a bullet of mass m and speed v passes completely through a pendulum bob of mass M. The bullet emerges with a speed v/2. Thependulum bob is suspended by a stiff rod of length and negligible mass. What is the minimum value of v such that the pendulum bob will barely swing through a complete vertical circle?

Answer:

y=-7(x+1)^2 +8

Step-by-step explanation:

Vertex as shown in vertex form, and solve for the coefficient by plugging in the point.

y=-9(x+1)^2+8

start with the vertex form of a parabola:

y=a(x-h)^2+k , "h" and "k" are the vertex coordinates, and "a" is the leading coefficient.

1. plug in the vertex coordinates

y=a(x+1)^2+8

2. to find "a", plug in the point coordinates in the function from step 1 for x and y

-1=a(-2+1)^2+8

when you solve this equation, you will find that a=-9

3. substitute "a" value in the equation from step 1

Done

Answer: R(7, 9), S(6, 7), T(2, 3), U(8, 5), V(5, 5)

Answer:

67.7215189873%

Step-by-step explanation:

The price of a desktop computer decreases from $3160 to $1020

Initial price of desktop =$3160

New Price= $1020

Change in price = 3160 - 1020 = 2140

Percentage decrease = [tex]\frac{2140}{3160}[/tex][tex]X[/tex][tex]100[/tex]=67.7215189873%

Hence , the answer is 67.7215189873%

Hope it helps u

Hypotheses: H0: μ1 = μ2 and H1: μ1 ≠ μ2.This hypothesis test is a two-tailed test.

Calculate the pooled standard deviation of the two samples.

Let x1 and x2 be the sample means of the National League and American League, respectively. Let s1 and s2 be the sample standard deviations of the National League and American League, respectively. Let n1 and n2 be the sample sizes of the National League and American League, respectively.

Pooled standard deviation = √[( (n1 - 1)s1^2 + (n2 - 1)s2^2 ) / (n1 + n2 - 2)]

s1 = 6.9282

s2 = 6.3246

n1 = 2

n2 = 2

Pooled standard deviation = √[( (2 - 1)6.9282^2 + (2 - 1)6.3246^2 ) / (2 + 2 - 2)]

Pooled standard deviation = 6.6759

Calculate the degrees of freedom (df).

Degrees of freedom (df) = n1 + n2 - 2

df = 2 + 2 - 2

df = 2

Calculate the t-statistic.

Let μ1 and μ2 be the population means of the National League and American League, respectively.

t-statistic = (x1 - x2 - (μ1 - μ2)) / √(s^2 / n1 + s^2 / n2)

x1 = 18

x2 = 19

μ1 = μ2

s2 = 6.6759

n1 = 2

n2 = 2

t-statistic = (18 - 19 - (μ1 - μ2)) / √(6.6759^2 / 2 + 6.6759^2 / 2)

t-statistic = (-1) / (4.4518)

t-statistic = -0.2244

At a significance level of 0.10,

The critical value for a two.

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Step 1

We are given a homogenous rod in a cubic curve shape having two free ends, upper end B

and lower end x

The distance of the upper end from x

axis is 1m

and from y axis is 2m.

The rod is bent in a cubic curve shape between two ends and the equation for the rod is given by

[tex]y=2 x^3[/tex]

Here, [tex]$\bar{x}_1$[/tex]and [tex]$\bar{y}_1$[/tex]are the centroidal distances of the strip element from [tex]x$and $y$[/tex] axes respectively.

Step 3

The given equation of the homogenous rod is,

[tex]\begin{gathered}y=2 x^3 \\\frac{d y}{d x}=6 x^2\end{gathered}[/tex]

The given equation of the homogenous rod is,

\begin{aligned}

[tex]& d L=\sqrt{d x^2+d y^2} \\& d L=d x \times \sqrt{1+\left(\frac{d y}{d x}\right)^2} \\& d L=\sqrt{1+\left(6 x^2\right)^2} \cdot d x \\& d L=\sqrt{1+36 x^4} \cdot d x\end{aligned}[/tex]

[tex]& d L=\sqrt{d x^2+d y^2} \\& d L=d x \times \sqrt{1+\left(\frac{d y}{d x}\right)^2} \\& d L=\sqrt{1+\left(6 x^2\right)^2} \cdot d x \\& d L=\sqrt{1+36 x^4} \cdot d x\end{aligned}[/tex]

