3. Find the radius of the object to the right.

Answer: 6.07 I believe

Step-by-step explanation:

Answer:

-6.07

Step-by-step explanation:

What is the absolute magnitude of a star that has a period of 50 days?

Answer:

[tex]\dfrac{1}{3}[/tex]

Step-by-step explanation:

[tex]\text{P(Captain William Hits}|\text{Pirate Miss)=} \dfrac{1}{3}[/tex]

[tex]\text{P(Captain William Hits}|\text{Pirate Hits)=} 0[/tex]

[tex]\text{P(Pirate Emily Hits}|\text{Captain Misses)=} \dfrac{1}{7}[/tex]

[tex]\text{P(Pirate Emily Hits}|\text{Captain Hits)=} 0[/tex]

Therefore:

Now, if the Captain hits, the Pirate will always miss.

P(Captain Hits and the Pirate Miss)[tex]=\dfrac{1}{3}X1 =\dfrac{1}{3}[/tex]

Answer:

The index of refraction for Medium 2 would be 1.25

Step-by-step explanation:

We have the following data:

Speed of light in Medium 1 = V₁

Speed of light in Medium 2 = V₂

The speed of Light in Medium 2 is related to speed of light in Medium 1 as:

V₂ = 0.8 V₁

Moreover, it is given that Medium 1 is air with index of refraction equal to 1. i.e.

n₁ = 1

We need to find the index of refraction for medium 2. Lets name it is as n₂.

Snell's law related the above mentioned 4 quantities by following relation:

The ratio of indices of refraction of 2 mediums is equivalent to the reciprocal of ratio of  phase velocities in those 2 mediums. Mathematically, this can be written as:

[tex]\frac{n_{1}}{n_{2}} = \frac{V_{2}}{V_{1}}[/tex]

Substituting the values we have gives us:

[tex]\frac{1}{n_{2}}=\frac{0.8V_{1}}{V_{1}} \\\\\frac{1}{n_{2}}=0.8\\\\ 1=0.8n_{2}\\\\\frac{1}{0.8}=n_{2}\\\\ n_{2}=1.25[/tex]

This means, the index of refraction for Medium 2 would be 1.25

To find the index of refraction for medium 2 (n2), one must use the relationship n = c/v. Since V2 = 0.8 V1 where V1 approximates c, the index of refraction n2 is calculated as n2 = 1/0.8, resulting in an index of 1.25.

The question asks about determining the index of refraction for a medium when a light beam travels from air into this medium. According to the given information, the speed of light in medium 2 (V2) is 0.8 times the speed of light in medium 1 (V1), with air being medium 1 where the speed of light is approximately the speed of light in a vacuum and the index of refraction (n1) is 1.

The law of refraction, or Snell's Law, relates the index of refraction of a medium to the speed of light in that medium through the formula
n = c/v, where
c is the speed of light in vacuum and
v is the speed of light in the medium. To find the index of refraction for medium 2 (n2), you would use the relation that n = c/v. Since the speed of light in medium 2 is given as 0.8 V1, and V1 is the speed of light in air (which is approximately equal to c since n1 = 1), you can deduce that
n2 = c/(0.8c). This simplifies to n2 = 1/0.8, which means that the index of refraction for medium 2 is 1.25.

Answer:

The pole is 15 feet tall

Step-by-step explanation:

Pythagora's Theorem

Let's call x the distance from the base of the pole to the spot where the guy wire is anchored. The height of the pole is 7 feet more, i.e. x+7.

The guy wire is 17 feet long. These dimensions form the sides of a right triangle where the guy wire is the hypotenuse.

Applying Pythagora's Theorem

[tex]x^2+(x+7)^2=17^2[/tex]

Operating

[tex]x^2+x^2+14x+49=289[/tex]

Rearranging and simplifying by 2

[tex]x^2+7x-120=0[/tex]

Factoring

[tex](x-8)(x+15)=0[/tex]

Solving

[tex]x=8,\ x=-15[/tex]

Only the positive solution is valid, thus x=8

The height of the pole is x+7=15 feet

The pole is 15 feet tall

Final answer:

Using the Pythagorean theorem, we find that the height of the pole is approximately 15 feet when solving the derived quadratic equation.

Explanation:

The question involves applying the Pythagorean theorem to solve for the height of the pole. Let's denote the distance from the base of the pole to the spot where the guy wire is anchored as x. Then, the height of the pole is x + 7 feet. Since the guy wire creates a right triangle with the pole and the ground, the Pythagorean theorem states that the square of the hypotenuse (guy wire) is equal to the sum of the squares of the other two sides (height of the pole and the distance from the base). Therefore, we can write the equation 17^2 = (x + 7)^2 + x^2. By solving this equation, we will find the value of x and then determine the height of the pole.

