The 5-lb collar slides on the smooth rod, so that when it is at A it has a speed of 10 ft/s. A) if the spring to which it is at- tached has an unstretched length of 3 ft and a stiffness of k-= 10 lb/ etermine the normal force on the collar at this instant. B)Determine the acceleration of the collar at this instant.

Answer:

Step-by-step explanation:The system of equations represented by the given points is:1x + 0y = 1   (equation 1)

1x + 6y = 1   (equation 2)

8x + 26y = 1  (equation 3)

8x - 22y = 1  (equation 4)

We can use the first equation to solve for x in terms of y:1x + 0y = 1

1x = 1

x = 1

Then we can substitute x=1 into equations 2-4 to obtain three equations in terms of y:1(1) + 6y = 1    =>   6y = 0   =>   y = 0

8(1) + 26y = 1   =>   26y = -7/8   =>   y = -7/208

8(1) - 22y = 1   =>   -22y = -7/8 - 7   =>   y = 15/44

Therefore, the solution to the system is x = 1 and y = -7/208 or y = 0 or y = 15/44.

However, we are given that x = -2, which contradicts our solution of x = 1. Therefore, there is no solution to the system with the given values.

Answer:

Step-by-step explanation:

Log₁₆(256b) in terms of the logarithm of b, which is the factor that was multiplied by 256 inside the logarithm is  2 + log₁₆(b)

We can use the product rule of logarithms, which states that the logarithm of a product is equal to the sum of the logarithms of the factors.

Therefore, we can write

log₁₆(256b) = log₁₆(256) + log₁₆(b)

We can simplify log₁₆(256) as follows:

log₁₆(256) = log₁₆(16^2) = 2

Therefore, we have:

log₁₆(256b) = log₁₆(256) + log₁₆(b)

= 2 + log₁₆(b)

So, we have rewritten log₁₆(256b) in terms of the logarithm of b, which is the factor that was multiplied by 256 inside the logarithm.

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The difference of p and z times the sum of p and z is p² - 2pz - z².

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations such as addition, subtraction, division and multiplication.

Hence, the difference of p and z times the sum of p and z can be represented as follows:

Therefore,

(p - z) × (p + z) = (p - z) (p + z)

(p - z) (p + z)  = p² - pz - pz - z²

p² - pz - pz - z² = p² - 2pz - z²

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The distribution of the sample is approximately normal with a mean of 0. 15 and a standard deviation of 0. 03852.

One can utilize the Central Limit Theorem (CLT) for proportions to detail the dispersion of the sample proportion. Explained by the CLT, if the size of the sample is sufficiently significant enough, then the distribution with respect to the sample proportion will be mostly indistinguishable from a typical distribution.

np ≥ 10

n(1-p) ≥ 10

Given that both conditions are fulfilled, we can essentially posit that the said sample proportion distribution  is almost normal. In light of this knowledge, it would be pertinent to ascertain the mean (μ) and standard deviation (σ) of the sample proportion distribution.

Mean = p = 0.15

Standard deviation:

= √ ( ( 0.15 x ( 1 - 0. 15 ) ) / 86 )

= 0.03852

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Answer:

92.

Step-by-step explanation:

To find the range of the set of numbers 20, 3, 95, 54, 71, 66, we first need to find the difference between the largest and smallest numbers in the set.

Largest number = 95

Smallest number = 3

Range = Largest number - Smallest number

Range = 95 - 3

Range = 92

Therefore, the range of the set of numbers 20, 3, 95, 54, 71, 66 is 92.

Answer:92

Step-by-step explanation: highest-lowest

it helps to put the terms in order first

95-3=92

The range, difference of maximum and minimum values, is larger for Class C with a range of 10 compared to Class D with a range of 3. The data provided is not sufficient to calculate the IQR (Interquartile Range) for either class.

