Zachary brought $38. 25 to the state fair. He bought a burger, a souvenir, and a pass. The burger was 1 6 as much as the souvenir, and the souvenir cost 3 4 the cost of the pass. Zachary had $4. 50 left over after buying these items

We can estimate that the expected number of even numbers picked in 35 picks is 15.

To estimate the expected number of even numbers picked in 35 picks, we need to first understand the probability of picking an even number in one pick. Out of the seven given numbers, there are three even numbers (2, 14, 8) and four odd numbers (7, 3, 11, 5). Therefore, the probability of picking an even number in one pick is 3/7.

To find the expected number of even numbers picked in 35 picks, we can multiply the probability of picking an even number in one pick (3/7) by the number of picks (35).

Expected number of even numbers picked = (3/7) x 35 = 15

Therefore, we can estimate that the expected number of even numbers picked in 35 picks is 15. This means that if we were to repeat the process of picking a card and replacing it 35 times, we would expect to pick 15 even numbers on average.

It is important to note that this is an estimate and the actual number of even numbers picked may vary. However, this estimation gives us a good idea of what to expect on average.

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The cost of 15 meters of ribbon at the factory is:

15 meters / 3 meters per $7 = 5 times $7 = $35

The cost of 15 meters of ribbon at the store is:

15 meters x $2.50 per meter = $37.50

Therefore, the amount saved by buying 15 meters of ribbon at the factory rather than at the store is:

$37.50 - $35 = $2.50

Answer:

The Fourier series of a periodic function f(x) with period 2L can be expressed as:

f(x) = a0/2 + Σ[n=1 to ∞] (ancos(nπx/L) + bnsin(nπx/L))

where

a0 = (1/L) ∫[-L,L] f(x) dx

an = (1/L) ∫[-L,L] f(x)*cos(nπx/L) dx

bn = (1/L) ∫[-L,L] f(x)*sin(nπx/L) dx

In this case, we have f(x) = 1 for 2k - 0.25 <= x <= 2k + 0.25, and f(x) = 0 otherwise. The period is 0.5, so L = 0.25.

First, we can find the value of a0:

a0 = (1/0.5) ∫[-0.25,0.25] 1 dx = 1

Next, we can find the values of an and bn:

an = (1/0.5) ∫[-0.25,0.25] 1*cos(nπx/0.25) dx = 0

bn = (1/0.5) ∫[-0.25,0.25] 1*sin(nπx/0.25) dx

Since the integrand is odd, we have:

bn = (2/0.5) ∫[0,0.25] 1*sin(nπx/0.25) dx

Using the substitution u = nπx/0.25, du/dx = nπ/0.25, dx = 0.25du/(nπ), we get:

bn = (4/nπ) ∫[0,nπ/4] sin(u) du = (4/nπ) (1 - cos(nπ/4))

Therefore, the Fourier series of f(x) can be written as:

f(x) = 1/2 + Σ[n=1 to ∞] [(4/nπ) (1 - cos(nπ/4))] * sin(nπx/0.25)

for 2k - 0.25 <= x <= 2k + 0.25, and f(x) = 0 otherwise.

A. 128CM CUBED

Step-by-step explanation:

THE FORMULLA : it's v(volume) =AB (BAZE AREA OR TOP AREA ) × HEIGHT SO

16 SQUARE CM ×8CM

The correct options are: A and D

Streets 2 and 3 are parallel and Street 1 is intersecting it

Parallel lines are two or more straight lines that continue indefinitely without ever crossing each other, despite their extended lengths. They have an equal inclination and remain the same distance apart at all times. Consequently, intersections will never occur between them.  

On the contrary, if non-parallel lines exist, they intersect to create one point, famously known as the 'point of intersection'. This specific point supplies the solution to the system of equations formed by the two lines.

Hence, we can see from the given image that Streets 2 and 3 are parallel and Street 1 is intersecting it

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The solutions for the equation in the interval [0, 2π) are x = 0, x = π/6, and x = 5π/6.