Step by step, we solve the equation: 289 = (x + 7)^2 + x^2, which simplifies to 289 = 2x^2 + 14x + 49. Subtracting 289 from both sides results in 0 = 2x^2 + 14x - 240. By factoring or using the quadratic formula, we find that x is approximately 8 feet. Therefore, the height of the pole is x + 7 feet, which is 15 feet tall.

Final answer:

To calculate the number of days needed to travel at least 4,325 miles at a rate of about 75 miles per day, divide 4,325 by 75, which gives approximately 57.67. Therefore, participants must ride for at least 58 days to cover the distance.

Explanation:

To find out the number of days participants must ride to travel at least 4,325 miles on a bicycle, assuming they cover about 75 miles per day, we need to divide the total distance by the daily distance covered.

Total distance to travel: 4,325 miles
Average distance per day: 75 miles

Number of days (d) = Total distance / Average distance per day

d = 4,325 miles / 75 miles per day
d ≈ 57.67 days

Since participants cannot travel for a fraction of a day, they must ride for at least 58 days to cover 4,325 miles, assuming they ride about 75 miles each day.

Answer:

Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 11.3%  

Alternate Hypothesis, [tex]H_A[/tex] : p > 11.3%

Step-by-step explanation:

We are given that U.S. Bureau of Labor Statistics reports that 11.3% of U.S. workers belong to unions.

Suppose a sample of 400 U.S. workers is collected in 2014 to determine whether union efforts to organize have increased union membership.

Let p = % of U.S. workers belonging to union membership

So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 11.3%  

Alternate Hypothesis, [tex]H_A[/tex] : p > 11.3%

Here, null hypothesis states that the union membership has decreased or remained same in 2014.

On the other hand, alternate hypothesis states that the union membership has increased in 2014.

Also, The test statistics that will be used here is One-sample z proportion statistics;

                               T.S.  = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

Hence, the above hypothesis is appropriate that can be used to determine whether union membership increased in 2014.

Answer:

y = -xe^x + xe^x ln(x) +C

See attachment for step by step guide please

Answer:

Combining the method of undetermined coefficients with the method of variation of parameters, the solution to the differential equation

y'' - 2y' + y = 4x² - 6 + x^(-1)e^x

is

y = (C1 + C2x)e^x + 4x² + 16x + 18 -xe^x + xe^x lnx

Step-by-step explanation:

Given the differential equation:

y'' - 2y' + y = 4x² - 6 + x^(-1)e^x........(1)

Firstly, we solve the homogeneous part of (1)

y'' - 2y' + y = 0

Let the characteristic equation be

m² - 2m + 1 = 0

(m - 1)(m - 1) = 0

m = 1 twice.

The complementary function

y_c = (C1 + C2x)e^x...........................(2)

Now, consider the differential equation:

y'' - 2y' + y = 4x² - 6 ..........................(3)

Solve (3) using the method of UNDETERMINED COEFFICIENTS.

The nonhomogeneous part is 4x² - 6, so we assume a particular solution of the form

y_p = Ax² + Bx + C

y'_p = 2Ax + B

y''_p = 2A

Using these in (3), we have

y''_p - 2y'_p + y_p

= 2A - 2(2Ax + B) + Ax² + Bx + C = 4x² - 6

Ax² + Bx - 4Ax - 2B + 2A + C = 4x² - 6

Comparing the coefficients of various powers of x, we have that

A = 4

B - 4A = 0 => B = 16

2A - 2B + C = -6

=> C = -6 - 8 + 32 = 18

Therefore,

y_p = 4x² + 16x + 18 .....................(4)

Next, consider the differential equation:

y'' - 2y' + y = x^(-1)e^x ....................(3)

We solve using the method of VARIATION OF PARAMETERS.

With g(x) = x^(-1)e^x

Using the complementary solution, we have

y1 = e^x, and y2 = xe^x

Find the Wronskian of y1 and y2.

