g(t) = 2t - 2
h(t) = 2t - 5
Find g(t) + h(t)

Given that the cost is $1.10 per pound, we can calculate the cost per servable pound by dividing the total cost ($1.10 * 4 pounds) by the servable weight (2 pounds). Therefore, the correct option is c. $2.20.

The original weight of the food item is 4 pounds, and the cost per pound is $1.10. Therefore, the total cost of the food item is 4 pounds * $1.10 = $4.40.

The servable weight of the food item is 2 pounds. To find the cost per servable pound, we divide the total cost ($4.40) by the servable weight (2 pounds):

Cost per servable pound = Total cost / Servable weight = $4.40 / 2 pounds = $2.20.

Hence, the cost per servable pound for this food item is $2.20. Therefore, the correct option is c. $2.20.

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          A

         / \

       /   \

     /     \

  B-------C

Since B is the midpoint of AC, we know that AB = BC = 2.

Since C is the midpoint of AD, we know that AC = CD.

Using the Pythagorean Theorem in triangle ABC, we have:

AB^2 + BC^2 = AC^2

2^2 + 2^2 = AC^2

8 = AC^2

AC = 2√2

Since AC = CD, we have CD = 2√2.

Therefore, the length of CD is 2 units.

A scientific calculator is typically used for pre-calculus.

This type of calculator is designed to handle more advanced mathematical functions, such as trigonometry, logarithms, and exponents, which are commonly used in pre-calculus.

It is important to have a scientific calculator for pre-calculus because it allows you to easily solve more complex equations and perform calculations quickly and accurately.

Additionally, many scientific calculators have graphing capabilities, which can be useful for visualizing equations and understanding how they behave. Overall, a scientific calculator is an essential tool for pre-calculus and can help you succeed in the course.

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Two samples can have the same mean but different standard deviations if one sample has more variability than the other. For example, one sample may have data points that are tightly clustered around the mean, while the other sample may have data points that are more spread out.

This can result in the same mean value for both samples, but different levels of variability.

Here's an example bar graph to illustrate this concept:

     Sample 1                Sample 2

 ╭────────────────╮   ╭────────────────╮

 │      Mean      │   │      Mean      │

 ├────────────────┤   ├────────────────┤

 │                │   │    ╭─╮         │

 │                │   │    │ │         │

 │                │   │    │ │         │

 │                │   │    ╰─╯         │

 │     o o o      │   │  o o o o o o  │

 │                │   │                │

 │                │   │                │

 │                │   │                │

 ╰────────────────╯   ╰────────────────╯

     Std. Dev.            Std. Dev.

In this example, both Sample 1 and Sample 2 have a mean value of 5. However, Sample 1 has lower variability with a standard deviation of 1, while Sample 2 has higher variability with a standard deviation of 3. The error bars on the graph represent the standard deviation for each sample.

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Answer:

get a tutor

Step-by-step explanation:

Answer:

I don't know the answer

Step-by-step explanation:

Do it by yourself

A differential equation that is homogeneous doesn’t have any term that doesn’t involve the dependent variable or its derivatives. Mathematically, it’s possible to recognize a homogeneous equation since all its terms have the same degree. For example,

\(y” – 3xy’ + 2y = 0\)  is a homogeneous second-order differential equation, because the sum of the exponents of

y, y’, and y” is always equal to two, or the degree of the highest derivative in the equation. For this equation, a solution y = e^x is a physically reasonable option since it reflects the behavior of exponentially growing functions such as populations or economies.

Any linear combination of e^x and e^(-2x) would be a solution for this homogeneous equation. If the equation were not homogeneous, it could also include additional terms that would affect the behavior of the dependent variable and modify the physical interpretation of the problem.

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It is possible for equivalent expressions to make the left and right expressions have the same value

An expression is combination of variables, numbers and operators.

We have to check whether it is  possible to make the left and right expressions have the same value

If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

For example 2x+4=2(x+2)

When we plug in x as 2

2(2)+4=2(2+2)

4+4=2(4)
8=8

Hence, its possible to make the left and right expressions have the same value when the expressions are equivalent.

