (m greater than (72 divided by 6 = 12  

Hope This Helps!!!!!!!!!!! :)

Integrate the force field along the given path (call it C):

\(W=\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=\int_0^{2\pi}\mathbf F(x(t),y(t))\cdot\frac{\mathrm d\mathbf r}{\mathrm dt}\,\mathrm dt\)

\(=\displaystyle\int_0^{2\pi}\bigg((t-\sin t)\,\mathbf i+(6-\cos t)\,\mathbf j\bigg)\cdot\bigg((1-\cos t)\,\mathbf i+\sin t\,\mathbf j\bigg)\,\mathrm dt\)

\(=\displaystyle\int_0^{2\pi}(t-t\cos t+5\sin t)\,\mathrm dt=\boxed{2\pi^2}\)

By direct calculation we will find that the work done is equal to 2π²

The formula to compute the work done is given by:

\(W = \int\limits^a_b {F(x(t), y(t))\cdot\frac{dr(t)}{dt} } \, dt\)

Here we have:

\(r(t) = (t - sin(t))i + (1 - cos(t))j\)

This means that:

\(x(t) = (t - sin(t))\\y(t) = (1 - cos(t))\\\\\frac{dr(t)}{dt} = (1-cos(t))i + sin(t)j = (1-cos(t), sin(t))\)

And we know that 0 ≤ t ≤ 2π, so b = 0 and a = 2π

Replacing that in the work integral we get:

\(W = \int\limits^{2\pi}_0 {(t - sin(t), 1 - cos(t) + 5)\cdot(1-cos(t), sin(t))} \, dt \\\\W = \int\limits^{2\pi}_0 {(t - sin(t), 6 - cos(t))\cdot(1-cos(t), sin(t))} \, dt\\\\W = \int\limits^{2\pi}_0 {(-t*cos(t) +t-sin(t)+ cos(t)*sin(t)+ 6*sin(t) - cos(t)*sin(t) )} \, dt\\\\W = \int\limits^{2\pi}_0 {(-cos(t)*t + 5*sin(t) + t)} \, dt \\\\\)

the sin(t) integral can be removed because it is equal to zero, so we get:

\(W = \int\limits^{2\pi}_0 {(-cos(t)*t + t)} \, dtW = [(-t*sin(t) - cos(t)) + \frac{t^2}{2} ]^{2\pi}_0\\\\W = -2\pi*sin(2\pi) - cos(2\pi) + 0*sin(0) + cos(0) + \frac{(2\pi)^2}{2} - \frac{(0)^2}{2}\\\\W = 2\pi^2\)

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Answer:

\(\displaystyle y' = \frac{3xln(x^2 + 6)^{\frac{1}{2}}}{x^2 + 6}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

Derivative Property [Multiplied Constant]:                                                                \(\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)\)

Derivative Rule [Chain Rule]:                                                                                     \(\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)\)

ln Derivative: \(\displaystyle \frac{d}{dx} [lnu] = \frac{u'}{u}\)

Step-by-step explanation:

Step 1: Define

\(\displaystyle y = ln(x^2 + 6)^{\frac{3}{2}}\)

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Derivatives

Book: College Calculus 10e

Answer:MY BUTT

Step-by-step explanation: WHY ARE U WAITING FOR OTHERS TO ANSWER YOUR QUSTION

As x tends to negative one from the left, the value of f(x) tends to positive infinity. As x → -1⁻, f(x) → ∞.

In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).

By critically observing the graph of this rational function f(x) shown below, we can logically deduce that its vertical asymptote is at x = -1 and x = 2, and its horizontal asymptote is at y = 3.

In this context, we can logically deduce that the value of f(x) tends towards positive infinity, as x tends to negative one from the left;

As x → -1⁻, f(x) → ∞.

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Answer:

number 3 the answer

Step-by-step explanation:

To solve systems of equations word problems, we can delegate certain variables to subjects mentioned in the word problem. From there, we can form equations based on the given values.

Let a be the older sibling's age and b be the younger sibling's age.

We're given:

All we've done so far is translate the given sentences into equations. Now, we have to solve for b, which is the age of the youngest sibling. Solve using substitution:

\(a+b=55\\(b+9)+b=55\\b+9+b=55\\2b+9=55\\2b=46\\b=23\)

Therefore, the younger sibling is 23 years old.