To find all solutions of the equation (8 csc x - 16)(4 cos x - 4) = 0 in the interval [0, 2π), we can set each factor equal to zero and solve for x separately.

1) 8 csc x - 16 = 0
8 csc x = 16
csc x = 2

Recall that csc x = 1/sin x, so:

1/sin x = 2
sin x = 1/2

In the interval [0, 2π), sin x = 1/2 at x = π/6 and x = 5π/6. So, the solutions for this part are x = π/6 and x = 5π/6.

2) 4 cos x - 4 = 0
4 cos x = 4
cos x = 1

In the interval [0, 2π), cos x = 1 at x = 0 and x = 2π. However, since 2π is not included in the interval, we only have x = 0 as a solution for this part.

Combining both parts, the solutions for the equation in the interval [0, 2π) are x = 0, x = π/6, and x = 5π/6.

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The critical points and their classifications are: (0, kπ/2), local minimum for all k.

To find the critical points of f(x, y), we need to find where the partial derivatives of f with respect to x and y are equal to zero:

∂f/∂x = 6x = 0

∂f/∂y = 2sin(2y) = 0

From the first equation, we get x = 0, and from the second equation, we get sin(2y) = 0, which has solutions y = kπ/2 for any integer k.

So the critical points are (0, kπ/2) for all integers k.

To classify these critical points, we need to use the second derivative test. The Hessian matrix of f is:

H = [6 0]

[0 -4sin(2y)]

At the critical point (0, kπ/2), the Hessian becomes:

H = [6 0]

[0 0]

The determinant of the Hessian is 0, so we can't use the second derivative test to classify the critical points. Instead, we need to look at the behavior of f in the neighborhood of each critical point.

For any k, we have:

f(0, kπ/2) = 1 + 3(0)² - cos(2kπ) = 2

So all the critical points have the same function value of 2.

To see whether each critical point is a maximum, minimum, or saddle point, we can look at the behavior of f along two perpendicular lines passing through each critical point.

Along the x-axis, we have y = kπ/2, so:

f(x, kπ/2) = 1 + 3x² - cos(2kπ) = 1 + 3x²

This is a parabola opening upwards, so each critical point (0, kπ/2) is a local minimum.

Along the y-axis, we have x = 0, so:

f(0, y) = 1 + 3(0)² - cos(2y) = 2 - cos(2y)

This is a periodic function with period π, and it oscillates between 1 and 3. So for each k, the critical point (0, kπ/2) is neither a maximum nor a minimum, but a saddle point.

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The measure of angle zxy is 125 degrees.

To solve the problem, we can use the fact that the sum of the measures of two adjacent angles is 180 degrees. Let's call the measure of angle zxy "x".

We know that the ratio of m angle wxz to m angle zxy is 11:25, which means that:

m angle wxz : m angle zxy = 11 : 25

We can write this as an equation:

m angle wxz / m angle zxy = 11/25

We also know that the two angles are adjacent, so their measures add up to 180 degrees:

m angle wxz + m angle zxy = 180

Now we can use these two equations to solve for x:

m angle wxz / x = 11/25

m angle wxz = (11/25)x

Substituting this into the second equation:

(11/25)x + x = 180

(36/25)x = 180

x = (25/36) * 180

x = 125

Therefore, the measure of angle zxy is 125 degrees.

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The quadratic function in vertex form that passes through the point (1, -3) is: f(x) = (x - 1)²  - 3

What is vertex form?

Vertex form is a way of expressing a quadratic function of the form:

f(x) = a(x - h)² + k

where (h, k) is the vertex of the parabola, and a is a constant that determines the shape and direction of the parabola.

The quadratic function in vertex form is given by:

f(x) = a(x - h)²  + k

where (h, k) is the vertex of the parabola.

We are given the point (1, -3), which lies on the parabola. This means that:

f(1) = -3

Substituting x = 1 into the vertex form of the equation, we get:

f(1) = a(1 - h)²  + k

-3 = a(1 - h)²  + k

Since we don't know the value of h or a, we can't solve for k directly. However, we can use the vertex form of the equation to find the values of h and k.