[tex]& L=\int_{x=0}^{x=1 \mathrm{~m}} d L \\& L=\int_{x=0}^{x=1 \mathrm{~m}} \sqrt{1+36 x^4} \cdot d x \\[/tex]

[tex]& L=6 \times \int_{x=0}^{x=1 \mathrm{~m}} \sqrt{\left(x^2\right)^2+\frac{1}{36}} \cdot d x \\[/tex]

[tex]& L=6 \times\left[x^2 \sqrt{x^4+\frac{1}{36}}+\frac{1}{36} \ln \left|\left(x^2+\sqrt{x^4+\frac{1}{36}}\right)\right|\right]_0^{1 \mathrm{~m}}\end{aligned}[/tex]

Substituting the values in the above expression and solving,

[tex]& \int_L y \cdot d L=\left[\frac{\left(36 \times(1 \mathrm{~m})^4+1\right)^{\frac{3}{2}}}{108}\right]-\left[\frac{\left(0+1 \mathrm{~m}^4\right)^{\frac{3}{2}}}{108}\right] \\& \int_L y \cdot d L=\frac{224.062}{108} \mathrm{~m}^2 \\& \int_L y \cdot d L=2.075 \mathrm{~m}^2[/tex]

Now according to the formula for the center of gravity of a curve, the expression for the center of gravity of the homogenous rod is given by,

[tex]& \bar{y}=\frac{\int_L \bar{y}_1 \cdot d L}{\int_L d L} \\& \bar{y}=\frac{2.075 \mathrm{~m}^2}{2.42 \mathrm{~m}} \\& \bar{y}=0.857 \mathrm{~m}[/tex]

Therefore, the center of gravity of the given homogeneous rod is

0.857 m above the horizontal axis

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Answer:

A) [tex]g(x) = (x - 2 )^{2}[/tex]

Explanation:

Since the equation g(x) is similar to f(x), but translated horizontally, then we can conclude that there is a change in the x value.

Since, the equation g(x) is slide to the right by 2 factor, then there will be a change in x value by -2 factor.

For equation B, the graph will move to the left of f(x) by two factor.

For equation C, the graph will move up of f(x) by two factor.

For equation D, the graph will move down of f(x) by two factor.

The estimated regression equation for these data is Ŷ = 23.194 + 0.318x for every i=1,...,6.

What is meant by regression equation?

In math, the linear regression analysis output delivers some important information, which helps the researcher to predict the estimation, accuracy, and efficiency of the model.

Here we have the data on price and the overall score for stereo headphones that were tested by consumer reports were as follows.

And we need to find the estimated regression equation for these data.

Here let us consider x be the price in dollars of the stereo headphones of brand ii (the independent variable). and let y be the overall score of the stereo headphones of brand ii (the dependent variable).

Here first, we will compute the value of SSE.

The formula is given by

= > SSE = 1∑n​ (yi ​− y​)²

Therefore, we will show the table of values of xi​, Ŷ​, Ŷ​​, (yi​−Ŷ​​) and (yi​−Ŷ​)².

Now, we have to calculate the value of yi​^​, plug in the value of xi​ in the equation 

=> Ŷ = 23.194 + 0.318x for every i=1,...,6.

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Answer: 23.49

Step-by-step explanation:

Look at the thousandths place and the hundredths place.

92

Now we round 92.

1-4 it stays the same

5 or more you raise it

92 is about 90.

So you would get 23.490

You can eliminate the excess zero.

Your answer is 23.49

The exact value of x (in ft) so that the greatest possible amount of light is admitted is 8.96 ft

According to the question,

A norman window has the shape of a rectangle surmounted by a semicircle.

Let The width of rectangle be x and height be y

It is given that  the diameter of the semicircle is equal to the width of the rectangle

Therefore , Diameter of circle = x

Radius = x/2

Perimeter of window  = 32 = Perimeter of rectangle + Perimeter of semi-circle

=> 32 = Width + 2height + πr

=> x + 2y + πx/2 = 32

=> 2x + 4y +  πx = 64

Solving for y,

=> 4y = 64 - 2x - πx

=> y = 64  - 2x - πx/ 4 ----------(1)

Area of the window = Area of rectangle + area of semi-circle

=> A = Width × hiegth +  πx²/8

=> A = xy + πx²/8

Substituting the value of y from equation (1)