Let their Wronskian be W, then

W = |y1............y2|

........|y1'...........y2'|

= |e^x.....................xe^x|

...|e^x...........xe^x + e^x|

= xe^(2x) + e^(2x) - xe^(2x)

W = e^(2x)

y_q = Py1 + Qy2

Where P = integral of y2g(t)/W dx

= integral of xe^x.x^(-1)e^x/e^(2x) dx

= -x

Where Q = integral if y1g(t)/W dx

= integral of e^x.x^(-1)e^x/e^(2x) dx

= lnx

y_q = -xe^x + xe^x lnx

Finally, the general solution is

y = y_c + y_p + y_q

= (C1 + C2x)e^x + 4x² + 16x + 18 -xe^x + xe^x lnx

Answer:

1176.5 square feet

Step-by-step explanation:

Let us recall from the following question,

Because  fuel tank is a cylinder, the first step to take is  get the surface area of this cylinder.

The Surface area of  a cylinder = 2. π. r. 2. +. 2. π.

Then,

The given values (h = 50, r = 7/2 = 3.5) as applied from the formula given,

The area Surface a of fuel tank  = 1176.5 square feet

Answer:

Surface area A = 76.979 + 21.994h

Where h will be the value of the lenght of the fuel tanker.

Step-by-step explanation:

The fuel tank is cylindrical so we solve as a cylinder.

Total surface area of a cylinder = the areas of the circles on the top and the bottom and the area of the body.

Area = (2¶d^2)/4 + ¶dh

= (¶d^2)/2 + ¶dh

= ¶d( d/2 + h)

If it has a diameter of 7 ft, then,

A = 3.142 x 7 ( 7/2 + h)

A = 21.994 ( 3.5 + h)

A = 76.979 + 21.994h

Answer:

The probability it will weigh between 2.95 and 3.1 ounces is 0.8186.

Step-by-step explanation:

We are given that Whitney Gourmet Cat Food has determined the weight of their cat food can is normally distributed with a mean of 3 ounces and a standard deviation of 0.05 ounces.

Let X = weight of their cat food can

So, X ~ Normal([tex]\mu=3,\sigma^{2} =0.05^{2}[/tex])

The z score probability distribution for normal distribution is given by;

                                Z =  [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)

where, [tex]\mu[/tex] = population mean = 3 ounces

            [tex]\sigma[/tex] = standard deviation = 0.05 ounces

Now, the probability it will weigh between 2.95 and 3.1 ounces is given by = P(2.95 ounces < X < 3.1 ounces)

P(2.95 ounces < X < 3.1 ounces) = P(X < 3.1 ounces) - P(X [tex]\leq[/tex] 2.95 ounces)

   P(X < 3.1 ounces) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{3.1-3}{0.05}[/tex] ) = P(Z < 2) = 0.97725

    P(X [tex]\leq[/tex] 2.95 ounces) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{2.95-3}{0.05}[/tex] ) = P(Z [tex]\leq[/tex] -1) = 1 - P(Z < 1)

                                                              = 1 - 0.84134 = 0.15866

The above probabilities is calculated by looking at the value of x = 2 and x = 1 in the z table which has an area of 0.97725 and 0.84134 respectively.

Therefore, P(2.95 ounces < X < 3.1 ounces) = 0.97725 - 0.15866 = 0.8186

Hence, the probability it will weigh between 2.95 and 3.1 ounces is 0.8186.

Answer:

57

Step-by-step explanation:

Answer:

The frequency of the purple and pink alleles in this field population are 84.7% and 15.3% respectively.

Step-by-step explanation:

According to the law of large numbers, in probability concept, as we increase the sample size (n), the sample statistic value approaches the value of the population parameter.

For example, as the sample size increases the sample mean ([tex]\bar x[/tex]) approaches the true population mean (μ).

Similarly, as the sample size is increased the the population proportion can be estimated by the sample proportion.

In this case, a random sample of n = 1000 tulips are selected.

Of these 1000 tulips, the number of purple flowers was 847 and the number of pink flower was 153.

Compute the proportion of purple flower as follows:

[tex]P(purple)=\frac{847}{1000}=0.847[/tex]

The frequency of purple flower is 0.847.

Since, the sample size is quite large, this proportion can be used to estimate the true proportion of purple alleles.

Compute the proportion of pink flower as follows:

[tex]P(pink)=\frac{153}{1000}=0.153[/tex]

The frequency of pink flower is 0.153.

Again since, the sample size is quite large, this proportion can be used to estimate the true proportion of pink alleles.

Thus, the frequency of the purple and pink alleles in this field population are 84.7% and 15.3% respectively.

Answer:

1

Step-by-step explanation:

We are given that an expression

[tex]{(-14)^0)^{-2}[/tex]

We have to find the value of given expression.