The vertex of the parabola is the point (h, k). Since the parabola passes through the point (1, -3), we know that the vertex lies on the axis of symmetry, which is the vertical line x = 1.

Therefore, the x-coordinate of the vertex is h = 1. Substituting this into the equation above, we get:

-3 = a(1 - 1)²  + k

-3 = a(0) + k

k = -3

Now that we know the value of k, we can substitute it back into the equation above and solve for a:

-3 = a(1 - h)²  + k

-3 = a(1 - 1)²  + (-3)

-3 = a(0) - 3

a = 1

Therefore, the quadratic function in vertex form that passes through the point (1, -3) is:

f(x) = (x - 1)²  - 3

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Answer: d=2√13  

Step-by-step explanation:

You need to use the distance formula or pythagorean.  Pythagorean is simpler. Let's use that.

c²=a²+b²

c= distance

a = how far point went in x direction =4

b=how far went in y direction =6

plug in:

d²=4²+6²

d²=16+36

d²=52                     take square root of both sides

d=√52                    

d=√(4*13                4 and 13 are factors of 52

d=2√13                   take square root of 4

a. The formula for the slope at (x, f(x)) is f'(x) = -2x

b. The slope at (0, 8) is 0

c. the slope at (-1, 7) is 2

The slope of a graph is the gradient of the graph.

Given the graph f(x) = 8 - x² to find the formula for the slope of the graph, we proceeed as follow.

a. To find the formula for the slope of the graph, we know thta the slope of the graph is the derivative of the graph. So, taking the derivative of the graph, we have that

f(x) = 8 - x²

df(x)/dx = d(8 - x²)/dx

= d8/dx - dx²/dx

= 0 - 2x

= -2x

So, the formula for the slope at (x, f(x) is f'(x) = -2x

b. To find the slope at (0, 8), substituting x = 0 into the equation for the slope, we have that

f'(x) = -2x

f'(0) = -2(0)

= 0

So, the slope at (0, 8) is 0

c. To find the slope at (-1, 7), substituting x = -1 into the equation for the slope, we have that

f'(x) = -2x

f'(0) = -2(-1)

= 2

So, the slope at (-1, 7) is 2

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The murder took place approximately 1.17 hours before the team arrived, which is 8:13 am.

Assuming that the body follows Newton's law of cooling, we can use the formula:

T(t) = Tm + (Ta - Tm) * e^(-kt),

where T(t) is the body temperature at time t, Tm is the temperature of the surrounding medium (in this case, the room), Ta is the initial temperature of the body, and k is a constant that depends on the properties of the body and the surrounding medium.

We can use the information given to find k:

At t = 0 (when the murder took place), T(0) = Ta = unknown

At t = 0.5 hours (30 minutes after the murder), T(0.5) = 85 degrees

At t = 1.5 hours (90 minutes after the murder), T(1.5) = 83.3 degrees

Using the formula above, we can write two equations:

85 = Ta + (72 - Ta) * e^(-0.5k)

83.3 = Ta + (72 - Ta) * e^(-1.5k)

Solving for Ta in the first equation, we get:

Ta = 72 + (85 - 72) / e^(-0.5k) = 72 + 13 / e^(-0.5k)

Substituting this expression for Ta into the second equation, we get:

83.3 = (72 + 13 / e^(-0.5k)) + (72 - (72 + 13 / e^(-0.5k))) * e^(-1.5k)

Simplifying and solving for e^(-0.5k), we get:

e^(-0.5k) = 0.979

the natural logarithm of both sides, we get:

-0.5k = ln(0.979)

Solving for k, we get:

k = -2 * ln(0.979) / 1 = 0.0427

Now we can use the formula again to find Ta:

Ta = 72 + (85 - 72) / e^(-0.5k) = 72 + 13 / e^(-0.5*0.0427) = 78.1 degrees

So the initial temperature of the body was 78.1 degrees.