=> A =  x (  64  - 2x - πx/ 4  ) + πx²/8

[tex]A = x ( \frac{64 - 2x -\pi x}{ 4} ) + \frac{\pi x^2}{8}\\A = ( \frac{ 64x - x^2 ( 2 + \pi)}{4 } ) + \frac{\pi x^2}{8}[/tex]

Differentiating A w.r.t x

=> [tex]\frac{dA}{dx} = (\frac{64 - 2x(2 + \pi)}{4} ) + \frac{\pi x}{4}[/tex]

Now , To find a maximum area

dA/dx = 0

=> [tex]\frac{dA}{dx} = (\frac{64 - 2x(2 + \pi)}{4} ) + \frac{\pi x}{4} = 0[/tex]

Solving for x ,

64 - 4x - 2π + πx = 0

=> x = 64 / 4 + π ------(2)

Differentiating A again w.r.t x

=> d²A / dx² = -2(2 + π)/4 + π/4

=> -π+4 / 4 which is less than zero

Therefore,

Area is maximum when x = 64 / 4 + π

The exact value of x (in ft) so that the greatest possible amount of light is admitted is  8.96 ft

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The rate of change (slope) of the distance in feet below sea level with respect to time that the submarine traveled is 11 feet .

Given :

The table below shows the linear relationship between the distance in feet below sea level and the time in seconds traveled by a submarine .

From the table:

Take any two points ( 0 , 380 ) and ( 15 , 545 )

slope m = 545 - 380 / 15 - 0

= 165 / 15

= 33 / 3

= 11 / 1

= 11 feet

Hence the slope m is 11 feet .

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The solution to the system of equations is x = 3 and y = -7. The correct option is C. (3, -7).

The system of equations is given as follows:

2x + 3y = −15  ....(1)

3x + y = 2       ....(2)

Multiply Equation 2 by 3:

9x + 3y = 6      ....(3)

Now, we can subtract Equation 1 from Equation 3 to eliminate y:

(9x + 3y) - (2x + 3y) = 6 - (-15)

9x + 3y - 2x - 3y = 6 + 15

7x = 21

x = 21/7

x = 3

Substituting the value of x into Equation 2 to solve for y:

3(3) + y = 2

9 + y = 2

y = 2 - 9

y = -7

Therefore, the solution to the system of equations is x = 3 and y = -7.

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Complete question:

Solve the system of equations using elimination.

2x + 3y = −15

3x + y = 2

A. (0, 5)

B. (1, −1)

C. (3, −7)

D. (4, −10)

As there is sufficient evidence to conclude that the population mean weight is at least 16 ounces.

What is standard deviation ?

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Think about the following data: 2, 1, 3, 2, 4. The average and the total square of the observations' departures from the mean will be 2.4 and 5.2, respectively. This means that (5.2/5) = 1.01 will be the standard deviation.

The following null and alternative hypotheses need to be tested

H0 :  µ  = 16

Hα :  µ  < 16

This corresponds to a left-tailed test , for which a z-test for one mean, with known population standard deviation will be used.

Based on the information provided, the significance level is α = 0.1, and the critical value for the left-tailed test is [tex]Z_{c}[/tex] = -1.28

The rejection region for this left-tailed test is R = {z : z < -1.282}

The z-statistics is computed as follow

[tex]z = \frac{X - µ _{0} }{sigma / \sqrt{n} }[/tex]

   = (15.84 - 16) / (0.4 / √16)

   = -1.6

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The true statement regarding the probability density function f(x) and the cumulative density function f(x) of a continuous random variable is 0 < F(x) < 1. and F(x) = 1 for at least one value of x,  F(x) = 1 for all values of x > a, where a is a constant.

What is meant by probability density function?

In math, probability density function refers most commonly associated with absolutely continuous univariate distributions.

Here we need to find the true statement regarding the probability density function f(x) and the cumulative density function f(x) of a continuous random variable.

In order to find the correct statement, we must know the definition of the cumulative density function also.

The cumulative density function means the probability function that X will take a value less than or equal to x.

Based on the both definition option (A), (B) and (C) are true.

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Answer:

1. 50 x 2 = 100

2. 60 x 3 = 180

3. 75 x 8 + 3 = 603

603 + 180 + 100 = 883

Step-by-step explanation:

Just multiply and add.