We know that

[tex]a^0=1[/tex]

Using the property

[tex](-14)^0=1[/tex]

We know that

[tex]a^{-b}=\frac{1}{a^b}[/tex]

Using the property

[tex](1)^{-2}=\frac{1}{1^2}[/tex]

[tex](1)^{-2}=1[/tex]

[tex]((-14)^0)^{-2}=1[/tex]

Answer :

Step-by-step explanation:

Given that a multiple-choice test contains 10 questions and there are 4 possible answers for each question.

∴ Answers=4 options for each question.

Solving this by product rule

Product rule :

If one event can occur in m ways and a second event occur in n ways, the number of ways of two events can occur in sequence is then m.n

From the given the event of choosing the answer of each question having 4 options is given by

The 1st event of picking the answer of the 1st question=4 ,

2nd event of picking the answer of the 2nd question=4 ,

3rd event of picking the answer of the 3rd question=4

,....,

10th event of picking the answer of the 10th question=4.

It can be written as  by using the product rule

[tex]=4.4.4.4.4.4.4.4.4.4[/tex]

[tex]=4^{10}[/tex]

[tex]=1048576[/tex]

Answer:

t = 2.9517 min

Step-by-step explanation:

Given

D = 40 m ⇒ R = D/2 = 40 m/2 = 20 m

ybottom = 2 m

ytop =  ybottom + D = 40 m + 2 m = 42 m

yref = 34 m

t = 10 min

The height above the ground (y) is a sinusoidal function.

The minimum height is ybottom = 2 m

The maximum height is ytop = 42 m;

The midline is (ybottom + ytop)/2 = (2 m + 42 m)/2 = 22 m

If we model the wheel as follows

x² + y² = R²

where

y = yref - (R + ybottom) = 34 m - (20 m + 2 m) = 12 m

R = 20 m

we have

x² + (12 m)² = (20)²

⇒ x = 16 m

then

tan (θ/2) = x/y

⇒ tan (θ/2) = 16 m/12 m

⇒ θ = 106.26°

Knowing the angle of the circular sector, we apply the relation

t = (106.26°)*(10 min/360°)

⇒ t = 2.9517 min

Since the period of revolution is 10 minutes, the ride is above 34 meters for 2.9517 minutes each revolution.

To determine how many minutes of the ride are spent higher than 34 meters, trigonometry can be used to find the proportion of the ride above this height. This results in a total time of 3.136 minutes spent higher than 34 meters.

This problem involves trigonometric calculations to solve real-world scenarios. A Ferris wheel is a circle, and when you boarded at the six o'clock position you are 2 meters above the ground. The diameter of this Ferris wheel is 40 meters, so the radius is 20 meters. The highest point you can get to on the Ferris wheel is the diameter plus the height of the platform, or 42 meters. We want to know how much time is spent higher than 34 meters.

When you are 34 meters in the air, you are 16 meters above the centre of the wheel (because the center is 20 + 2 = 22 meters off the ground). The angle θ that satisfies this condition is the arcsin of 16/20, which is 56.44 degrees (or 0.986 radians). Since the Ferris wheel turns around completely, we should consider the same angle on the other side of the wheel, meaning you spend 2*56.44 = 112.88 degrees or (112.88/360) = 31.36% of the time above 34 meters. Since one full revolution takes 10 minutes, this corresponds to 31.36% * 10 = 3.136 minutes above 34 meters.

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Answer:

93% confidence interval for the mean number of days of sick leave is [10.39 days , 14.01 days].

Step-by-step explanation:

We are given that the firm's statistician randomly selects 100 personnel files and notes the number of sick days taken by each employee. The sample mean is 12.2 days and the sample standard deviation is 10 days.

Assume the population standard deviation is 10.

Firstly, the pivotal quantity for 93% confidence interval for the population mean is given by;

                          P.Q. = [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = sample mean = 12.2 days

            [tex]\sigma[/tex] = population standard deviation = 10 days

            n = sample of files = 100

            [tex]\mu[/tex] = population mean

Here for constructing 93% confidence interval we have used One-sample z  test statistics because we know about population standard deviation.

So, 93% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-1.8121 < N(0,1) < 1.8121) = 0.93  {As the critical value of z at 3.5%

                                           level of significance are -1.8121 & 1.8121}  

P(-1.8121 < [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < 1.8121) = 0.93

P( [tex]-1.8121 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]{\bar X -\mu}[/tex] < [tex]1.8121 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.93

P( [tex]\bar X-1.8121 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.8121 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.93

93% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.8121 \times {\frac{\sigma}{\sqrt{n} } }[/tex] , [tex]\bar X +1.8121 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ]

                                       = [ [tex]12.2-1.8121 \times {\frac{10}{\sqrt{100} } }[/tex] , [tex]12.2+1.8121 \times {\frac{10}{\sqrt{100} } }[/tex] ]

                                       = [10.39 days , 14.01 days]

Therefore, 93% confidence interval for the mean number of days of sick leave is [10.39 days , 14.01 days].