To begin, let's understand what the terms 'range' and 'IQR' (Interquartile Range) refer to in statistics. The range is simply the difference between the largest and smallest data values. The IQR is the range of the middle 50% of the values when ordered from lowest to highest.

For Class D, the lowest absence number is 0 and the highest is 3, thus the range is 3-0 = 3. For Class C, the lowest absence number is 0 and the highest is 10, so the range is 10-0 = 10. Thus, the range for the distribution of absences is larger for Class C.

Calculating IQR requires determining the 1st Quartile (Q1) and 3rd Quartile (Q3) values and subtracting Q1 from Q3. The data given doesn't include enough information to directly calculate these values and hence, it is impossible to definitively say which class has a larger IQR based on the provided information.

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The key features of the function f(x) = 2log₃(x+7) graphed below include the following:

In Mathematics and Geometry, a domain refers to the set of all real numbers for which a particular function is defined.

Furthermore, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph of this logarithmic function shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-7, ∞].

Range = [-∞, ∞].

In conclusion, we can logically deduce that this logarithmic function has a vertical asymptote is at x equal to negative seven.

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The lengths of the legs, the circumference and the radius of the circles are;

First part; The diameter = 18 units

The second leg = 9 units

Second part; The circumference = 34·π units

Third part; The radius is r = 36 cm

The radius of a circle is the distance from the center to the circumference.

First part;

cos(30°) = 9·√3 ÷ The diameter = (√3)/2

The diameter = (9·√3) ÷ ((√3)/2) = 18

The length of the other leg, using the relationship between special triangles is 18/2 = 9

Second part;

The lengths of the legs of the right triangle indicates that we get;

The square of the diameter, D² = 30² + 16² = 1156

The length of the diameter, D = √(1156) = 34

The formula for finding the circumference of a circle, C, based on the diameter can be presented as follows;

C = π × D

Therefore;

The circumference of the circle, C = π × 34

The circumference of the circle = 34·π units

Third part

The length of the 20° arc = 4·π cm

Therefore;

4·π = 2·π·r × 20/360

Where;

r = The radius of the circle

Therefore;

r = (360/20) × 4·π ÷ (2·π) = 36

The radius of the circle, r = 36 cm

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Answer:

Step-by-step explanation:

[tex]\frac{x}{18} =cot~30\\x=18cot~30=18 \times \sqrt{3} =18\sqrt{3} \\base=36\sqrt{3} \\area~of~triangle=3\times \frac{1}{2} \times36\sqrt{3} \times 18=972\sqrt{3} \approx 1683.55~mm^2[/tex]

The two-way table constructed from the data showing the numbers of boys and girls that choose each dance category should look like this:

                         Boys      Girls         Total

Fall Fling            82          81             163

Spring Social     62         75             137

Total                 144        156            300

A two-way table is a data display tool that displays the frequencies for two different categories collected from a single group.

A two-way table use rows to represent one category variable and the columns to represent a second category variable, while the cells display the proportions or frequencies of each row and column combination.

The total number of boys in eighth grade = 144

The number of boys who choose to attend the Fall Fling = 82

Therefore, the number of boys who attend the Spring Social = 62 (144 - 82)

The total number of girls in eighth grade = 156

The number of girls who choose to attend the Spring Social = 75

Therefore, the number of girls who attend the Fall Fling = 81 (156 - 75)

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Answer:

62,  82, 163, 300

Step-by-step explanation:

I got this on study island

The area of triangle ABC is :  33.44 cm²

The area of a triangle is the region enclosed within the sides of the triangle. The area of a triangle varies from one triangle to another depending on the length of the sides and the internal angles. The area of a triangle is expressed in square units, like, m2, cm2, in2, and so on.

We have the information from the question is:

In triangle ABC :

AB=6 cm,

AC=15 cm, and

m ∠A=48°.