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N(b) =75 because p(b) =n(b) /n(s)

0.75=n(b)/100

n(b)=0.75*100=75

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The value of x in terms of the length of the chord BC is x = (1/2) * arcsin(BC / (2 * r)) - 30 degrees

Draw a diagram of the circle and label the given points and segments.

Identify the relevant circle properties: Recall the properties of circles such as the radius, diameter, circumference, and central angle. Identify any angles or lengths that can be determined from the given information.

Use the tangent-chord theorem: Since AD is tangent to the circle, we can use the tangent-chord theorem to find that angle ADB is equal to angle ABD.

This implies that triangle ABD is an isosceles triangle.

Use the properties of isosceles triangles: Since triangle ABD is isosceles, we know that angle BAD is equal to angle ADB.

We also know that the sum of the angles in a triangle is 180 degrees.

Therefore, angle ABD is equal to (180 - 2x) degrees.

Use the angle sum property: Since A, B, C, and D are points on the circle, angle BAC is equal to half of the central angle BOC.

Therefore, angle BOC is equal to 2 * angle BAC.

Use the angle subtraction property: Since angle ABD is an exterior angle of triangle BCD, we know that angle ABD is equal to the sum of angles BCD and BDC.

Therefore, (180 - 2x) degrees is equal to (2 * angle BAC) + angle BDC.

Use the angle sum property again: Since B, C, and D are points on the circle, angle BDC is equal to half of the central angle BOC.

Therefore, angle BDC is equal to angle BAC.

Substituting this value into the equation from step 6, we get (180 - 2x) degrees

= (2 * angle BDC) + angle BAC

= 2 * angle BAC + angle BAC

= 3 * angle BAC.

Therefore, angle BAC is equal to (180 - 2x) / 3 degrees.

2 * angle BAC = 2 * (180 - 2x) / 3 degrees.

Use the chord length formula: Using the chord length formula, we can find that BC

= 2 * r * sin(angle BOC / 2), where r is the radius of the circle.

Substituting the value of angle BOC from step 9, we get BC = 2 * r * sin[(2 * (180 - 2x) / 3) / 2]

= 2 * r * sin[(180 - 2x) / 3] .

Solve for x:

We need to express x in terms of BC, so we can use the formula from step 10 to get 2 * r * sin[(180 - 2x) / 3] = BC.

Solving for x gives x = (1/2) * arcsin(BC / (2 * r)) - 30 degrees.

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The distance to the radio horizon for an antenna that is 40 ft above the top of a 4000 ft mountain peak is approximately 78.18 miles.

The radio horizon refers to the point beyond which radio signals from a given transmitter can no longer be received due to the curvature of the Earth's surface. It can be calculated using the formula d = 1.23√h, where d is the distance to the radio horizon in miles and h is the height of the antenna above ground level in feet.

So, the height of the antenna above ground level is as follows:

4000 + 40 = 4040 ft.

Substituting into the formula, we get

d = 1.23√4040 ≈ 78.18 miles.

Therefore, the distance to the radio horizon for an antenna that is 40 ft above the top of a 4000 ft mountain peak is approximately 78.18 miles.

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The value of x from the given figures is 2.8

Shapes are known to be similar if the ratio of their similar sides is equal to a constant.

From the given pentagons, the ratio of their sides is equal to a constant as shown;

2/1.4 = 4/x

Cross multiply

2x = 4 * 1.4

2x = 5.6

Divide both sides by 2 to have:

2x/2 = 5.6/2

x. = 5.6/2

x = 2.8

Hence the value of x from the given figures is 2.8

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Answer:

-2 and -8

Step-by-step explanation:

Since the sum of the numbers is negative and the product is a positive, we know that two of the digits are negative because a negative time a negative is positive, and two negatives added are negative.

We can do these two ways.

1.) List out the multiples of 16 and see which ones add to -10

-1 (-16)

-2 (-8)

-4 (-4)

Only -2 and -8 add to get -10, so -2 and -8 are the answers.

2.) List the factors that add up to -10

-1 - 9

-2 - 8

-3 - 7

-4 - 6

-5 - 5

When multiplied, only -2 and -8 have a product of 16, so -2 and -8 are the answers.

Hope this helps. if not, please leave a comment and I will respond when I can. :)

(a) `T1:0 = [cos150 sin150 0 0; -sin150 cos150 0 0; 0 0 1 0; 0 0 0 1]`

(b) `T1:0 = [1 0 0 0; 0 cos150 sin150 0; 0 -sin150 cos150 0; 0 0 0 1]`

(c) `T1:0 = [cos150 0 -sin150 0; 0 1 0 0; sin150 0 cos150 0; 0 0 0 1]`

Given that Frame zero, F0 is the fixed global frame.

For each of the cases below find T1

Case (a)

F1 is rotated by an angle θ about zo.

Let O be the origin of the fixed frame F0, A be the origin of the frame F1 and α be the angle between the x-axis of the frame F0 and the projection of the x-axis of the frame F1 on the xy plane of the frame F0.

Let l, m, n be the direction cosines of the vector from O to A, expressed in F0.

The content-loaded frame zero F0 is the fixed global frame, which means that the vectors i, j, k representing the x, y, and z-axis of F0 are fixed and cannot be transformed.

Therefore, the transformation matrix T1:0

in this case is:

`T1:0 = [l1 m1 n1 0; l2 m2 n2 0; l3 m3 n3 0; 0 0 0 1]`

Case (b)

F1 is rotated by θ about xo.

Let β be the angle between the y-axis of F0 and the projection of the y-axis of F1 on the yz plane of F0.

Let γ be the angle between the z-axis of F0 and the projection of the z-axis of F1 on the zx plane of F0.

The transformation matrix T1:0

in this case is given by:

`T1:0 = [1 0 0 0; 0 cosθ sinθ 0; 0 -sinθ cosθ 0; 0 0 0 1]`

Case (c)

F1 is rotated by θ about yo.

Let β be the angle between the y-axis of F0 and the projection of the y-axis of F1 on the yz plane of F0.

Let γ be the angle between the z-axis of F0 and the projection of the z-axis of F1 on the zx plane of F0.

The transformation matrix T1:0

in this case is given by:

`T1:0 = [cosθ 0 -sinθ 0; 0 1 0 0; sinθ 0 cosθ 0; 0 0 0 1]`

Thus, the transformation matrix T1:0

for the three cases (a), (b), and (c) are given as follows:

(a) `T1:0 = [cosθ sinθ 0 0; -sinθ cosθ 0 0; 0 0 1 0; 0 0 0 1]`

(b) `T1:0 = [1 0 0 0; 0 cosθ sinθ 0; 0 -sinθ cosθ 0; 0 0 0 1]`

(c) `T1:0 = [cosθ 0 -sinθ 0; 0 1 0 0; sinθ 0 cosθ 0; 0 0 0 1]`

Given θ = 150,

T1:0 for the three cases are:

(a) `T1:0 = [cos150 sin150 0 0; -sin150 cos150 0 0; 0 0 1 0; 0 0 0 1]`

(b) `T1:0 = [1 0 0 0; 0 cos150 sin150 0; 0 -sin150 cos150 0; 0 0 0 1]`

(c) `T1:0 = [cos150 0 -sin150 0; 0 1 0 0; sin150 0 cos150 0; 0 0 0 1]`

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The slope of a line perpendicular to line x + 4y = 28 is - 4.

A number that identifies the direction and steepness of a line is its slope or gradient.

Consider the equation of a line,

x + 4y = 28

Subtracting x from each side of the equation,

x + 4y - x = 28 - x

4y = - x + 28

Dividing each side of the equation by 4,

y = ( - 1/4 )x + 7

Comparing the above equation with the slope-intercept form y = mx + b where m is the slope and b is the y-intercept.

Then, we have:

m = - 1/4 and b = 7

Now, let the slope of the perpendicular line be m₂.

Now we know that

m × m₂= - 1

1/4 × m₂= - 1

m₂= - 4

Hence, the slope of the perpendicular line is - 4.

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Using mathematical operations we can conclude that Jada drinks 8/15 liters of water.

So, liters of water Jada drinks:

We know that,

The container holds 4/5 liters of water.

Jada drinks 2/3 liters of water.

Now, liters of water Jada drinks is:

4/5 × 2/3

4×2/5×3

8/15

Therefore, using mathematical operations we can conclude that Jada drinks 8/15 liters of water.

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Given:

The total number of marbles are 26.

Red marbles=10

Black marbles=8

Green marbles=8

The two marbles are drawn randomly,

To find the probability that both marbles are green,

The probability that first marbles chosen is green,

Condition is given that the first is not returned before the second one is drawn.

Now the we have 7 green marbles and total marbles are 25.

Probability is given by,

The total probability of getting both green marbles without replacement is,

Answer: Probability is 0.08615.

Answer: Choice A)

\(H = \frac{SA}{2(L+W)} - \frac{LW}{L+W}\\\\\)

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

Work Shown:

\(SA = 2(LW + LH + HW)\\\\2(LW + LH + HW) = SA\\\\LW + LH + HW = \frac{SA}{2}\\\\LH + HW = \frac{SA}{2} - LW\\\\H(L + W) = \frac{SA}{2} - LW\\\\H = \frac{\frac{SA}{2} - LW}{(L + W)}\\\\H = \frac{SA}{2(L+W)} - \frac{LW}{L+W}\\\\\)

This is not the only way to solve for H.

The distance between both the ship and the lighthouse's base is 328 feet.

If a line of sight is slightly down from the horizontal line, it forms an angle with the horizontal line. If the object being observed is below the observer's level, the angle formed between both the horizontal line and also the observer's lines of sight is known as the angle of depression.

Given the circumstances, a right angle triangle is constructed. The lighthouse's height represents the right angle triangle's opposite side.

The adjacent side of a right angle triangle is represented by the horizontal distance, h, between both the ship and thus the base of the lighthouse.

Because they are opposite angles, is if angle of depression to the fire is 26°, the angle of elevation of a lighthouse from the ship is also 26°.

To calculate h, we would use

the trigonometric tangent ratio;

Tan θ = opposite side/adjacent side. Therefore,

Tan 26 = 160/h

h = 160/tan26 = 160/0.4877

h = 328 feet

Therefore, the distance between the ship and the base of the light house is 328 feet.

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Answer:

2. I think. Sorry if its wrong. Have a beautiful day! :)

Step-by-step explanation:

Answer:

It will be worth about £885.59.

Step-by-step explanation:

The art piece originally costs £600.

And it appreciates at a rate of 3.97% each year.

And we want to find the value of the art after 10 years.

We can write an exponential function to model the situation. The standard exponential function is given by:

\(f(t)=a(r)^t\)

Where t is the time in years.

Since it appreciates at a rate of 3.97% each year, the value after each year will be (100% + 3.97%) or 103.97%.

103.97% = 1.0397. So, r = 1.0397:

\(f(t)=a(1.0397)^t\)

Our a is the initial value. Therefore:

\(f(t)=600(1.0397)^t\)

Then the value of the piece of art after 10 years is:

\(f(t)=600(1.0397)^{10}=885.5879...\approx \pounds 885.59\)

It will be worth about £885.59 after 10 years.

Answer:

885.59

Step-by-step explanation:

1. 600 + 23.82

2. 623.82 + 24.77

3. 648.59 +25.75

4. 674.34 + 26.77

5. 701.11 + 27.83

6. 728.94 + 28.94

7. 757.88 + 30.09

8. 787.97 + 31.28

9. 819.25 + 32.52

10. 851.77 + 33.82

After 10 years the art valued for 885.59 British Pounds.

In this case, we'll have to carry out several steps to find the solution.

Step 01:

diameter = 12 km

angle = 150°

lenght arc = ?

Step 02:

length arc = (angle / 360) 2πr

r = 6 km

length arc = 15.71 km

The answer is:

The length of the arc is 15.71 km.

The proportion of the jury selected that are Hispanic would be = 1,350,000 people.

To calculate the proportion of the selected jury that are Hispanic, the following steps needs to be taken as follows:

The total number of residents = 3 million

The percentage of people that are Hispanic race = 45%

The actual number of people that are Hispanic would be;

= 45/100 × 3,000,000

= 1,350,000 people.

