Estimate a 15% tip on a dinner bill of $58.12 by first rounding the bill amount to the nearest ten dollars.

The function g(t) is defined as:

g(t) = 1/√(16-t^2)

The function is continuous for all values of t that satisfy the following conditions:

The denominator is non-zero:

The denominator of the function is √(16-t^2). Therefore, the function is undefined when 16-t^2 < 0, or when t is outside the interval [-4,4].

There are no vertical asymptotes:

The function does not have any vertical asymptotes, because the denominator is always positive.

Thus, the function g(t) is continuous on the interval [-4,4].

If a relation R is an equivalence relation, then R will be circular.

If a relation R is an equivalence relation, then it must satisfy three properties: reflexivity, symmetry, and transitivity.

(i) Reflexivity: For any element "a" in the set, "aRa" must be true.

(ii) Symmetry: For any elements "a" and "b" in the set, if "aRb" then "bRa" must be true.

(iii) Transitivity: For any elements "a", "b", and "c" in the set, if aRb and bRc then "aRc" must be true.

A Circular relation is where "aRb" and "bRc" imply "cRa".

This is a stronger condition than the transitivity property of an equivalence relation, which only requires that "aRb" and "bRc" together imply "aRc".

Therefore, a relation that is an equivalence-relation have to be circular.

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The given question is incomplete, the complete question is

A relation R is called circular if "aRb" and "bRc" imply that "cRa". if R is an equivalence relation, then would R be circular?

Answer:

A

Step-by-step explanation:

because___________________________________

Answer:

B) True

Step-by-step explanation:

SSS or Side-Side-Side is used to prove two triangles are congruent.

The approximate volume of a human head is 4000 cubic centimeter.

A sphere is simply a geometrical object that is a three-dimensional analogue to a two-dimensional circle.

The circumference of a sphere is given by the formula:

C = 2πr

Where r is the radius of the sphere. In this case, we are given that the circumference of the sphere (which approximates the human head) is 60 cm, so:

60 cm = 2πr

Solve for r

r = 60/2π

r = 30/π

The volume of a sphere is given by the formula:

V = (4/3)πr³.

Substituting the value we found for r, we get:

V = (4/3) × π × ( 30/π )³

V = (4/3) × π × ( 30/π )³

V = 3647.566 cm³

V = 4000 cm³

Therefore, the volume to the nearest 1,000 cubic cm is 4000 cm³.

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The measurement of angle PCD in equilateral triangle  is 67.38°.

Let $s$ be the side length of the square $abcd$, and let $O$ be the center of the square. Then $OP = s/\sqrt{2}$.

Since triangle $ABP$ is equilateral, we have $\angle ABP = 60^\circ$ and $AP=BP=s$. Let $E$ be the foot of the perpendicular from $P$ to $AB$. Then $AE=BE=s/2$ and $EP=s\sqrt{3}/2$.

Since $EP$ is perpendicular to $AB$ and $AB$ is parallel to $CD$, we have $\angle PCD = \angle ACE$.

Since $OP$ is perpendicular to $AB$, we have $\angle OEP = \angle AEP = 30^\circ$. Also, $OE=OP/\sqrt{2}=s/2$.

Using the Pythagorean theorem in triangle $OCE$, we have

CE= [tex]\sqrt{(OE)^{2} + (OC)^{2}} = \sqrt{(s/2)^{2} + s^{2}} = s\sqrt{5}/2[/tex]

Therefore, $\sin \angle ACE = CE/CP = \sqrt{5}/2$. Thus,

∠PCD = ∠ACE = arcsin(√5/2) ≈ 67.38°

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The area of a sector is a region bounded by two radii of a circle and an arc between is  (320/9) π sq. units.

Radius is a straight line segment that connects the center of a circle or sphere to any point on its circumference or surface, respectively. In other words, it is the distance from the center of the circle or sphere to any point on its edge or surface.

The given sector is EFG = 128°.

The area of a sector is a region bounded by two radii of a circle and an arc between them.

A = (θ/360) × πr²

Where:

The fraction (θ/360) represents the fraction of the entire circle that the sector occupies. Multiplying this fraction by the total area of the circle (πr²) gives the area of the sector.

Use the formula for the area of a sector with the central angle in degrees:

A = (n/360) × πr²

From the given figure, n = 128 and r = 10

A = (128/360) × π(10)²

  = (320/9) π sq. units.

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The inequality is X > 0 and a word sentence represent the graph is  X  the graph of a number line with an open circle on zero and an arrow pointing to the right.

The inequality X > 0 represents the graph of a number line with an open circle on zero to left and an arrow pointing to the right. This means that any value of X that is greater than zero is a valid solution for the inequality.

In other words, X can be any positive number, such as 1, 2, 3, and so on. However, X cannot be zero or any negative number, as those values do not satisfy the inequality. Therefore, the word sentence that represents this inequality is "X is greater than zero."

This means that X must be a positive number, and it can be any value that is greater than zero.

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The answer is 41 minutes.

explaination:

540 secs = 9 minutes

2/3 of 60 mins= 40 mins

(to find a fraction of a number you divide it by the denominator and times it after by the numerator)

9+40= 49

homework: 90 mins

reading and making lunch: 49 minutes

we want the difference so:

90-49= 41

Roberto spent 41 more minutes doing his homework than reading and making lunch.

Answer:

What rotation centered about the origin maps (4, − 7) to (7,4) ? 90° counterclockwise 180° counterclockwise 270° counterclockwise I don't know. ←​

Step-by-step explanation:

To map the point (4, -7) to (7, 4) by a rotation centered about the origin, we need to find the angle of rotation and direction.

We can start by finding the vector from the origin to (4, -7), which is <4, -7>. We want to rotate this vector to the vector from the origin to (7, 4), which is <7, 4>.

To do this, we need to find the angle between these two vectors. Using the dot product, we have:

<4, -7> · <7, 4> = (4)(7) + (-7)(4) = 0

Since the dot product is zero, we know that the two vectors are orthogonal, and the angle between them is 90 degrees.

To map (4, -7) to (7, 4) with a 90-degree rotation counterclockwise, we can use the matrix:

[0 -1]

[1 0]

Multiplying this matrix by the vector <4, -7>, we get:

[0 -1] [4] = [-7]

[1 0] [-7] [ 4]

which corresponds to the point (-7, 4). This matches our desired endpoint, so the answer is 90° counterclockwise.

Answer:

90° counterclockwise

Step-by-step explanation:

I am not sure if the picture helps or not.  I am trying to show that I traced the point (4,-7).  Then I have a plus sign at (0,0).  I start rotating the tracing paper counterclockwise until  I get to the point (7,4).  I needed to turn one turn of the plus sign.  That would be 90°

Helping in the name of Jesus.

The least important value to today's college students according to the yearly values survey is Political involvement. So the option B is correct.

The survey found that only 32% of college students believed that political involvement was important. This is significantly lower than the other values surveyed such as Financial Success (86%) and Community Involvement (71%). As such, it can be concluded that Political Involvement is the least important value to today's college students.

This may be due to a variety of factors, such as a lack of understanding of the political system, a lack of interest in politics, or a sense that individual political action will not make a difference.

It is important to recognize, however, that political involvement is still an important part of civic engagement and an essential part of the democratic process. As such, college students should strive to become more informed about politics and to find ways to get involved in the political process.

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The complete question is:

Which of the following values, which is least important to today's college students according to the yearly values survey?

A. Career success

B. Political involvement

C. Healthy lifestyle

D. Social media presence

Hi!
The percent change is 15%.
Hope this helps!

~~~PicklePoppers~~~

Answer:

See below, please.

Step-by-step explanation:

The rise of democracy has had a significant impact on the African continent, with many countries transitioning from authoritarian rule to democratic governance since the 1990s. For example, South Africa emerged from decades of apartheid and transitioned to democracy in 1994, with the election of Nelson Mandela as the country's first black president. Similarly, in Ghana, the return to multiparty democracy in 1992 after years of military rule led to the establishment of a more stable political system.

The impact of democracy has not been uniform across Africa, with some countries experiencing significant challenges in their democratic transitions. For instance, in Zimbabwe, President Robert Mugabe, who came to power after independence in 1980, held on to power for over three decades through rigged elections and suppression of political opposition. It wasn't until a military coup in 2017 that he was forced to step down.

Despite the challenges, democracy has brought about some significant improvements on the African continent. With democratic governance, there has been a greater emphasis on human rights, the rule of law, and good governance. Free and fair elections have become the norm in many African countries, and citizens have become more involved in the political process, leading to greater accountability from leaders.

The rise of democracy in Africa has had both positive and negative impacts, but overall it has contributed to the establishment of more accountable and transparent governance systems. With democratic institutions in place, African nations are better positioned to address the political and socio-economic challenges that they face.

Answer: D. As x → -∞, y → -∞.

Step-by-step explanation:

The graph shows the function approaching negative infinity on the x-axis (left side).  When the x-axis is decreasing, the y-axis is also decreasing towards negative infinity.

Answer:

12×2, 3×8, 4×6

Step-by-step explanation:

To find the area of a parallelogram, the formula is A = bh.

1. Height: 6 ft

Base: 2 ft

6 × 2 = 12 ft

So it does not work.

2. Height: 12 ft

Base: 2 ft

12 × 2 = 24 ft

So it does work.

3. Height: 10 ft

Base: 14 ft

14 × 10 = 140 ft

So it does not work.

4. Height: 3 ft

Base: 4 ft

3 × 4 = 12 ft

So it does not work.

5. Height: 3 ft

Base: 8 ft

3 × 8 = 24 ft

So it does work.

6. Height: 4 ft

Base: 6 ft

4 × 6 = 24 ft

So it does work.

Rounding to four decimal places, the answer is 0.8926. So the probability that at least one of the ten college students has not taken a mathematics course is approximately 0.8926.

what is probability?

Probability is a measure of the likelihood or chance that a particular event will occur. It is usually expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

The probability that a college student has taken a mathematics course is 0.80. Therefore, the probability that a student has not taken a mathematics course is

1 - 0.80 = 0.20.

The probability that at least one of ten college students has not taken a mathematics course can be found using the complement rule. That is, the probability that at least one student has not taken a mathematics course is equal to one minus the probability that all ten students have taken a mathematics course.

The probability that all ten students have taken a mathematics course is:

0.80¹⁰ = 0.1074

Therefore, the probability that at least one student has not taken a mathematics course is:

1 - 0.1074 = 0.8926

Therefore, Rounding to four decimal places, the answer is 0.8926. So the probability that at least one of the ten college students has not taken a mathematics course is approximately 0.8926.

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Answer:

the coordinate of C is 10.5, and the distance between A and C is 10.5 - 5 = 5.5, and the distance between B and C is 15 - 10.5 = 4.5.

Step-by-step explanation:

If C is 2 units closer to B than it is to A, then we can find the distance between A and C and between B and C by using the distance formula:

Distance between two points (x1, y1) and (x2, y2) = sqrt[(x2 - x1)^2 + (y2 - y1)^2]

Let x be the coordinate of C. Then, the distance between A and C is x - 5, and the distance between B and C is 15 - x. We know that the distance between B and C is 2 units greater than the distance between A and C, so we can set up an equation:

15 - x = 2 + (x - 5)

Simplifying and solving for x, we get:

15 - x = 2 + x - 5

18 - x = x - 3

2x = 21

x = 10.5

Therefore, the coordinate of C is 10.5, and the distance between A and C is 10.5 - 5 = 5.5, and the distance between B and C is 15 - 10.5 = 4.5.

Answer:

Step-by-step explanation:

2

Answer:

57

57

123

123

57

57

123

that's all.

Answer:

m<1 = 57°

m<2 = m<1 = 57°

m<3 = x = 123°

m<4 = x = 123°

m<5 = m<1 = 57°

m<6 = m<5 = 57°

m<7 = m<4 = 123°

Step-by-step explanation:

[tex]{ \tt{m \angle 1 + x = 180 \degree}} \\ { \colorbox{silver}{corresponding \: angles}} \\ { \tt{m \angle 1 = 180 - 123}} \\ { \tt{ \underline{ \: m \angle 1 = 57 \degree \: }}}[/tex]

Yes, the apparent under representation of Hispanics on the jury duty calls into question the fairness of the jury selection system, as the results of the hypothesis test suggest that the system may be systematically excluding Hispanics.

To determine whether the apparent underrepresentation of Hispanics on the jury selection system is statistically significant and calls into question its fairness, we need to perform a hypothesis test.

First, we set up the null hypothesis, which is the assumption that there is no difference between the proportion of Hispanics in the county population and the proportion of Hispanics in the jury pool. That is, the proportion of Hispanics in the jury pool is expected to be equal to 19%.

The alternative hypothesis is that there is a difference between the proportion of Hispanics in the county population and the proportion of Hispanics in the jury pool.

We can use a one-tailed z-test to test the null hypothesis, where the test statistic is calculated as:

z = (p - P) / sqrt(P(1-P)/n)

where p is the proportion of Hispanics in the jury pool, P is the proportion of Hispanics in the county population (0.19), and n is the sample size (72).

Plugging in the values, we get

z = (9/72 - 0.19) / sqrt(0.19*(1-0.19)/72) = -2.39

Assuming a significance level of 0.05, we compare the calculated z-value with the critical z-value of -1.645 (obtained from a standard normal distribution table). Since the calculated z-value is less than the critical z-value, we reject the null hypothesis and conclude that the proportion of Hispanics in the jury pool is significantly different from the proportion of Hispanics in the county population.

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The value of the variable, x, obtained using the formula for the perimeter of a sector of a circle is; x = 6 cm

A sector of a circle is the region of the circle that has two radii of the circle and the arc between the two radii as the boundary of the region.

The perimeter of a sector of a circle can be obtained using the formula;

Perimeter = 2·r + (θ/360°) × (2·π·r)

The radius of sector OAD, r = 6 cm

Therefore;

The perimeter of sector OAD = 2 × 6 + (50/360) × 2 × π × 6 = 12 + 5·π/3

The perimeter of sector OBC = 2 × The perimeter of sector OAD

Therefore;

The perimeter of sector OBC = 2 × (12 + 5·π/3) = 24 + 10·π/3

Which indicates;

The perimeter of sector OBC = 2  × (6 + x) + (50/360) × 2 × π  × (6 + x)

2  × (6 + x) + (50/360) × 2 × π  × (6 + x) = (5·π·x + 30·π + 36·x + 216)/18

24 + 10·π/3 = (5·π·x + 30·π + 36·x + 216)/18

432 + 60·π = 5·π·x + 30·π + 36·x + 216

432 - 216 + 60·π - 30·π  = x·(5·π + 36)

216 + 30·π = x·(5·π + 36)

6 × (5·π + 36 ) = x·(5·π + 36)

x·(5·π + 36) = 6 × (5·π + 36 )

x = 6 × (5·π + 36 )/(5·π + 36 ) = 6

x = 6 cm

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According to the problem the answer is cos 9 = sin 56.3.

Cos is a mathematical function that returns the ratio of the side adjacent to a given angle of a right triangle to the hypotenuse of the triangle. It is one of the most commonly used trigonometric functions and is used in various mathematical calculations such as finding angles, distances, and wave lengths. Cos is often written as cosine and is typically abbreviated as "cos." It can also be written as COS or csc. Cos is typically used in conjunction with sin and tan to measure angles and distances in a triangle. Cos can also be used to calculate wave lengths in physics and to determine the magnitude of a vector in vector calculus. Cos is an important concept in mathematics and is used in many areas of science, engineering, and technology.

Use the identity sin(90°-x) = cos x:

sin 56.3 = cos (90° - 56.3)

cos 9 = cos (90° - 56.3)

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For cos 9°, angle lies between 0° and 90° (First Quadrant). Since cosine function is positive and in the first quadrant, thus cos 9° value = 0.9876883. Also Cos 9 = √(1-sin²(9°)).

Cos is a mathematical function that returns the ratio of the side adjacent to a given angle of a right triangle to the hypotenuse of the triangle. It is one of the most commonly used trigonometric functions and is used in various mathematical calculations such as finding angles, distances, and wave lengths. Cos is often written as cosine and is typically abbreviated as "cos." It can also be written as COS or csc.