We have to find the area of Triangle ABC

Area of triangle is : 1/2 × bc × (SinA)

Area of Triangle = 1/2 × 6 × 15 × (Sin 48° )

We know the value of Sin 48° is 0.7431

Area of Triangle = (1/2) × 66.88

Area of triangle = 33.44 cm²

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Step-by-step explanation:

First group of five    total score   =    5 * 6.5 = 32.5

Group of fifteen total score         =   15 * 4.5 = 67.5

total score of  20    is    67.5 + 32.5 = 100

Average =  100 /20 = 5.0

Note that the difference in the radii of the two circular tracks is about 13.68 ft

recall that the circumference of a circle is denoted by the expression

C = 2πr

In this case, C = Circumference
and r   radius

Since we have two tracks

Let ra = radius of the purple track and

rb = radius of the yello track

So

265 = 2πra

170 = 2πrb

making ra and rb subject of the expression we have

ra = 256/(2π)  =40.7436654315 ≈ 40.74

rb = 170 / (2π) = 27.0563403256 ≈ 27.06

Hence, the difference is

40.74 - 27.06 = 13.68ft

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Full Question:

at a fair Daniel and Claire went on a ride that has two separate circular tracks. Daniel rode in a purple car that travels a total distance of 265 feet around the track . Ciara rode in a yellow car that travels a total distance of 170 feet around the track. They drew drew a sketch of the ride. What is the difference ofthe radii of the two circle tracks

The computations of the net profit or loss using the following cost valuation methods are as follows:

FIFO, net profit = $20,000

Weighted Average, net profit = $17,555.54.

The inventory cost valuation methods include FIFO (First In, First Out), LIFO (Last In, First Out), WAC (Weighted Average Cost), and Specific Identification.

Under the FIFO basis, the cost of inventory is evaluated based on the assumption that inventory that are first brought in are the first to be sold.

Under the Weighted Average Cost method, the average cost is computed by dividing the total cost of goods available for sale by the number of units.

Other inventory cost valuation methods include LIFO and Specific Identification.

Cost of Goods Sold = $80,000 ($10,000 x 3 + $12,000 x 2 + $13,000 x 2)

Sales Revenue = $106,000 ($15,000 x 7)

Overhead = $6,000

Net Profit = $20,000 ($106,000 - $80,000 - $6,000)

Weighted Average Cost per tractor = $11,777.78 ($106,000 ÷ 9)

Cost of Goods Sold = $82,444.46 ($11,777.78 x 7)

Sales Revenue = $106,000 ($15,000 x 7)

Overhead = $6,000

Net Profit = $17,555.54 ($106,000 - $82,444.46 - $6,000)

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The number of cans brought by Joes team is J = 299 cans

Given data ,

Let the number of cans brought by Joes team be J

Now , sage team brought 224 cans

And , sage team brought 3 times cans as asifs team

And , joes team brought 4 times as asifs team

On simplifying the equation , we get

Asif's team brought 224/3 = 74.67 (rounded to the nearest whole number) cans.

Joe's team brought 74.67 x 4 = 298.68

So , J = 299 cans

Hence , the equation is solved and J = 299 cans

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Answer:

it is b got it right on my test

Step-by-step explanation:

The required graph that shows Ellen's steps where her mean steps for a week is 10000 is graph 2 where the data are as,

Day 1 = 11000 , Day 2 = 9000, Day 3 = 10000, Day 4 = 12000, Day 5 = 8000, Day 6 ≈ 10000, Day 7 ≈ 10000

Mean of ungrouped data is the average of all the values of the observation in the data set.

Mean = (Summation of all values in data set)/ (Number of observations)

Here there are 7 observations and the mean number of steps is 10000.