23 years old.

The tourist's investment function can be expressed as follows:

f(x) = 720 + 35x

According the question,

The tourist's investment function can be expressed as follows:

f(x) = 720 + 35x

Where x represents the quantity of additional tours that the tourist wants to add to their travel package.

The function f(x) represents the total cost of the travel package plus the additional cost of the extra tours.

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Answer:

The vertex of the function is at (–3,–16)

The graph is increasing on the interval x > –3

The graph is positive only on the intervals where x < –7 and where

x > 1.

Step-by-step explanation:

The graph of \(f(x)=(x-1)(x+7)\) has clear zeroes at \(x=1\) and \(x=-7\), showing that \(f(x) > 0\) when \(x < -7\) and \(x > 1\). To determine where the vertex is, we can complete the square:

\(f(x)=(x-1)(x+7)\\y=x^2+6x-7\\y+16=x^2+6x-7+16\\y+16=x^2+6x+9\\y+16=(x+3)^2\\y=(x+3)^2-16\)

So, we can see the vertex is (-3,-16), meaning that where \(x > -3\), the function will be increasing on that interval

The total length of the centre circle and the two goal semi circles to be repainted is 56.22 meters.

Given:

Court lines are 50 mm wide.

Court paint covers 7 m² per litre of paint.

The centre circle is a complete circle, so the circumference is given by the formula: Circumference = 2πr

Radius of the entire circle = 9 m / 2 = 4.5 m

Radius of the centre circle = 4.5 m - 0.05 m (converted 50 mm to meters) = 4.45 m

Circumference of the centre circle = 2π(4.45 m) = 27.94 m

Next, let's calculate the circumference of the semicircles:

The semicircles are half circles, so the circumference is given by the formula: Circumference = πr

The radius (r) of the semicircles is the same as the radius of the entire circle, which is 4.5 m.

Circumference of a semicircle = π(4.5 m) = 14.14 m

Total length = Circumference of the centre circle + 2 x Circumference of a semicircle

Total length = 27.94 m + 2(14.14 m)

Total length = 56.22 m

Therefore, the total length of the centre circle and the two goal semi circles to be repainted is 56.22 meters.

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Answer:

C. rectangular prism

Step-by-step explanation:

The distance between points P and Q is √73

First, remember that the distance between two points whose coordinates are (a, b) and (c, d) is given by:

distance = √( (a - c)² + (b - d)²)

Here we can see that the coordinates of the two shown points are:

P = (-3, 2)

Q = (5, -1)

Replacing that in the distance formula we will get:

distance = √( (-3 - 5)² + (2 + 1)²)

distance = √( (-8)² + (3)²)

distance = √73

So the correct option is the third one.

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The range of h(x) is {-2, 0, 2, 4}, and the graph of the function is a straight line that slopes downwards to the left.

To find the range of the function h(x)=2-2x, we can substitute each value of the domain given into the function to get the corresponding range values.

h(-1) = 2 - 2(-1) = 4

h(0) = 2 - 2(0) = 2

h(1) = 2 - 2(1) = 0

h(2) = 2 - 2(2) = -2

Thus, the range of the function h(x) for the given domain is {-2, 0, 2, 4}.

To graph the function h(x), we can plot the domain values on the x-axis and the corresponding range values on the y-axis. The resulting graph will be a set of four points: (-1,4), (0,2), (1,0), and (2,-2).

The graph of h(x) is a simple straight line that starts at the point (2,0) and slopes downwards to the left with a slope of -2. The graph intersects the y-axis at (0,2) and the x-axis at (1,0).

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Answer:

  (a)  twenty-eight ninths, square root of nineteen, cube root of eighty-eight

Step-by-step explanation:

When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.

The attachment shows the ordering, least to greatest, to be ...

  \(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)

__

Additional comment

We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.

One way to do the comparison is to convert these to values that need to have the same root:

  √19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)

  ∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)

The roots will have the same ordering as 19³ and 88².

Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...

  19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859

  88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744

Then the ordering is ...

  28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Answer:

the ordering is

28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Step-by-step explanation: