A game is played by drawing 4 cards from an ordinary deck and replacing each card after it is drawn. Find the probability that at least 1 ace is drawn.

Answer:

Podemos hacer la conversión entre [\text{H}^+][H

+

]open bracket, start text, H, end text, start superscript, plus, end superscript, close bracket y \text{pH}pHstart text, p, H, end text mediante las siguientes ecuaciones:

\begin{aligned}\text{pH}&=-\log[\text{H}^+]\\ \\ [\text H^+]&=10^{-\text{pH}}\end{aligned}

pH

[H

+

]

=−log[H

+

]

=10

−pH

Answer:

(0,9) (-1,0), (2,0), (3,0),

Step-by-step explanation:

add me on discord LD BrxzyYT#8144 :)

The tax revenue is $ 9000 and Deadweight loss is $500.

We have,

Hotel rooms in Smalltown go for $100, and 1,000 rooms are rented on a typical day.

So, The tax revenue is calculated by :

Tax revenue = Tax Imposed × Quantity sold

= 10 x 900

= $ 9000

Now, The deadweight loss is calculated as:

= 1/2 × Tax imposed × change in quantity sold

= 1/2 x 10 x (1000-900)

= $500

Learn more about Tax revenue here:

https://brainly.com/question/25558844

#SPJ1

This is the same as writing y = sqrt(4(x+5)) - 1

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

Explanation:

The given graph appears to be a square root function.

The marked points on the curve are:

Reflect those points over the line y = x. This will have us swap the x and y coordinates.

Recall the process of reflecting over y = x means we're looking at the inverse. The inverse of a square root function is a quadratic.

----------

Let's find the quadratic curve that passes through (1,-4), (3,-1) and (5,4).

Plug the coordinates of each point into the template y = ax^2+bx+c.

For instance, plug in x = 1 and y = -4 to get...

y = ax^2+bx+c

-4 = a*1^2+b*1+c

-4 = a+b+c

Do the same for (3,-1) and you should get the equation -1 = 9a+3b+c

Repeat for (5,4) and you should get 4 = 25a+5b+c

We have this system of equations

Use substitution, elimination, or a matrix to solve that system. I'll skip steps, but you should get (a,b,c) = (1/4, 1/2, -19/4) as the solution to that system.

In other words

a = 1/4, b = 1/2, c = -19/4

We go from y = ax^2+bx+c to y = (1/4)x^2+(1/2)x-19/4

----------

Next we complete the square

y = (1/4)x^2+(1/2)x-19/4

y = (1/4)( x^2+2x )-19/4

y = (1/4)( x^2+2x+0 )-19/4

y = (1/4)( x^2+2x+1-1 )-19/4

y = (1/4)( (x^2+2x+1)-1 )-19/4

y = (1/4)( (x+1)^2-1 )-19/4

y = (1/4)(x+1)^2- 1/4 - 19/4

y = (1/4)(x+1)^2 + (-1-19)/4

y = (1/4)(x+1)^2 - 20/4

y = (1/4)(x+1)^2 - 5

The equation is in vertex form with (-1,-5) as the vertex. It's the lowest point on this parabola. Placing it into vertex form allows us to find the inverse fairly quickly.

----------

The last batch of steps is to find the inverse.

Swap x and y. Then solve for y.

y = (1/4)(x+1)^2 - 5

x = (1/4)(y+1)^2 - 5

x+5 = (1/4)(y+1)^2

(1/4)(y+1)^2 = x+5

(y+1)^2 = 4(x+5)

y+1 = sqrt(4(x+5))

y = sqrt(4(x+5)) - 1

I'll let the student check each point to confirm they are on the curve y = sqrt(4(x+5)) - 1.

You can also use a tool like GeoGebra to verify the answer.

The function notation of 9x + 3y = 12 is given as follows:

f(x) = 4 - 3x.

The function in the context of this problem is given as follows:

9x + 3y = 12.

The format for the function notation is given as follows:

Hence we must isolate the variable y, as follows:

3y = 12 - 9x

y = 4 - 3x (each term of the expression is divided by 3).

f(x) = 4 - 3x.

More can be learned about functions at https://brainly.com/question/10687170

#SPJ1

Answer:

5

Step-by-step explanation:

in a 45 45 90 triangle the 2 equal smaller sides (a) are the same and the hyp is a√2

Answer:

the first table

Step-by-step explanation:

We see that the first table represents the logarithmic function \(y = \log_2x\), so it's the first table.

The first table represents the graph of a logarithmic function in the form y=log _(b)x.

Exponentiation's inverse function is the logarithm. That is, the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised in order to obtain that number x.

The given table has data where y is a function of x;

y=F(x)

\(y=log _{b}x \\\\ -2 = log _{b}\frac{1}{4} \\\\ \frac{1}{4} = log _{b}{-2} \\\\ -1= log _{b}\frac{1}{2} \\\\ 0=log _{b}1 \\\\ 1=log _{b}2\)

Hence the first table represents the graph of a logarithmic function in the form y=log _(b)x.

To learn more about the logarithm refer to the link;

https://brainly.com/question/7302008

The area of the shaded region for the normal distribution is approximately 0.6985.

We have,
To find the area of the shaded region under the standard normal distribution curve between z = -0.87 and z = 1.24, we can use a standard normal distribution table or a calculator with a standard normal distribution function.

Using a standard normal distribution table, we look up the area to the left of z = -0.87 and the area to the left of z = 1.24 and then subtract the smaller area from the larger area to find the area between z = -0.87 and z = 1.24.

The table value for z = -0.87 is 0.1949, and the table value for z = 1.24 is 0.8934.

The area between z = -0.87 and z = 1.24 is:

= 0.8934 - 0.1949

= 0.6985

So the area of the shaded region is approximately 0.6985.

Thus,

The area of the shaded region for the normal distribution is approximately 0.6985.

Learn more about normal distribution here:

https://brainly.com/question/31327019

#SPJ1

The approximation for each of the given function and interval below is 1.12

The term function refers the special relationship where each input has a single output.

Here we have given that (a) R5, f(x) = x2 + x on the interval [−1,1]

And we need to find the the approximation for each of the given function and interval

Here we want to to calculate the right-endpoint approximation (the right Riemann sum) for the function:

=> f(x) = x² + x

For the interval [-1, 1] using five equal rectangles.

Let us find the width of each rectangle:

=> Δx = (1 - (-1))/5 = 2/5

Now, we have to list the x-coordinates starting with -1 and ending with 1 with increments of 2/5:

=> -1, -3/5, -1/5, 1/5, 3/5, 1.

Here we are find the right-hand approximation, we use the five coordinates on the right.

Then we have to evaluate the function for each value. This is shown in the table below.

And then each area of each rectangle is its area (the y-value) times its width, which is a constant 2/5.

Therefore, the approximation for the area under the curve of the function f(x) over the interval [-1, 1] using five equal rectangles is:

=> R₅ = 2/5 [-0.24  - 0.16 + 0.24 + 0.96 + 2] = 1.12

To know more about function here.

https://brainly.com/question/28193995

#SPJ4

Answer:

1) r = 32

2) symbol is '÷'

3) h = 15/19

Step-by-step explanation:

The value of integral is 3.

Let's evaluate the integral over the positive half of the interval:

∫[0 to π] (cos(x) / √(4 + 3sin(x))) dx

Let u = 4 + 3sin(x), then du = 3cos(x) dx.

Substituting these expressions into the integral, we have:

∫[0 to π] (cos(x) / sqrt(4 + 3sin(x))) dx = ∫[0 to π] (1 / (3√u)) du

Using the power rule of integration, the integral becomes:

∫[0 to π] (1 / (3√u)) du = (2/3) . 2√u ∣[0 to π]

Evaluating the definite integral at the limits of integration:

(2/3)2√u ∣[0 to π] = (2/3) 2(√(4 + 3sin(π)) - √(4 + 3sin(0)))

(2/3) x 2(√(4) - √(4)) = (2/3) x 2(2 - 2) = (2/3) x 2(0) = 0

So, the value of integral is

= 3-0

= 3

Learn more about Definite integral here:

https://brainly.com/question/30760284

#SPJ1

Answer:

\(3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x\approx 0.806\; \sf (3\;d.p.)\)

Step-by-step explanation:

First, compute the indefinite integral:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x\)

To evaluate the indefinite integral, use the method of substitution.

\(\textsf{Let} \;\;u = 4 + 3 \sin x\)

Find du/dx and rewrite it so that dx is on its own:

\(\dfrac{\text{d}u}{\text{d}x}=3 \cos x \implies \text{d}x=\dfrac{1}{3 \cos x}\; \text{d}u\)

Rewrite the original integral in terms of u and du, and evaluate:

\(\begin{aligned}\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\int \dfrac{\cos x}{\sqrt{u}}\cdot \dfrac{1}{3 \cos x}\; \text{d}u\\\\&=\int \dfrac{1}{3\sqrt{u}}\; \text{d}u\\\\&=\int\dfrac{1}{3}u^{-\frac{1}{2}}\; \text{d}u\\\\&=\dfrac{1}{-\frac{1}{2}+1} \cdot \dfrac{1}{3}u^{-\frac{1}{2}+1}+C\\\\&=\dfrac{2}{3}\sqrt{u}+C\end{aligned}\)

Substitute back u = 4 + 3 sin x:

                            \(= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

Therefore:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

To evaluate the definite integral, we must first determine any intervals within the given interval -π ≤ x ≤ π where the curve lies below the x-axis. This is because when we integrate a function that lies below the x-axis, it will give a negative area value.

Find the x-intercepts by setting the function to zero and solving for x in the given interval -π ≤ x ≤ π.

\(\begin{aligned}\dfrac{\cos x}{\sqrt{4+3\sin x}}&=0\\\\\cos x&=0\\\\x&=\arccos0\\\\\implies x&=-\dfrac{\pi }{2}, \dfrac{\pi }{2}\end{aligned}\)

Therefore, the curve of the function is:

So to calculate the total area, we need to calculate the positive and negative areas separately and then add them together, remembering that if you integrate a function to find an area that lies below the x-axis, it will give a negative value.

Integrate the function between -π and -π/2.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_1=-\displaystyle \int^{-\frac{\pi}{2}}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=- \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{-\frac{\pi}{2}}_{-\pi}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(-\pi\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (-1)}+\dfrac{2}{3}\sqrt{4+3 (0)}\\\\&=-\dfrac{2}{3}+\dfrac{4}{3}\\\\&=\dfrac{2}{3}\end{aligned}\)

Integrate the function between -π/2 and π/2:

\(\begin{aligned}A_2=\displaystyle \int^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\&=\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}\\\\&=\dfrac{2}{3}\sqrt{4+3 (1)}-\dfrac{2}{3}\sqrt{4+3 (-1)}\\\\&=\dfrac{2\sqrt{7}}{3}-\dfrac{2}{3}\\\\&=\dfrac{2\sqrt{7}-2}{3}\end{aligned}\)

Integrate the function between π/2 and π.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_3=-\displaystyle \int^{\pi}_{\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= -\left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\pi}_{\frac{\pi}{2}}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(\pi\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (0)}+\dfrac{2}{3}\sqrt{4+3 (1)}\\\\&=-\dfrac{4}{3}+\dfrac{2\sqrt{7}}{3}\\\\&=\dfrac{2\sqrt{7}-4}{3}\end{aligned}\)

To evaluate the definite integral, sum A₁, A₂ and A₃:

\(\begin{aligned}\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\dfrac{2}{3}+\dfrac{2\sqrt{7}-2}{3}+\dfrac{2\sqrt{7}-4}{3}\\\\&=\dfrac{2+2\sqrt{7}-2+2\sqrt{7}-4}{3}\\\\&=\dfrac{4\sqrt{7}-4}{3}\\\\ &\approx2.194\; \sf (3\;d.p.)\end{aligned}\)

Now we have evaluated the definite integral, we can subtract it from 3 to evaluate the given expression:

\(\begin{aligned}3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x&=3-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9}{3}-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9-(4\sqrt{7}-4)}{3}\\\\&=\dfrac{13-4\sqrt{7}}{3}\\\\&\approx 0.806\; \sf (3\;d.p.)\end{aligned}\)

Therefore, the given expression cannot be zero.

Answer:

The statements that can be used to compare the characteristics of the functions are:

1. g(x) has the greatest maximum value.

2. All three functions share the same domain.

Explanation:

- The table shows the values of three functions - f(x), g(x), and h(x) - evaluated at different values of x.

- We cannot determine the domain of f(x) or h(x) from the given table but we can see that g(x) has a domain of all real numbers.

- We can see that g(x) has the highest maximum value among the three functions, which is 8.

- We cannot determine the range of f(x) or g(x) from the given table but we can see that h(x) has a range of all negative numbers.