To find the time of death, we can use the formula again and solve for t when T(t) = 78.1:

78.1 = 72 + (Ta - 72) * e^(-0.0427t)

Substituting Ta = 85 (the initial temperature of the body) and solving for t, we get:

t = -ln((85 - 72) / (78.1 - 72)) / 0.0427 = 1.17 hours

Therefore, the murder took place approximately 1.17 hours before the team arrived, which is 8:13 am.

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The value of the test statistic is approximately -2.49

To find the value of the test statistic for the marketing executive's claim that the percentage of laptop owners is different from the reported 30%, we will use the following formula for a proportion hypothesis test:

[tex]Test Statistic (Z) =\frac{ (Sample Proportion - Hypothesized Proportion)}{Standard Error}[/tex]

Here are the given values:
- Hypothesized proportion (p) = 0.30
- Sample size (n) = 130
- Sample proportion (p-hat) = 0.20

First, we need to calculate the standard error (SE) using this formula:
[tex]SE+\frac{\sqrt{p(1-p)} }{n}[/tex]
[tex]SE+\frac{\sqrt{0.30(1-0.30)} }{130}[/tex]
[tex]SE=\sqrt{\frac{0.21}{130} }[/tex]
[tex]SE=\sqrt{0.0016153846}[/tex]
[tex]SE = 0.04019[/tex]

Now, we can calculate the test statistic (Z) using the given formula:
[tex]Z=\frac{ (0.20 - 0.30)}{0.04019}[/tex]
[tex]Z=\frac{-0.10}{ 0.04019}[/tex]
[tex]Z = -2.49[/tex]

So, the value of the test statistic is approximately -2.49, rounded to two decimal places.

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The probability that the 25th flip will result in the counter landing on orange side up is fraction 1 over 2. The correct answer is D.

The probability of an event occurring is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, Stephen has flipped the counter 24 times and he wants to know the probability of getting an orange side up on the 25th flip.

Since the counter has two sides - orange and brown, the probability of landing on the orange side is 1/2 or 0.5.

Each flip of the counter is independent of the others, so the previous flips do not affect the outcome of the 25th flip. Therefore, the probability of the 25th flip landing on the orange side up is still 1/2 or 0.5. The correct answer is D.

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If the parallelogram has an area of 25.2 cm² and the height is 4 cm, the length of the base is 6.3 cm.

To start, we know that the area of a parallelogram is given by the formula:

A = bh

where A is the area, b is the length of the base, and h is the height. We also know that the area of the parallelogram in this case is 25.2 cm² and the height is 4 cm.

Substituting these values into the formula, we get:

25.2 = b(4)

To solve for b, we can divide both sides by 4:

b = 25.2/4

b = 6.3

So the length of the base is 6.3 cm.

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The equation for the displacement of the pendulum as a function of time is: displacement = 7 sin(π/3 t)

The motion of a pendulum can be modeled using a sine function:

displacement = A sin(ωt + φ)

where A is the amplitude (the furthest distance from the equilibrium point), ω is the angular frequency (related to the period T by ω = 2π/T), t is time, and φ is the phase angle (determines the starting point of the oscillation).

In this case, the pendulum has an amplitude of 7 inches and a period of 6 seconds (since it takes 6 seconds to swing to one side and then back to the other). Therefore, the angular frequency is:

ω = 2π/T = 2π/6 = π/3

The phase angle is 0, since the pendulum starts at its equilibrium position.

So, the equation for the displacement of the pendulum as a function of time is:

displacement = 7 sin(π/3 t)

where t is measured in seconds and the displacement is measured in inches.

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The total mass of the wire is [tex]M = 9\rho * (\pi/2).[/tex]

Using the formula for finding the centroid of a two-dimensional object with uniform density:

cy = (1/Area) * ∫(y*dA)

The equation of the circle is [tex]x^2 + y^2 = 25[/tex]. Solving for y, we get:

[tex]y = \sqrt(25 - x^2)[/tex]

Since the wire is in the first quadrant, the limits of integration are 0 ≤ x ≤ 5 and 0 ≤ y ≤ [tex]\sqrt(25 - x^2).[/tex]

To find the area of the wire, we integrate:

[tex]Area = \int \int dA = \int 0^5 \int 0^{\sqrt(25-x^2)}dy dx[/tex]