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Complete question:

Twelve jurors are randomly selected from a population of 3 million residents. Of these 3 million residents, it is known that 45% are Hispanic. Of the 12 jurors selected, 2 are Hispanic. What proportion of the jury described is from Hispanic race?

The probability that a bottle selected at random will contain at least one defect can be found using the complement probability of having no defect.

Let us denote the probability of having at least one defect in a bottle as P(A). P(A') is the probability of not having any defect in the bottle. Since the probability of an event occurring plus the probability of it not occurring is equal to 1, then \(P(A') = 1 - P(A).\)

Thus, the probability of having no defect in a bottle is

\(P(A') = (1 - 0.00001) = 0.99999\)

.Since a bottle has either no defect or at least one defect,

\(P(A) = 1 - P(A') = 1 - 0.99999 = 0.00001.\)

Therefore, the probability that a bottle selected at random will contain at least one such defect is \(0.00001 or 1/100,000.\)

This means that on average, only 1 bottle in 100,000 will contain such a defect.

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The term which is used for describing the number of voters who casted their votes using the ballots is called as voter turnout.

The process of selecting a candidate for a suitable post who takes care of the policies which will be framed for the people is called as voting. In this process, the members/ citizens casts their vote in the favor of their suitable candidate. Many times voters are not valid and their votes are considered as null and void.

The voter turnout is either the percentage of registered voters, eligible voters, or all voting-age people ( this varies from place to place depending upon the minimum voting age required). The voter turnout is also referred to the number of people who go to it or take part in it. High voter turnout is generally considered a sign of a healthy democracy.

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Answer:

Step-by-step explanation:

The formula is incorrect. V = 4πr³/3

Radius r = 10/2 = 5 cm

V = 4πr³/3 ≈ 4×3.14×5³/3 = 523⅓ cm³

The volume of the sphere is 523.3 cm³ if the diameter of the sphere is 10 cm option (B) is correct.

It is defined as three-dimensional geometry when half-circle two-dimensional geometry is revolved around the diameter of the sphere that will form.

We have the diameter of the sphere shown in the picture,

Let's denote the diameter of the sphere as D then,

D = 10 cm

the radius r will be half the diameter.

r = 10/2 ⇒5 cm

The formula for finding the volume of the sphere is given:

\(\rm V = \frac{4}{3} \pi r^3\\\\\rm V = \frac{4}{3} \pi 5^3\)  (r = 5 cm)

\(\rm V =\frac{4}{3} \pi 75\)

V = 166.66π

V = 166.66×3.14      (π = 3.14)

V = 523.31 cm³

Thus, the volume of the sphere is 523.3 cm³ if the diameter of the sphere is 10 cm option (B) is correct.

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Answer:

Step-by-step explanation:

17/20 x 2/3

Then 17/10 x 1/3 = 17/30

The measure of arc BC is 720 times the measure of angle BAC.

Given that AC is the diameter of the circle and AB is a chord with a length of 16 units, we need to find BC (the length of the other chord) and mBC (the measure of angle BAC).

To find BC, we can use the property of chords in a circle. If two chords intersect within a circle, the products of their segments are equal. In this case, since AB = BC = 16 units, the product of their segments will be:

AB * BC = AC * CE

16 * BC = 2 * r * CE (AC is the diameter, so its length is twice the radius)

Since the area of the circle is given as 289 square units, we can find the radius (r) using the formula for the area of a circle:

Area = π * r^2

289 = π * r^2

r^2 = 289 / π

r = √(289 / π)

Now, we can substitute the known values into the equation for the product of the segments:

16 * BC = 2 * √(289 / π) * CEBC = (√(289 / π) * CE) / 8

To find mBC, we can use the properties of angles in a circle. The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the circumference. Since AC is a diameter, angle BAC is a right angle. Therefore, mBC will be half the measure of the arc BC.

mBC = 0.5 * m(arc BC)

To find the measure of the arc BC, we need to find its length. The length of an arc is determined by the ratio of the arc angle to the total angle of the circle (360 degrees). Since mBC is half the arc angle, we can write:

arc BC = (mBC / 0.5) * 360

arc BC = 720 * mBC

Therefore, the length of the arc BC equals 720 times the length of the angle BAC.

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