The polynomial f(x) of degree 3 is

f(x) = x³ + x² - 20x

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

The zeroes of the polynomial are 0, -5, and 4.

This can be written as,

x = 0, x

x = -5, (x + 5)

x = 4, (x - 4)

x(x + 5)(x - 4)

(x² + 5x)(x - 4)

x³ - 4x² + 5x² - 20x

x³ + x² - 20x

Thus,

The polynomial is f(x) = x³ + x² - 20x

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Answer:

14x+41

Step-by-step explanation:

Answer:

14x + 41

Step-by-step explanation:

4(2X - 1) + 3(2X + 15)  distribute the 4 and 3.

8x - 4 + 6x + 45  Combine like terms

14x + 41  This is your answer simplified.

Answer:

hey

4y = 2x – 8

Step-by-step explanation:

2x – 4y = 8

–4y = –2x + 8

multiply both sides by (–)

–(–4y) = –(–2x + 8)

4y = 2x – 8

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Answer:

TVM calculator: N = 40, PV = -1,075.25, PMT = 30.25, FV = 1,000; CPT I = 2.714% YTM = 2.714% × 2 = 5.43%

Step-by-step explanation:

When the data set is extremely small, the algorithm might fail to detect the inherent clusters in the data set. When the data set has a high degree of overlap between clusters, the algorithm might generate too many clusters and fail to capture the underlying structure of the data.

Partitional clustering algorithms can automatically determine the number of clusters, which is often perceived as an advantage. However, this is not always the case. For example, when the data set is small the algorithm might be unable to detect the true clusters in the data set. Additionally, when the data set has high levels of overlap between clusters, the algorithm might generate too many clusters and fail to recognize the underlying structure of the data. In these cases, the automatic determination of the number of clusters can be disadvantageous as it fails to capture the true structure of the data.

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The difference between the circumference of the circle and the perimeter of the triangle is 28.2 units. (Option B)

To find the length of each side of triangle, the distance is calculated between the vertices using the formula:

d = √((x2 – x1)^2 + (y2 – y1)^2)

Hence,

AB =√((-4 – 0)^2 + (9 – 0)^2) = 9.85 units

AC = √((9 – 0)^2 + (4 – 0)^2) = 9.85 units

BC = √((9 – (-4))^2 + (4 –9)^2) = 13.93 units

Hence, the perimeter of the triangle = 9.85 + 9.85 + 13.93 = 33.6 units

As AB and AC is the radius of the circle, the circumference of the circle is:

C = 2πr = 2π(9.85) = 61.8 units.

Hence, the difference between the circumference of the circle and the perimeter of the triangle = 61.8 – 33.6 = 28.2 units.

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The length of the diagonal from point A to point G is √89.

Blank 1: Using the Pythagorean Theorem

Blank 2: Finding the AC.

Blank 3: Now use CG as a adjacent side.

Blank 4: Now AG is being Hypotenuse.

Blank 5: Now find AG.

In the given question, we have to find the length of the diagonal from point A to point G.

We would first use on the bottom of the box rectangle to find the diagonal AC.

Then we use CG as of the triangle ACG.

Blank 1: Using the Pythagorean Theorem

In this theorem; a^2+b^2=c^2

Where a=adjacent side, b=base, c=hypotenuse

Blank 2: Finding the AC.

Now in the triangle ABC, use Pythagorean Theorem

So AC = √(AB)^2+(BC)^2

AC = √(8)^2+(3)^2

AC = √64+9

AC = √73

Blank 3: Now use CG as a adjacent side.

Blank 4: Now AG is being Hypotenuse.

Blank 5: Now find AG.

Now in the triangle ACG, use Pythagorean Theorem

So AG = √(AC)^2+(CG)^2

AG = √(√73)^2+(4)^2

AG = √73+16

AG = √89

Hence, the length of the diagonal from point A to point G is √89.

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The appropriate distribution to use is t distribution with df = 80.

Variance

Distribution

Given that:

n1 = 37

n2 = 45

The variances of the populations are not know so we can use t distribution

Degree of freedom = n1 + n2 - 2

                                = 37 + 45 - 2

                                = 80

Therefore, t distribution with df = 80

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[tex]-4-4[/tex]

[tex]-4+(-4)[/tex]

[tex]=\fbox{-8}[/tex]

[tex]-4+(-4)[/tex] on a number line:

Answer:

  a. $461.67

  b. $12771.73

Step-by-step explanation:

You want to know the monthly payment and total amount paid for a car that costs $12500 when $4000 is the down payment and the interest is 3.8% for 19 months.