For graph 1 the values for each day of the week are as,

Day 1 = 8000 , Day 2 = 9000, Day 3 = 12000, Day 4 = 2000, Day 5 = 6000, Day 6 = 10000, Day 7 = 10000

Thus, the mean number of steps is = (8000+ 9000+ 12000+ 2000+ 6000+ 10000 + 10000) / 7

= 8143 (approximately) ≠ 10000

For graph 2 the values for each day of the week are as,

Day 1 = 11000 , Day 2 = 9000, Day 3 = 10000, Day 4 = 12000, Day 5 = 8000, Day 6 ≈ 10000, Day 7 ≈ 10000

Thus, the mean number of steps is = (11000+ 9000+ 10000+ 12000+ 8000+ 10000 + 10000) / 7

= 10000

For graph 3 the values for each day of the week are as,

Day 1 = 7000 , Day 2 = 14000, Day 3 = 11500, Day 4 = 10000, Day 5 = 4500, Day 6 = 6000, Day 7 = 11000

Thus, the mean number of steps is = (7000+ 14000+ 11500+ 10000+ 4500+ 6000 + 11000) / 7

= 9143 (approximately) ≠ 10000

For graph 4 the values for each day of the week are as,

Day 1 = 8000 , Day 2 = 9000, Day 3 = 9500, Day 4 = 10000, Day 5 = 9000, Day 6 = 7000, Day 7 = 11000

Thus, the mean number of steps is = (8000+ 9000+ 9500+ 10000+ 9000+ 7000 + 11000) / 7

= 9071 (approximately)  ≠ 10000

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Since ΔJKL was transformed to create ΔMNO, the sequence of transformations that were used include the following:

Reflection over the y-axis.

(x, y) → (x, y - 9).

In Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).

By applying a reflection over the y-axis to the coordinate of the given triangle JKL, we have the following coordinates:

Coordinate J = (3, 7)   →  Coordinate J' = (-(3), 7) = (-3, 7).

Next, we would apply a vertical translation by shifting triangle J'K'L' down by 9 units to produce ΔMNO;

(x, y)                   →         (x, y - 9).

J' (-3, 7)               →        (-3, 7 - 9) = M' (-3, -2).

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The volume of the flower vase, can be found to be 2, 199 cm ³.

The volume of the flower vase can be found by subtracting the volume of the cone from the volume of the rectangular prism.

Volume of rectangular prism :
= Length x Width x Height

= 20 x 12 x 10

= 2, 400 cm ³

The volume of the cone is:

=  π x radius ² x height / 3

= π x 4 ² x 12 / 3

= 201. 06 cm ³

Volume of vase:

= 2, 400 -  201. 06

= 2198.94

= 2, 199 cm ³

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The expression 16x⁹y¹⁸√3xy is equivalent to √769x¹⁹y³⁷

If a > O and y > 0, which expression is equivalent to √769x¹⁹y³⁷

Factor and rewrite the radicand in exponential form:

√16²×3x¹⁸×xy³⁶×y

Simplify the radical expression:

16x⁹y¹⁸ √2²×3xy

Factor and rewrite the radicand in exponential form:

8x⁹y¹⁸√2²×3xy

8x⁹y¹⁸.2√3xy

Multiply the monomials:

16x⁹y¹⁸√3xy

Hence, the expression 16x⁹y¹⁸√3xy is equivalent to √769x¹⁹y³⁷

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Answer:

2.38 s

4.62 s

Step-by-step explanation:

The height of a projectile is given by the function:

[tex]h(t) = -t^2 + 7t + 9[/tex]

where:

To determine the time(s) at which the rocket is 20 ft above the ground, set h(t) = 20 and solve for t.

[tex]-t^2+7t+9=20[/tex]

To solve the equation for t, complete the square.