[tex]= \int 0^{5 (sqrt(25-x^2))}dx[/tex]

[tex]= (1/2) * [25sin^{(-1)(x/5)} + x\sqrt(25-x^2)] from 0 to 5[/tex]

[tex]= (1/2) * [25\pi/2] = 25\pi/4[/tex]

To find the centroid (cy), we integrate:

[tex]cy = (1/Area) * \int(ydA) = (1/(25\pi/4)) * \int0^5 \int0^{\sqrt(25-x^2)} y dy dx[/tex]

[tex]= (4/25*\pi) * \int0^5 [(1/2)*y^2]_0^{\sqrt(25-x^2)} dx[/tex]

[tex]= (4/25\pi) * \int 0^5 [(1/2)(25-x^2)] dx[/tex]

[tex]= (4/25\pi) * [(25x - (1/3)*x^3)/2]_0^5[/tex]

[tex]= (4/25\pi) * [(255 - (1/3)*5^3)/2][/tex]

[tex]= 50/3[/tex]

Therefore, the centroid of the wire is cy = 50/3.

Now use the formula for the mass of a thin wire for total mass:

M = ∫ρ ds

Since the wire has uniform density, the linear density is constant and can be factored out of the integral:

M = ρ * ∫ds

The differential element of arc length is:

[tex]ds = \sqrt(dx^2 + dy^2) = \sqrt((-9sin t)^2 + (9cos t)^2) dt[/tex]

[tex]= 9\sqrt(sin^2 t + cos^2 t) dt = 9 dt[/tex]

Integrating from 0 to pi/2, we get:

[tex]M = \rho * \int ds = \rho * \int 0^{(\pi/2)} 9 dt[/tex]

[tex]= 9\rho * [t]_0^{(\pi/2)} = 9\rho * (\pi/2)[/tex]

Therefore, the total mass of the wire is [tex]M = 9\rho * (\pi/2).[/tex]

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Answer:

21

Step-by-step explanation:

70 · .30 = 21

The circumference of the well is 3.93 ft.

Given, Emma is making a scale drawing of her farm using the scale 1 cm=2.5 ft

Diameter of the well she drew = 0.5 cm

We need to convert the diameter of the well from centimeters to feet, using the given scale.

i.e. 0.5cm = 2.5/2 = 1.25 ft

We know the radius is half of the diameter.

So, r = 1.25/2 = 0.625

We know that the formula for the circumference of a circle is C = 2πr

C = 2*3.14*0.625

= 3.93 ft

Hence, the circumference of the well is 3.93 ft.

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The total lease cost for Clayton's SUV is $23,056.24.

Before any additional fees or deposits, the total lease cost is $421.38 per month for 48 months, which equals:

Total cost of the lease  = $421.38/month x 48 months = $20,236.24

Clayton also paid a $2,500 down payment, a $85 title charge, and a $235 license cost in addition to the monthly lease payments.

The entire cost of the lease is $20,236.24 + $2,500 + $85 + $235 = $23,056.24 in total.

Therefore, the total lease cost for Clayton's SUV is $23,056.24.

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The measure of angle U in triangle UVW is approximately 28 degrees. This is found by using the inverse tangent function to solve for angle U given the lengths of two sides and the fact that angle W is a right angle.

To find the measure of ∠U in ΔUVW, we can use trigonometry. We know that sin(∠U) = opposite/hypotenuse, which is equal to UW/VW. Therefore, we can plug in the given values and solve for sin(∠U)

sin(∠U) = UW/VW = 2.2/4.7 = 0.4681

Next, we can use the inverse sine function (sin⁻¹) to find the measure of ∠U

∠U = sin⁻¹(0.4681) = 28.34 degrees (rounded to the nearest degree)

Therefore, the measure of ∠U in ΔUVW is approximately 28 degrees.

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The volume of the solid is (7π - 8√2)/12 cubic units.

To find the volume of the solid enclosed by the cone and sphere in cylindrical coordinates, we first need to express the equations of the cone and sphere in cylindrical coordinates.

Cylindrical coordinates are expressed as (ρ, θ, z), where ρ is the distance from the origin to a point in the xy-plane, θ is the angle between the x-axis and a line connecting the origin to the point in the xy-plane, and z is the height above the xy-plane.

The cone z = x^2 + y^2 can be expressed in cylindrical coordinates as ρ^2 = z, and the sphere x^2 + y^2 + z^2 = 2 can be expressed as ρ^2 + z^2 = 2.

To find the limits of integration for ρ, θ, and z, we need to visualize the solid. The cone intersects the sphere at a circle in the xy-plane with radius 1. We can integrate over this circle by setting ρ = 1 and integrating over θ from 0 to 2π.

The limits of integration for z are from the cone to the sphere. At ρ = 1, the cone and sphere intersect at z = 1, so we integrate z from 0 to 1.

Therefore, the volume of the solid enclosed by the cone and sphere in cylindrical coordinates is

V = ∫∫∫ ρ dz dρ dθ, where the limits of integration are

0 ≤ θ ≤ 2π

0 ≤ ρ ≤ 1

0 ≤ z ≤ ρ^2 for ρ^2 ≤ 1, and 0 ≤ z ≤ √(2 - ρ^2) for ρ^2 > 1.

Integrating over z, we get

V = ∫∫ ρ(ρ^2) dρ dθ for ρ^2 ≤ 1, and

V = ∫∫ ρ(√(2 - ρ^2))^2 dρ dθ for ρ^2 > 1.

Evaluating the integrals, we get

V = ∫0^1 ∫0^2π ρ^3 dθ dρ = π/4

and

V = ∫1^√2 ∫0^2π ρ(2 - ρ^2) dθ dρ = π/3 - 2√2/3

Therefore, the total volume of the solid enclosed by the cone and sphere in cylindrical coordinates is

V = π/4 + π/3 - 2√2/3

= (7π - 8√2)/12 cubic units

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The given question is incomplete, the complete question is:

Use cylindrical coordinates Find the volume of the solid that is enclosed by the cone z = x^2 + y^2 and the sphere x^2 + y^2 + z^2 = 2

According to the given information in the question to find the length of side v in triangle VWX, we can use the Law of Sines. the length of side v is approximately [tex]281.8[/tex] cm.

image for "define centimeters in high-level mathematics." A centimeter is a metric unit used to quantify small distances and the object's length. Cm is used to represent it in writing.

It can also be described as the measure of length in the current metric system, referred to as the International System of Units (SI). It is equal to one-hundredth of a meter.

which states that:

[tex]a/sin(A) = b/sin(B) = c/sin(C)[/tex]

where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the opposite angles.

In this case, we know the length of side w (600 cm), and the measures of angles V and W.

To find the length of side v, we can use the Law of Sines with sides v and w and angle V:

[tex]v/sin(V) = w/sin(W)[/tex]

[tex]v/sin(26^\circ) = 600/sin(80^\circ)[/tex]

[tex]v = (600 \times sin(26^\circ))/sin(80^\circ)[/tex]

[tex]v \approx 281.8 cm[/tex] (rounded to the nearest 10th of a centimeter)

Therefore, the length of side v is approximately [tex]281.8 cm[/tex].

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Sure, I'd be happy to help you with that. Based on the information provided, we know that HA Leonardo received three books for his birthday and two of them cost a total of 760. To find out the cost of the third book, we need to subtract the cost of the two books from the total amount paid, which is 1125.

To do this, we can use a simple equation:

Total cost of three books - Total cost of two books = Cost of third book

So, we can plug in the values we know:

1125 - 760 = Cost of third book

Solving for the cost of the third book:

365 = Cost of third book

Therefore, the third book cost 365.

In summary, HA Leonardo received three books for his birthday and two of them cost 760. The total amount paid was 1125, so the cost of the third book was 365.

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The number line that represents the solution to this inequality is 6.10, with an open circle at 25 and shading to the right.