- We cannot say anything about the domain or range of f(x) based on the given table.

- Therefore, the two statements that can be used to compare the characteristics of the functions are: g(x) has the greatest maximum value and all three functions share the same domain.

Answer:

Number 4 has a value of 3.

Step-by-step explanation:

1. 4 + 1 = 5

2. 12 - 4 = 8

3. 12 / 3 = 4

4. 12 / 4 = 3

The perimeter of the square with side of 5 cm is 20 cm.

The perimeter of the square with side length of 15 cm is 60 cm.

The area of each square is calculated as follows;

Let the dimension of first square = x

Let the dimension of second square = y

x² + y² = 250 ---- (1)

4(x + y) = 80 ----- (2)

x + y = 80/4

x + y = 20

x = 20 - y

Substitute x in equation (1)

(20 - y)² + y² = 250

400 - 40y + y² + y² = 250

2y² - 40y + 150 = 0

y² - 20y + 75 = 0

solve for y, using formula method;

y = 15 or 5

Solve for x;

x = 20 -15 = 5 or

x = 20 - 5 = 15

The perimeter of first = 4x = 4 x 5 = 20 cm

The perimeter of the second = 4y = 4 x 15 = 60 cm

Learn more about perimeter here: https://brainly.com/question/19819849

#SPJ1

Answer:

-5,2

Step-by-step explanation:

make one side equal zero, x2 + 3x - 10

use guess and check to reverse foil and find (x+5)(x-2)

solve and get x = -5 , 2

Answer (it has two solutions):

I hope this helps!

Answer:

Step-by-step explanation:

To find the surface area of the solid given the net, we need to identify all of the faces and add up their areas. Looking at the net, we can see that the solid consists of a rectangular prism and two triangular prisms attached to its sides.

To find the area of the rectangular prism, we need to multiply the length, width, and height. From the net, we can see that the length is 12 units, the width is 5 units, and the height is 8 units. So, the area of the rectangular prism is:

Area = length * width * height

Area = 12 units * 5 units * 8 units

Area = 480 units²

To find the area of the triangular prisms, we need to multiply the base, height, and half the width. From the net, we can see that the base of each triangular prism is 12 units and the height is 8 units. To find the width, we can use the Pythagorean theorem:

width² = height² + base²/4

width² = 8² + 12²/4

width² = 64 + 36

width² = 100

width = 10 units

So, the area of each triangular prism is:

Area = 1/2 * base * height * width

Area = 1/2 * 12 units * 8 units * 10 units

Area = 480 units²

Now, we can add up the areas of all three faces to find the total surface area:

Surface area = area of rectangular prism + area of two triangular prisms

Surface area = 480 units² + 480 units² + 480 units²

Surface area = 1440 units²

Therefore, the surface area of the solid given the net is 1440 units². None of the answer choices match exactly, but the closest one is A. 1292 units².

Since the probabilities lie exclusively between 0 and 1 and the sum of probabilities is equal to 1 , therefore the yes , the distribution is discrete probability distribution.

As the probabilities range from 0 to 1, and the sum of probability equals 1.

Discrete probability distribution is a sort of probability distribution that provides all potential values of a discrete random variable along with the related probabilities. In other words, a discrete probability distribution describes the possibility of each potential value of a discrete random variable occurring.

Some common discrete probability distributions are geometric distributions, binomial distributions, and Bernoulli distributions. This page defines a discrete probability distribution, as well as its formulas, types, and numerous instances.

To learn more about discrete probability distribution

brainly.com/question/17145091

#SPJ4

Answer:

Step-by-step explanation:

Since AE is equal to 3x + 3 and BD is equal to 36, we can set up an equation to solve for x. If we let the width of the rectangle be x, then the length would be 3x + 3.

Area of the rectangle = width * length

36 * (3x + 3) = (3x + 3) * x

Expanding the right side, we get:

36 * (3x + 3) = 3x^2 + 3x + 3x + 9

36 * (3x + 3) = 3x^2 + 6x + 9

Dividing both sides by 3, we get:

12 * (3x + 3) = x^2 + 2x + 3

Expanding the left side, we get:

12 * (3x + 3) = x^2 + 2x + 3

36 * 3x + 36 * 3 = x^2 + 2x + 3

108x + 108 = x^2 + 2x + 3

Subtracting 3 from both sides, we get:

108x + 105 = x^2 + 2x

Expanding the left side, we get:

x^2 + 2x - 108x - 105 = 0

Combining like terms on the left side, we get:

x^2 - 106x - 105 = 0

Using the quadratic formula, we can solve for x:

x = (-b ± √(b^2 - 4ac)) / 2a

where a = 1, b = -106, and c = -105.