Answer:

B.The matrix is invertible because the determinant is defined.

Step-by-step explanation:

Definition: A matrix is invertible if the determinant is not equal to zero.

Given the matrix:

[tex]A=\left(\begin{array}{ccc}20&5&3\\4&-15&6\\0&25&-9\end{array}\right)[/tex]

The determinant of the matrix:

[tex]|A|=20\left|\begin{array}{ccc}-15&6\\25&-9\end{array}\right|-5\left|\begin{array}{ccc}4&6\\0&-9\end{array}\right|+3\left|\begin{array}{ccc}4&-15\\0&25\end{array}\right|[/tex]

[tex]|A|=20(-15*-9-25*6)-5(-9*4-6*0)+3(4*25-0*-15)\\=20(135-150)-5(-36-0)+3(100+0)\\=20(-15)-5(-36)+3(100)\\=-300+180+300\\|A|=180[/tex]

Since the determinant, [tex]|A|\neq 0[/tex], the matrix is invertible because the determinant is defined.

The matrix in question is invertible because its determinant is not zero. This is an essential rule in linear algebra, where a non-zero determinant implies an invertible matrix.

In linear algebra, a square matrix is invertible if and only if its determinant is not zero. The determinant being different from zero implies that the matrix has full rank and hence is invertible. In your case, the determinant of the matrix is 180180, which is not zero. Thus, the matrix is invertible.

The option: B. The matrix is invertible because the determinant is defined is not entirely correct because a matrix could have a defined determinant that equals zero which would make it non-invertible. The correct answer should be: C. The matrix is invertible because the determinant is not zero.

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Hello!

[tex]\boxed{ \bf Each~side~is~4~in~long.}[/tex]

We know that the formula for volume of a cube is:

V = a³

64 = a³

To find the side length, all we have to do is find the cube root of both sides.

[tex]\sqrt{64} = \sqrt{a^3}[/tex]

  4  =  a

Answer:

32.40

Step-by-step explanation:

The distance between the two ships is changing at approximately 26.87 km/h at 4:00 PM, calculated using the Pythagorean theorem and the differentiation principles of related rates in calculus.

To determine how fast the distance between the two ships is changing at 4:00 PM, we need to apply the concept of related rates in calculus. Since at noon ship A is 130 km west of ship B and moving east, and ship B is moving north, we can imagine their paths as legs of a right triangle, where the hypotenuse represents the distance between the two ships.

Let's denote the distance that ship A has traveled east as x (in kilometers), the distance that ship B has traveled north as y (in kilometers), and the distance between the two ships as z (in kilometers). At 4:00 PM, ship A has been sailing east for 4 hours at 25 km/h, so x = 25 km/h * 4 h = 100 km. Ship B has sailed north for the same amount of time at 20 km/h, so y = 20 km/h * 4 h = 80 km.

To find the rate at which the distance z is changing, we use the Pythagorean theorem z =  x^2 +  y^2.

Differentiating both sides with respect to time t, we get 2zdz/dt = 2xdx/dt + 2ydy/dt. We can cancel the 2's and plug in the values for x, y, dx/dt (25 km/h) and dy/dt (20 km/h) to find dz/dt, which represents the rate at which the distance between the ships is changing.

Solving for dz/dt, we have:

z dz/dt = x dx/dt + y dy/dt
z dz/dt = 100 km * 25 km/h + 80 km * 20 km/h

First, we must find z, which is the distance between the ships at 4:00 PM:

z =
sqrt{130^2 + 80^2} =
sqrt{16900 + 6400} =
sqrt{23300} ≈ 152.65 km

Now, we solve for dz/dt:
152.65 km * dz/dt = 100 km * 25 km/h + 80 km * 20 km/h
dz/dt ≈ (2500 km²/h + 1600 km²/h) / 152.65 km
dz/dt ≈ 4100 km²/h / 152.65 km
dz/dt ≈ 26.87 km/h

Therefore, the distance between the ships is changing at approximately 26.87 km/h at 4:00 PM.

at 4:00 PM, the rate of change of the distance between the ships is[tex]\( \frac{7350}{10\sqrt{593}} \)[/tex] km/h.