To solve the inequality 12t > 300, we need to isolate t on one side of the inequality. We can do this by dividing both sides by 12:

12t/12 > 300/12

t > 25

This means that Tina must sell more than 25 tickets in order to meet her goal of selling more than $300 worth of tickets.

To represent this solution on a number line, we can start by plotting a point at 25. Since the inequality is greater than (>) and not greater than or equal to (≥), we use an open circle at 25.

Then, we need to shade the area to the right of 25 to represent all the possible values of t that satisfy the inequality. This is because any value of t greater than 25 will make 12t greater than 300.

Out of the answer choices given, the number line that represents the solution to this inequality is 6.10, with an open circle at 25 and shading to the right.

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Lindsey can put together 27 different outfits if she has 3 tops, 3 bottoms, and 3 scarves to choose from. The answer is (D) 27 outfits.

To find the number of different outfits that Lindsey can put together, we need to use the counting principle, which states that if there are m ways to do one thing and n ways to do another thing, then there are m x n ways to do both things together.

In this case, there are 3 ways for Lindsey to choose a top, 3 ways to choose a bottom, and 3 ways to choose a scarf. To find the total number of outfits, we multiply these numbers together:

Total number of outfits = number of tops x number of bottoms x number of scarves

Total number of outfits = 3 x 3 x 3

Total number of outfits = 27

Therefore, Lindsey can put together 27 different outfits if she has 3 tops, 3 bottoms, and 3 scarves to choose from. The answer is (D) 27 outfits.

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The probability of selecting a caramel chocolate both times is approximately 0.103.

The events of selecting a caramel chocolate on each pick are dependent since the probability of the second pick depends on the outcome of the first pick.

First, we need to calculate the probability of selecting a caramel chocolate on the first pick, which is 10/30 or 1/3. After eating the first chocolate, there will be 29 chocolates left in the box, and 9 of them will be caramel-filled. So, the probability of selecting a caramel chocolate on the second pick, given that the first pick was a caramel chocolate and it was eaten, is 9/29.

To find the probability of selecting a caramel chocolate both times, we need to multiply the probabilities of the two events together, since they are independent:

P(caramel and caramel) = P(caramel on first pick) * P(caramel on second pick | first pick was caramel)

= (1/3) * (9/29)

= 0.103 or 0.1034 rounded to four decimal places.

Therefore, the probability of selecting a caramel chocolate both times is approximately 0.103.

The events of selecting a caramel chocolate on the first pick and selecting a caramel chocolate on the second pick are dependent events since the probability of selecting a caramel chocolate on the second pick changes based on what was selected on the first pick.

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The measure of arc DF is given as follows:

mDF = 58º.

We have two secants in this problem, and point E is the intersection of the two secants, hence the angle measure of 52º is half the difference between the angle measure of the largest arc of 162º by the angle measure of the smallest arc.

Then the measure of arc DF is obtained as follows:

52 = 0.5(162 - mDF)

52 = 81 - 0.5mDF

0.5mDF = 29

mDF = 58º.

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Tomas earns a commission of $122.50 on the sale of the new car.

Tomas earns a 0.5% commission on the sale price of a new car. On Wednesday, he sells a new car for $24,500. To determine the commission Tomas earns, we need to multiply the sale price by the commission rate. The commission rate is given as 0.5%, which can be expressed as a decimal by dividing by 100. So, 0.5% is equal to 0.005 as a decimal.

Now, we can calculate Tomas's commission by multiplying the sale price by the commission rate. In this case, we multiply $24,500 by 0.005:

$24,500 x 0.005 = $122.50

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The probability of the next elk caught being unmarked is 0.96 when the total number of elks is 5625 and the number of elks marked is 225.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Total number of elks = 5625

Number of elks marked = 225

We need to find the total number of elks not marked or  unmarked we can find it by,

= 5625 - 225

= 5500

Therefore, the total number of elks unmarked is 5500.

We can determine determined the likelihood of the next elk caught being unmarked by using probability. The probability is given by:

P = 5500/5625

= 44 / 45

= 0.96

Therefore, The total number of elks unmarked is 0.96.

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The complete question is,

Describe the likelihood of the next elk caught being unmarked.