The formula for the monthly payment is ...

  A = P(r/12)/(1 -(1 +r/12)^-n)

where P is the amount borrowed at interest rate r compounded monthly for n months.

Here, the down payment of $4000 reduces the loan amount to ...

  $12500 -4000 = 8500

So, the monthly payment is ...

  A = 8500(0.038/12)/(1 -(1 +0.038/12)^-19) ≈ 461.67

Matteo needs to pay $461.67 each month.

The total Matteo pays for the car will be the sum of the down payment and the 19 monthly payments:

  total = $4000 +19×461.67 = $12771.73

Matteo will end up paying $12771.73 for his car.

Comparison analysis is defined as describing the data in the sample with the use of percentages or averages. Hence, option A is the most suitable answer to this question.

Comparative analysis talks about the comparison of two or more data sets, or other objects. Comparing data becomes very easy when the data is consolidated with the help of average or mean, percentages, and rounding up of the decimals.

Comparison is a very important method to check the difference in the parameters of the two data sets. Not just comparing, summarization of this data is vital for understanding what that data actually means. Hence, we can say that comparison analysis is defined as describing the data in the sample with the use of percentages or averages.

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The complete question is -

Fill in the blanks -

________ analysis is defined as describing the data in the sample with the use of percentages or averages.

A) Comparison

B) Generalization

C) Relationship

D) Summarization

E) Confidence

1)The regression equation is Age--26.7+809 LN [(1+(R/1))/(1-(R/L))]. Hence, the value of the regression coefficients by is-26.7 and by is 809

2)The forecasted value for 0.0901 LN [(1+(RL)) (1- (RL))) is 46.103.

3)The 95% prediction interval for the age at death of Sherlock Holmes' surprise garden visitor is 41.013,51.193.

4)Yes, a man in Sherlock Holmes's neighborhood thought that the body because; the man's age comes under the age in years that is, the smaller age is 14 and the larger age is 69. Thus, this is the body of that man.

Exponential law=The first law states that to multiply two exponential functions with the same base, we simply add the exponents. The second law states that to divide two exponential functions with the same base, we subtract the exponents.

MINITAB procedure:

Choose Stat > Regression Regression

Step 2: In Responses, enter the column of Age (yrs)

Step 3: In Predictors, enter the column of LN [(1+(R/L))/ (1-(R/1))] Step 4: In Options, enter the value of Prediction interval for new observation as 0.0901

The regression equation  Age (year 26,7 809 28(13+1/233/4-1-26.7252.025 -13.20 0.00025.61 31.37 0.000)

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Answer:

y > 5x + 14

Step-by-step explanation:

5x – y > –14

–y > –5x–14

divide both sides by (–)

–(–y) > –(–5x–14)

y > 5x + 14

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The meaning of the y-coordinate of the graph when x = 15 is given as follows:

B. Erin has completed 25% of her exercise program.

The graph is a relation that represents a function between two variables.

The variables for this problem are given as follows:

One ordered pair for the graph in this problem is given as follows:

(15, 25).

This means that when Erin spends 15 minutes exercising, she has completed a percentage of 25% of her exercise program, and thus option B is correct.

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A farmer needs to construct two adjoining rectangular pens with each pen is to have an area of 1200 square feet. So dimeosions will minimize the length of fencing is length = 40 ft and width = 30 ft.

For pictures of two rectangular pens, see the attachment.

Area of rectangle = length × width

A = x × y

1200 = xy

     y = 1200/x

The entire length of the fence

P = 3x + 4y

P = 3x + 4 (1200/x)

P = 3x + 4800/x

P = 3x + 4800x⁻¹

Find dimentions will minimize the length of fencing, if P' = 0.

P = 3x + 4800x⁻¹

P' = 3 - 1 × 4800x⁻¹⁻¹

0 = 3 - 4800x⁻²

4800x⁻² = 3

4800/x² = 3

4800 = 3x²

     x² = 4800/3

     x² = 1600

     x = 40

y = 1200/x

y = 1200/40

y = 30

So dimeosions will minimize the length of fencing is length = 40 ft and width = 30 ft.

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