To find the rate of change of the distance between the ships at 4:00 PM, we'll first find expressions for the positions of each ship at that time. Then, we'll differentiate the distance formula with respect to time and evaluate it at 4:00 PM.

Let ( t ) be the time in hours since noon.

Ship A's position [tex]\( x_A \)[/tex] at time \( t \) is given by:

[tex]\[ x_A = 130 + 25t \][/tex]

And ship B's position [tex]\( y_B \)[/tex] at time \( t \) is given by:

[tex]\[ y_B = 20t \][/tex]

Using these positions, the distance between the ships ( D ) at time ( t ) is given by the distance formula:

[tex]\[ D(t) = \sqrt{(130 + 25t)^2 + (20t)^2} \][/tex]

Now, let's differentiate [tex]\( D(t) \)[/tex] with respect to time [tex]\( t \)[/tex] using the chain rule:

[tex]\[ \frac{dD}{dt} = \frac{1}{2\sqrt{(130 + 25t)^2 + (20t)^2}} \times \left(2(130 + 25t)(25) + 2(20t)(20)\right) \][/tex]

Now, plug in ( t = 4 ) to find the rate of change of the distance between the ships at 4:00 PM:

[tex]\[ \frac{dD}{dt} \Bigg|_{t=4} = \frac{1}{2\sqrt{(130 + 25(4))^2 + (20(4))^2}} \times \left(2(130 + 25(4))(25) + 2(20(4))(20)\right) \][/tex]

[tex]\[ \frac{dD}{dt} \Bigg|_{t=4} = \frac{1}{2\sqrt{(130 + 100)^2 + (80)^2}} \times \left(2(130 + 100)(25) + 2(80)(20)\right) \][/tex]

[tex]\[ \frac{dD}{dt} \Bigg|_{t=4} = \frac{1}{2\sqrt{230^2 + 80^2}} \times \left(2(230)(25) + 2(80)(20)\right) \][/tex]

[tex]\[ \frac{dD}{dt} \Bigg|_{t=4} = \frac{1}{2\sqrt{52900 + 6400}} \times \left(2(5750) + 2(1600)\right) \][/tex]

[tex]\[ \frac{dD}{dt} \Bigg|_{t=4} = \frac{1}{2\sqrt{59300}} \times (11500 + 3200) \][/tex]

[tex]\[ \frac{dD}{dt} \Bigg|_{t=4} = \frac{1}{2\sqrt{59300}} \times 14700 \][/tex]

[tex]\[ \frac{dD}{dt} \Bigg|_{t=4} = \frac{14700}{2\sqrt{59300}} \][/tex]

[tex]\[ \frac{dD}{dt} \Bigg|_{t=4} = \frac{7350}{\sqrt{59300}} \][/tex]

[tex]\[ \frac{dD}{dt} \Bigg|_{t=4} = \frac{7350}{\sqrt{100 \times 593}} \][/tex]

[tex]\[ \frac{dD}{dt} \Bigg|_{t=4} = \frac{7350}{10\sqrt{593}} \][/tex]

So, at 4:00 PM, the rate of change of the distance between the ships is[tex]\( \frac{7350}{10\sqrt{593}} \)[/tex] km/h. This can be simplified further, but it's best to leave it in this form to retain the exact value.

Answer:

1.) We cannot say for certain which candidate will win. But A has a statistical edge.

2.) We can say certainly that candidate A will win the election; albeit with a not so big margin.

3.) Candidate A will win this election based on the results of the final poll's before the election.

4.) We cannot say for certain which candidate will win. But A has a statistical edge.

The reasons are explained below.

Step-by-step explanation:

Confidence interval expresses a range of values in the distribution where the true proportion or mean can be found with some level of confidence.

Confidence Interval = (Sample Mean or Proportion) ± (Margin of error)

1. Candidate A: 54% & Candidate B:46% with Margin of error: + 5%

The confidence interval for candidate A

(54%) ± (5%) = (49%, 59%)

The confidence interval for candidate B

(46%) ± (5%) = (41%, 51%)

Since values greater than 50% occur in both intervals, we cannot say for certain that either of the two candidates will outrightly win the election. It just slightly favours candidate A who has A bigger range of confidence interval over 50% for the true sample proportion to exist in.