The value of cos 9 degrees in decimal is 0.987688340, since Cos 9 degrees can also be expressed using the equivalent of the given angle (9 degrees) in radians (0.15707)

Using degree to radian conversion, θ in radians is:

= θ in degrees × (pi/180°)

⇒ 9 degrees

= 9° × (π/180°) rad

= π/20 or 0.1570

∴ cos 9° = cos(0.1570)

= 0.9876883

Since the cosine is the periodic function, we can represent cos 9° as,

So, cos 9 degrees = cos(9° + n × 360°).

⇒ cos 9°

= cos 369°

= cos 729°, and so on.

Cos 9 = √(1-sin²(9°))

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Answer:

Step-by-step explanation:

Let weight of fourth parcel be x

Mean = Sum of all values/total number of values.

8.5 = 7.7 + 7.6 + 8.2 + x/4

8.5 = 23.5 + x/4

8.5 × 4 = 23.5 + x

34 = 23.5 + x

34 - 23.5 = x

10.5 = x

Therefore, weight of the fourth parcel will be 10.5 kg

Answer:

A = 32

Step-by-step explanation:

A= (a+b divided by 2) mulitiplied by height

a = 6

b = 2+6+2 = 10

h = 4

a+b = 6 + 10= 16

16 divided by 2 = 8

8 x 4 = 32

Therefore, the area is 32.

Answer: (-3, -1)

Step-by-step explanation:

First, we can use the first equation to solve for one variable in terms of the other.

y = -2x - 7

Next, we can substitute this expression for y into the second equation:

2y - x = 1

2(-2x - 7) - x = 1

Simplifying:

-4x - 14 - x = 1

-5x - 14 = 1

-5x = 15

x = -3

Now that we have the value of x, we can substitute it back into either of the original equations to find y. Using the first equation:

y = -2(-3) - 7

y = 6 - 7

y = -1

Therefore, the ordered pair that satisfies both equations is (-3, -1).

Answer: (-3,-1)

Explanation Step By Step

Answer:

x = 18

Step-by-step explanation:

Alternate exterior angles are congruent.  Set the equations equal to each other and solve for x.

7x + 11 = 10x - 43  Subtract 7 x from both sides

7x - 7x + 11 = 10x - 7x - 43

11 = 3x - 43  Add 3 to both sides

11 + 43 = 3x -43 + 43

54 = 3x  Divide both sides by 3

[tex]\frac{54}{3}[/tex] = [tex]\frac{3x}{3}[/tex]

18 = x

Helping in the name of Jesus.

Step-by-step explanation:

my previous answer assumed we need a kind of average change rate.

but it seems you need the immediate change rate ?

or what ? the question does not specify.

I would appreciate if you would leave a comment, when you find that my answer is seemingly not matching some expected answers.

so, let's try now the immediate change rate (as I have no information to go - I have also no information about what you are currently learning in your class, and if you do already derivatives or not, so, this might be now above your learning level ...) :

again, the area between the inner circle and the outer square is

A = As - Ac = s² - pi×r²

where s is the square's side length, and r is the radius of the circle.

the immediate change rate of that area is the sum of first derivatives of A based on both used variables multiplied by their individual change rates :

dA/dt = dAs/ds × ds/dt - dAc/dr × dr/dt

and this is then calculated for the given data point (s = 16, r = 3) and the individual change rates of the variables (ds/dt = 2 meters/minute, dr/dt = 1 meter/minute).

so, we have

dA/dt = 2s × 2 - 2×pi×r × 1

as (s²)' = 2s, (pi×r²)' = 2×pi×r

dA(16, 3)/dt = 2×16×2 - 2×pi×3×1 = 64 - 6pi =

= 45.15044408... meters²/minute ≈

≈ 45.15 meters²/minute

so, you see, for a curved function (not a line) there has to be a difference between the average change rate between 2 points and the immediate change rate directly at a point.

I hope this works now for you.

and here now the original answer for an average change rate :

right now the radius is 3 m, and the square side lengths are 16 m.

1 minute ago the radius was 2 m, and the square side lengths were 14 m.

the area between the circle and the square is always the area of the square minus the area of the circle.

these areas are right now

circle : pi×3² = 9pi m²

square : 16² = 256 m²

area between = 256 - 9pi = 227.7256661... m²

these areas were one minute ago

circle : pi×2² = 4pi m²

square : 14² = 196 m²

area between = 196 - 4pi = 183.4336294... m²

the change rate of the area between the circle and the square is

227.7256661... - 183.4336294... = 44.29203673... m² per minute

Answer:

82

Step-by-step explanation:

So the radius of the sphere is approximately 2.88 feet (rounded to two decimal places).

Volume is the amount of space occupied by a three-dimensional object as measured in cubic units. It is the measure of the amount of material or substance that a container, object, or shape can hold.

Here,

To express r as a function of V, we can rearrange the equation V = 4/3πr³ to solve for r:

V = 4/3πr³

V / (4/3π) = r³

r = ³√(V / (4/3π))

r = ³√(3V / 4π)

To find the radius of a sphere with volume 100 cubic feet, we can substitute V = 100 into the equation:

r = ³√(3V / 4π)

= ³√(3(100) / (4π))

≈ 2.88 units

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