Determine two pairs of polar coordinates for the point (3, -3) with 0° ≤ θ < 360°

To find for the value of the confidence interval, let us first calculate for the values of x and s, the mean and standard deviation respectively.

x = (5 + 18 + 12 + 24 + 28) / 5

x = 17.4 months

s = sqrt{[(5 – 17.4)^2 + (18 – 17.4)^2 + (12 – 17.4)^2 + (24 – 17.4)^2 + (28 – 17.4)^2]/(5-1)}

s = 9.21

The formula for the confidence interval is given as:

Confidence Interval = x ± t s / sqrt(n)

Where t can be taken from standard distribution tables at 95% level at degrees of freedom = n – 1 = 4, t = 2.132. Therefore:

Confidence Interval = 17.4 ± 2.132 * 9.21 / sqrt(5)

Confidence Interval = 17.4 ± 8.78

Confidence Interval = 8.62 months, 26.18 months

Final answer:

To construct a 95% confidence interval for the mean number of months elapsed since the last visit to a dentist, use the sample mean and sample standard deviation. Calculate the confidence interval using the formula and given data.

Explanation:

In order to construct a confidence interval for the mean number of months elapsed since the last visit to a dentist for the population of students participating in the program, we can use the sample mean and sample standard deviation. The formula for constructing a confidence interval for the mean is:

Confidence Interval = sample mean ± (critical value) × (sample standard deviation / √sample size)

Using the given data, the sample mean is 17.4 months and the sample standard deviation is 9.18 months. With a confidence level of 95%, the critical value is 2.776. Plugging these values into the formula, we get:

Confidence Interval = 17.4 ± (2.776) × (9.18 / √5)

Calculating this, we find that the 95% confidence interval for the mean number of months elapsed since the last visit to a dentist is approximately 4.81 to 29.99 months.

In a circle, the point of symmetry is the centerpoint; any straight line that passes through this point is a line of symmetry. The standard form of equation of a circle is given as:

(x – h)^2 + (y – k )^2 = r^2

Where,

h = x coordinate of the center

k = y coordinate of the center

In the problem statement, we are given that the equation of the circle is:

(x – 5)^2 + (y + 4)^2 = 25

So identifying the variables from the standard form of equation of a circle:

h = 5

k = - 4

Therefore the point of symmetry is (5, -4).

The number of significant figures in 0.01500 is 4.

Significant figures (or significant digits) are the number of digits in a given value or a measurement, necessary to decide the accuracy and precision of measurement.

The given decimal number is 0.01500.

Certain rules help us determine the number of significant figures. These rules are as follows:

(1) All non-zero digits are significant.

(2) All zeros in between non-zero digits are significant.

(3) Zeros on the right of a decimal point and before (or to the left of) the first non-zero digit are not significant. They only represent the position of the decimal point.

(4) Zeros on the right of a decimal point are significant, provided there is no non-zero digit after them.

(5) Zeros on the right of the last non-zero digit after a decimal point are significant. So, final zeros or trailing zeros in the decimal part are significant.

(6) In a measurement value, zeros that occur on the right of the last non-zero digit are significant.

In the given decimal 0.01500, two non zero digits and two leading zeros are significant

So, number of significant figures are 4

Therefore, the number of significant figures in 0.01500 is 4.

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In this scenario involving an elevator's movement, the negative velocity indicates downward motion and corresponds to the slope in the equation of a line. By applying the slope and initial conditions, we calculated that Monica was initially 470 feet above the ground, which is the y-intercept in the slope-intercept form.

The student's question involves understanding the implications of negative velocity in a real-world situation involving an elevator, calculating an initial position based on this velocity and elapsed time, and tying these concepts to algebraic representations in slope-intercept form.

Answer:

We have to find a graph which represents a  reflection of f(x) = 1/10 (10)x across the y-axis.

As we know that on reflecting the graph across the y-axis the x-coordinate of the point changes to opposite sign nut with same magnitude and the y-coordinate remains same.

Hence, the function f(x) is transformed to:

[tex]f(x)=\dfrac{1}{10}\times 10^{-x}[/tex]

The graph of the function passes through the point (0,0.1) and is a strictly decreasing function.

and the end behavior of the graph is that:

when x→∞    f(x)→ 0

when x→ -∞    f(x) → ∞

We know from physics class that the formula for distance of a linear motion is given as:

d = v t

Where,

d = distance travelled

v = average velocity

t = time it took to reach the destination

Since the distance going to the office and back is just similar, therefore we can simply equate the two:

v1 t1 = v2 t2

Where 1 signifies going to the office and 2 signifies going back from the office. Therefore this yields to:

v1 * 5 hours = 65 mph * 4 hours

v1 = 52 mph

Answer: The average speed going to the office is 52 mph.

The average speed of Jill's trip to the ferry office was 52 mph, calculated by dividing the distance of 260 miles by the time of 5 hours.

To find the average speed of the trip there, we need to know the distance Jill traveled to the ferry office. Since she averaged 65 mph on the return trip which took 4 hours, the distance is calculated as speed x time, which equals 260 miles (65 mph x 4 hours).

The distance to the ferry office is the same as the distance back, so Jill also traveled 260 miles on the trip there. Given that the trip there took 5 hours, we can find the average speed by dividing the distance by the time. The average speed is 260 miles / 5 hours, which equals 52 mph.

Both the bells will ring after 30 minutes at 6:30 pm.

The smallest common positive number that is a multiple of two or more numbers.

Given that, a bell tolls every 10 minutes. another bell tolls every 15 minutes. both bells toll at 6:00pm.

To find the time for which both will ring together, we will find LCM of 10and 15

10 = 5x2

15 = 5x3

LCM = 5x2x3 = 30

The LCM of 15 and 10 is 30

So, both will ring after 30 minutes.

Right now the time is 6:00 pm, so after 30 minutes it will be 6:30 pm

Hence, Both the bells will ring after 30 minutes at 6:30 pm.

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The final price of the tablet is c(t) = 0.918.

A sale price is the discounted price at which goods or services are being sold.

According to the given question

Tablets are on sale for 15% off the original price(t), which can be expressed with the function:

p(t) = 0.85t

The additional taxes of 8% of the discounted price(p), which can be expressed as a function:

c(p) = 1.08p

Therefore,

The final price of a tablet with the discount and taxes applied based on its original price is given by

c(p(t)) = 1.08 ×p(t)

c(p(t)) = 1.08×(0.85t)

c(p(t)) = 0.918t

⇒ c(t) =0.918t

Hence, the final price of the tablet is c(t) = 0.918.

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The solution is, the volume of the square pyramid is 605 cm^3.

and, the surface area of the cylinder in terms of pi is 522 pi in^2.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

we know that,

volume of pyramid is:

V = 1/3 B h

here, we have,

B = 11*11

  = 121

h = 15

so, we get,

V = 605 cm^3

again, we have,

surface area of the cylinder :

s = 2πr( r + h)

here, we have,

r = 9

h = 20

so, we get,

s = 522 pi in^2

Hence, The solution is, the volume of the square pyramid is 605 cm^3.

and, the surface area of the cylinder in terms of pi is 522 pi in^2.

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The volume of the square pyramid is A) 126 cm³ and the surface area of the cylinder is B) 522π in².

The volume of a square pyramid is expressed as:

Volume = l² × h/3

The surface area of a cylinder is expressed as:

Surface area = 2πrh + 2πr²

From the diagram:

For the square pyramid:

Length l = cm

Height h = 15cm

Volume =?

Volume = l² × h/3

Plug in the values:

Volume = 11² × 15/3

Volume = 121 × 5

Volume = 605 cm³

Option C) 605 cm³ is the correct answer.

Next, we find the surface area of the cylinder:

Radius r = 9 in

Height h = 20 in

Surface area = 2πrh + 2πr²

Plug in the values:

Surface area = (2π × 9 × 20) + (2π × 9²)

Surface area = 522π in²

Therefore, the surface of the cylinder is 522π in².

Option B) 522π in² is the correct answer.

The correct option is that a score of 79 on a psychology test is relatively better than a score of 48 on an economics test.

To determine which score is relatively better, we can calculate the z-scores for each test score. The z-score tells us how many standard deviations away from the mean a particular score is.

For the psychology test, the mean is 85 and the standard deviation is 5. The score is 79. The z-score can be calculated using the formula:

[tex]\[ z = \frac{X - \mu}{\sigma} \][/tex]

where [tex]\( X \)[/tex] is the score,[tex]\( \mu \)[/tex] is the mean, and [tex]\( \sigma \)[/tex] is the standard deviation.

For the psychology test:

[tex]\[ z_{psychology} = \frac{79 - 85}{5} = \frac{-6}{5} = -1.2 \][/tex]

For the economics test, the mean is 52 and the standard deviation is 3. The score is 48. Using the same formula:

[tex]\[ z_{economics} = \frac{48 - 52}{3} = \frac{-4}{3} \approx -1.33 \][/tex]

Now, comparing the z-scores:

- The z-score for the psychology test is -1.2, which means the score is 1.2 standard deviations below the mean.

- The z-score for the economics test is approximately -1.33, which means the score is about 1.33 standard deviations below the mean.

Since a lower (more negative) z-score indicates a worse relative performance, the score of 79 on the psychology test is relatively better than the score of 48 on the economics test, because -1.2 is greater than -1.33. This means that the psychology test score is closer to its mean relative to its standard deviation than the economics test score is to its mean relative to its standard deviation.

Scientific notation of distance between the earth and the sun is approximately 9.3 x 10^7 miles.

What is Scientific notation ?

Scientific notation is the way to express the large value in short form. The number in scientific notation have two parts. The digits (decimal point will place after first digit) × 10 ( the power which put the decimal point where it should be).

Here it is given that The distance between the earth and the sun is approximately 93 million miles and 1 million miles equals 1,00,000 miles.

Now, writing 93 millions Scientific notation by writing 1,00,000 in power of 10 and 93 as 9.3 x 10 :

93 million miles = 9.3 x 10 x 1,00,000

                          = 9.3 x 10^7

Therefore, Scientific notation of distance between the earth and the sun is approximately 9.3 x 10^7 miles.

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The distance between the Earth and the Sun (93 million miles) in scientific notation is [tex]9.3 *10^7 miles[/tex].

To write the distance between the Earth and the Sun (93 million miles) in scientific notation, follow these steps:

First, write 93 million as a standard numeral: 93,000,000.

Next, identify how many places to move the decimal point to get a number between 1 and 10. For 93,000,000, the decimal point moves 7 places to the left.

After moving the decimal point in 93,000,000.00 by 7 places, you get 9.3, which is between 1 and 10. This is known as mantissa.

Mantissa = 9.3

Write the number as a coefficient multiplied by 10 raised to the number of places the decimal was moved. This is called the exponent term. Exponent term = [tex]10^7[/tex].

Scientific notation of a number = Mantissa*Exponent term

So, 93,000,000 = [tex]9.3 *10^7[/tex].

Therefore, the distance between the Earth and the Sun in proper scientific notation is [tex]9.3 *10^7 miles[/tex].

C=14 +1.5(x-4)

 c= total cost

x = number of cards

cost for 9 cards:

x=9

c=14+1.5(9-4)

14+1.5(5) = 21.50

 total cost = $21.50

Using the friction equation mg sin A = μmg cos A and the given coefficient of friction (μ) of 0.17, the angle at which a waxed wood block begins to slide on wet snow is calculated to be approximately 9.6°.

To find the angle at which a waxed wood block on an inclined plane of wet snow begins to slide, we can use the equation mg sin A = μmg cos A, where A is the angle of inclination, m is the mass of the block, g is the acceleration due to gravity, and μ is the coefficient of friction. Since the mass (m) and gravity (g) are both common factors on each side of the equation, they can be canceled out, leaving us with tan A = μ, where tan A is the tangent of the angle A, and μ is the coefficient of friction (0.17 in this case). Solving for A gives us A = arctan(μ). So, A = arctan(0.17), which calculates to approximately 9.6°. This is the angle at which the block begins to slide.

Answer:

i) t = 5

ii) a = 3√7

iii)  x =3√13

Step-by-step explanation:

We have right triangles.

Know the two sides of the triangle and need to find the third missing side.

In order to find the third side of the right triangle, we use pythagoras theorem.

It is,

(Hypotenuse)² = (base)² + (height)²

i)

13² = 12² + t²

169 = 144 + t²

t² = 25

t = 5.

ii)

12² = 9² + a²

144 = 81 + a²

144 - 81 = a²

a² = 63

a = √63

iii)

x² = 9² + 6²

x² = 81 + 36

x² = 117

x = √117

x = 3√13

Answer:

Option B. B = 70.05° B' = 109.95°

Step-by-step explanation:

By the sine rule in a given triangle

sin 45°/16.5 = sinB/22

1/(1.414×16.5) = sinB/22

sinB = 22/(1.414×16.5) = 0.94

[tex]B = sin^{-1}(0.94)[/tex]

B = 70.05°

Now we know B' = 180 - Supplementary angle of B'

and B = B' ( opposite angles of equal sides are equal)

B' = 180 - B = 180 - 70.05 = 109.95°

Therefore option B is the answer.