2. Candidate A: 52% & Candidate B:48% with Margin of error: + 1%

The confidence interval for candidate A

(52%) ± (1%) = (51%, 53%)

The confidence interval for candidate B

(48%) ± (1%) = (47%, 49%)

Here, it is outrightly evident that candidate A will win the elections based on the result of the final polls. The overall range of the confidence interval that contains the true sample proportion of voters that support candidate A is totally contained in a region that is above 50%. So, candidate A wins this one, easily; albeit with a close margin though.

3. Candidate A: 53% & Candidate B:47% with Margin of error: + 2%

The confidence interval for candidate A

(53%) ± (2%) = (51%, 55%)

The confidence interval for candidate B

(47%) ± (2%) = (45%, 49%)

Here too, it is outrightly evident that candidate A will win the elections based on the result of the final polls. The overall range of the confidence interval that contains the true sample proportion of voters that support candidate A is totally contained in a region that is above 50%. Hence, statistics predicts that candidate A wins this one.

4. Candidate A: 58% & Candidate B:42% with Margin of error: + 10%

The confidence interval for candidate A

(58%) ± (10%) = (48%, 68%)

The confidence interval for candidate B

(42%) ± (10%) = (32%, 52%)

Since values greater than 50% occur in both intervals, we cannot say for certain that either of the two candidates will outrightly win the election. It just slightly favours candidate A who has A bigger range of confidence interval over 50% for the true sample proportion to exist in.

Hope this Helps!!!

Answer:

[tex]\lambda=8,\ \lambda=-5[/tex]

Step-by-step explanation:

Eigenvalues of a Matrix

Given a matrix A, the eigenvalues of A, called [tex]\lambda[/tex] are scalars who comply with the relation:

[tex]det(A-\lambda I)=0[/tex]

Where I is the identity matrix

[tex]I=\left[\begin{array}{cc}1&0\\0&1\end{array}\right][/tex]

The matrix is given as

[tex]A=\left[\begin{array}{cc}3&5\\8&0\end{array}\right][/tex]

Set up the equation to solve

[tex]det\left(\left[\begin{array}{cc}3&5\\8&0\end{array}\right]-\left[\begin{array}{cc}\lambda&0\\0&\lambda \end{array}\right]\right)=0[/tex]

Expanding the determinant

[tex]det\left(\left[\begin{array}{cc}3-\lambda&5\\8&-\lambda\end{array}\right]\right)=0[/tex]

[tex](3-\lambda)(-\lambda)-40=0[/tex]

Operating Rearranging

[tex]\lambda^2-3\lambda-40=0[/tex]

Factoring

[tex](\lambda-8)(\lambda+5)=0[/tex]

Solving, we have the eigenvalues

[tex]\boxed{\lambda=8,\ \lambda=-5}[/tex]

Answer: 3, 7 and 14

Step-by-step explanation:

We want 3 numbers with a mean of 8, and a MAD of 4.

if we have the numbers a, b and c.

The mean is:

M = (a + b + c)/3

MAD = ( Ia - MI + Ib - MI + Ic - MI)/3

now, we know that M = 8 and MAD = 4, so we can replace those values:

8 = (a + b + c)*/3

3*8 = 24 = a + b + c

and

4 = ( Ia - 8I + Ib - 8I + Ic - 8I)/3

4*3 = 12 = Ia - 8I + Ib - 8I + Ic - 8I

So now we have the two equations:

24 = a + b + c

12 = Ia - 8I + Ib - 8I + Ic - 8I

Let's took the numbers 3, 7 and 14

I selected those because are the numbers where the distance between them is the biggest, and they add up to 24, and you can see that the MAD is a big number, which implies that our 3 numbers are not close between them.

3 + 7 + 14 = 10 + 14 = 24

and for the MAD

I3 -8I + I7 - 8I + I14 - 8I = 5 + 1 + 6 = 12

So the correct options are 3, 7 and 14

Answer:

Medicare!

Step-by-step explanation:

Answer:

The answer is D

Step-by-step explanation:

An equilateral triangle can not be a right triangle. Here is why: In an equilateral triangle, all angles are congruent, since all 3 of the sides are congruent.This is because in a right triangle, one angle equals 90 degrees. Therefore, you can't have 3 angles equal 90 degrees.

Given:

In Ms. Perron’s class, 75% of the students are boys. There are 18 boys in the class.

We need to determine the total number of students in Ms. Perron's class.

Total number of students:

Let n denote the total number of students in Ms. Perron's class.

Thus, we have;

[tex]\frac{75}{100}n=18[/tex]

Multiplying both sides of the equation by [tex]\frac{100}{75}[/tex], we get;

[tex]n=18\times \frac{100}{75}[/tex]

Simplifying, we get;

[tex]n=\frac{1800}{75}[/tex]

[tex]n=24[/tex]

Therefore, the total number of students in Ms. Perron's class are 24.