Plugging in the values, we get:

x = (-(-106) ± √((-106)^2 - 4 * 1 * -105)) / 2 * 1

x = (106 ± √(11,336 + 420)) / 2

x = (106 ± √11,756) / 2

x = (106 ± 34) / 2

Since x has to be positive, we take the positive square root:

x = (106 + 34) / 2

x = 70 / 2

x = 35.

So the width of the rectangle is 35 units.

Answer:

16/c of the class are boys

Step-by-step explanation:

If there are a total number of children, c, and 16 of them are boys, you are going to put the total number of children on the bottom of the fraction as the denominator and put the number that are boys on top of the fraction as the numerator.

(I hoped this helped)

Answer:

Step-by-step explanation:

if the number of the children is c and we have 16 boys

the fraction will be c/16

The dimensions of the rectangular box are given as follows:

All the dimensions.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The box's volume is obtained as follows:

54 x 1³ = 128 x (3/4)³ = 54 cubic inches. (the volume of a cube is the side length cubed)

Hence all the options can be the dimensions of the box, as all the options have a multiplication resulting in 54.

More can be learned about the volume of a rectangular prism at brainly.com/question/22070273

#SPJ1

The height of the school is 13.27 m.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have.

From the information given, we can draw the figure given below,

Now,

Triangle ABC and Triangle DCE are similar.

So,

x / 1.25 = 11.15 / 1.05

x = (11.15 x 1.25) / 1.05

x = 13.27 m

Thus,

The height of the school is 13.27 m.

Learn more about triangles here:

https://brainly.com/question/25950519

#SPJ1

Answer:

smaller: -37, larger: -27

Step-by-step explanation:

say one number is x the other one is y

x+y = -64

x-y = -10

subtract the two equations to get

2y = -54

y = -27

x = -37  

-27 is larger, -37 is smaller

Answer:

What is this it's okay but thanks for points

Step-by-step explanation:

The value of the expression \(\sqrt[4]{a}^3\) when evaluated is \(a^\frac34\)

From the question, we have the following parameters that can be used in our computation:

\(\sqrt[4]{a}^3\)

Consider an expression expressed as xⁿ

The expression can be expanded as

xⁿ = x * x * x .... in n places

Using the above as a guide, we have the following:

\(\sqrt[4]{a}^3 = \sqrt[4]{a} * \sqrt[4]{a} * \sqrt[4]{a}\)

Apply the exponent rule of indices

\(\sqrt[4]{a}^3 = a^\frac14 * a^\frac14 * a^\frac14\)

Apply the power rule of indices

\(\sqrt[4]{a}^3 = a^\frac34\)

Hence, the expression \(\sqrt[4]{a}^3\) when evaluated is \(a^\frac34\)

Read more about expression at

https://brainly.com/question/32302948

#SPJ1

Answer:

486 square inches

Step-by-step explanation:

Answer:

the football players salary is more that 71,000

Step-by-step explanation:

what ever way the open part of the arrow is facing means more than

for example

10>3

or

1<5

Answer:

xyz = - \(\frac{21}{2}\)

Step-by-step explanation:

substitute the given values into the expression

xyz

= \(\frac{4}{5}\) × - 15 × \(\frac{7}{8}\)

= - 12 × \(\frac{7}{8}\)

= - 3 × \(\frac{7}{2}\)

= - \(\frac{21}{2}\)

Answer:

Step-by-step explanation:

ax² + bx + c = y

( 0 , 3 ) ⇒ c = 3

( 1 , - 3 )

a(1)² + b(1) + 3 = - 3 ⇒ a + b = - 6 ⇒ a = - b - 6 ........ (1)

( 2 , - 5 )

a(2)² + b(2) + 3 = - 5 ⇒ 4a + 2b + 3 = - 5 ......... (2)

(1) -----> (2)

4( - b - 6 ) + 2b = - 8  ⇒  b = - 8

a = 2

y = 2x² - 8x + 3

Answer:

ABCD paralleogram, AE is perpendicular to EC, and DF is perpendicular to EC. Prove AEFD is a triangle