Subtract 9 from both sides:

[tex]-t^2+7t=11[/tex]

Divide both sides by -1:

[tex]t^2-7t=-11[/tex]

Add the square of half the coefficient of the term with the variable "t" to both sides of the equation:

[tex]t^2-7t+\left(\dfrac{-7}{2}\right)^2=-11+\left(\dfrac{-7}{2}\right)^2[/tex]

Simplify:

[tex]t^2-7t+\dfrac{49}{4}=\dfrac{5}{4}[/tex]

We have now created a perfect square trinomial on the left side of the equation. Factor the perfect square trinomial:

[tex]\left(t-\dfrac{7}{2}\right)^2=\dfrac{5}{4}[/tex]

To solve for t, square root both sides:

[tex]t-\dfrac{7}{2}=\pm \sqrt{\dfrac{5}{4}}[/tex]

[tex]t-\dfrac{7}{2}=\pm\dfrac{\sqrt{5}}{2}[/tex]

Add 7/2 to both sides of the equation:

[tex]t=\dfrac{7}{2}\pm\dfrac{\sqrt{5}}{2}[/tex]

[tex]t=\dfrac{7\pm\sqrt{5}}{2}[/tex]

Therefore, the times at which the rocket is 20 ft above the ground is:

[tex]t=\dfrac{7-\sqrt{5}}{2}=2.38\; \rm s[/tex]

[tex]t=\dfrac{7+\sqrt{5}}{2}=4.62\; \rm s[/tex]

Answer:

C)  1/2  and 8

Step-by-step explanation:

-2x + y = 7              Eq. 1

6x + y = 11               Eq. 2

From Eq. 1:

y = 7 + 2x               Eq. 3

From Eq. 2:

y = 11 - 6x              Eq. 4

Equalyzing Eq. 3 and Eq. 4:

7 + 2x = 11 - 6x

2x + 6x = 11 - 7

8x = 4

x = 4/8

x = 1/2

From Eq. 3:

y = 7 +2* 1/2

y = 7 + 1

y = 8

Check:

From Eq. 2

6x + y = 11

6*1/2 + 8 = 11

3 + 8 = 11

The amount of water needed is 72 liters.

Given that, the ratio of the alcohol and water in a mixture of 72 units is 2 ratio 1, we need to find the amount of water that must be added to the mixture in order to make this ratio 1 ratio 2,

So,

The quantity of water in it = 72 / 3 × 1 = 24

New ratio =

48 / 24+x = 1/2

96 = 24+x

x =72

Hence, the amount of water needed is 72 liters.

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In the circle the measure of arc YP as per the given measurements is equal to option D. 166°

In the circle,

Measure of arc ST = 70°

Measure of arc RS = 96°

Measure of angle YZP = 128°

Arc formed by vertically opposite angles are equal

This implies,

Measure of arc YT = Measure of arc PR

Measure of arc ST + Measure of arc RS + Measure of arc YT = 180°

⇒70° + 96° + Measure of arc YT = 180°

⇒Measure of arc YT = 180° - 166°

⇒Measure of arc YT = 14°

⇒ Measure of arc PR = 14°

Measure of arc YP = 360° - ( Measure of arc (PR + RS + ST + TY ))

⇒ Measure of arc YP = 360° - ( 14° + 96° + 70° + 14° )

⇒Measure of arc YP = 360° -194°

⇒ Measure of arc YP = 166°

Therefore, the measure of arc YP is equal to option D. 166°

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The value of Tan A + B is 6.009.

[tex]sin^2 A + cos^2 A = 1sin^2 A = 1 - cos^2 Asin A = sqrt(1 - cos^2 A)sin A = sqrt(1 - (28/45)^2)sin A = sqrt(1 - 784/2025)sin A = sqrt(1241/2025)cos A = 28/45\geq[/tex]

We have to solve for Tan B

[tex]sin^2 B + cos^2 B = 1sin^2 B = 1 - cos^2 Bsin B = sqrt(1 - cos^2 B)sin B = sqrt(1 - (13/12)^2)sin B = sqrt(55/144)Therefore, tanB = sinB / cosB = (sqrt(55/144)) / (13/12) = (12 sqrt(55)) / 143[/tex]

[tex]tan(A+B) = (3207 \sqrt{55}) + 1804 \sqrt{124})) / (3115 - 207 \sqrt{(341)}[/tex]

= 6.009.

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