Answer:

Time t = 2 seconds

It will reach the maximum height after 2 seconds

Completed question;

Amir stands on a balcony and throws a ball to his dog who is at ground level. The ball's height, in meters above the ground, after t seconds that Amir has thrown the ball is given by:

H (t) = -(t-2)^2+9

many seconds after being thrown will the ball reach its maximum height?

Step-by-step explanation:

The equation of the height!

h(t) = -(t-2)^2 + 9 = -(t^2 -4t +4) + 9

h(t) = -t^2 +4t -4+9

h(t) = -t^2 + 4t +5

The maximum height is at dh/dt = 0

dh/dt = -2t +4 = 0

2t = 4

t = 4/2 = 2

Time t = 2 seconds

It will reach the maximum height after 2 seconds

The ball hits the ground at [tex]\( t = 5 \)[/tex] seconds.

Let's analyze the given height function of the ball:

[tex]\[ H(t) = -(t-2)^2 + 9 \][/tex]

This function describes the height of the ball [tex]\( H \)[/tex] in meters at any time [tex]\( t \)[/tex] in seconds.

The function is in the vertex form of a quadratic equation, which is generally written as:

[tex]\[ H(t) = a(t - h)^2 + k \][/tex]

Here, [tex]\( a = -1 \), \( h = 2 \), and \( k = 9 \).[/tex]

Time When the Ball Hits the Ground

- The ball hits the ground when [tex]\( H(t) = 0 \):[/tex]

[tex]\[ 0 = -(t-2)^2 + 9 \] \\\ (t-2)^2 = 9 \][/tex]

 Taking the square root of both sides:

[tex]\[ t-2 = \pm 3 \\\ t = 2 + 3 \quad \text{or} \quad t = 2 - 3 \\\ t = 5 \quad \text{or} \quad t = -1 \][/tex]

 Since negative time doesn't make sense in this context, we discard [tex]\( t = -1 \):[/tex]

[tex]\[ t = 5 \, \text{seconds} \][/tex]

 Therefore, the ball hits the ground at [tex]\( t = 5 \)[/tex] seconds.

The complete question is:

Amir stands on a balcony and throws a ball to his dog, who is at ground level. The ball's height (in meters above the ground), x seconds after Amir threw it, is modeled by: h(x)=-(x-2)^2+16 How many seconds after being thrown will the ball hit the ground?

Answer:

72

Step-by-step explanation:

multiply by 16

Answer:

4 1/2 lb = 72 oz

brainliest?

Answer:

4 action figures per friend

Step-by-step explanation:

To split the 12 action figures between 3 friends, divide 12 by 3.

12/3 = 4

Therefore, each friend gets 4 action figures.

Answer:

each friend gets 12 divided by 3 action figures. Each friend gets 12/3 action figures. Each friend gets 4 of the 12 action figures.

Step-by-step explanation:

i put this and i got it right.

Answer:

a) [tex] f(x) = \frac{1}{40-30}, 30 \leq x \leq 40[/tex]

b) [tex] E(X) = \frac{a+b}{2}= \frac{30+40}{2}=35[/tex]

c) [tex] Var(X) = \frac{(b-a)^2}{12}= \frac{(40-30)^2}{12}= 8.33[/tex]

And the deviation would be:

[tex] Sd(X) = \sqrt{8.33}= 2.887[/tex]

d) [tex]P(34< X <38) = F(38) -F(34)= \frac{38-30}{10} -\frac{34-30}{10}= 0.8-0.4=0.4[/tex]

Step-by-step explanation:

For this case we define the random variable X with this distribution:

[tex] X \sim Unif (a=30, b=40)[/tex]

Part a

The density function since is an uniform distribution is given by:

[tex] f(x) = \frac{1}{40-30}, 30 \leq x \leq 40[/tex]

Part b

The expected value is given by:

[tex] E(X) = \frac{a+b}{2}= \frac{30+40}{2}=35[/tex]

Part c

The variance is given by:

[tex] Var(X) = \frac{(b-a)^2}{12}= \frac{(40-30)^2}{12}= 8.33[/tex]

And the deviation would be:

[tex] Sd(X) = \sqrt{8.33}= 2.887[/tex]

Part d

For this case we want this probability:

[tex] P(34< X <38)[/tex]

And we can use the cumulative distribution function given by:

[tex] F(x)= \frac{x-30}{40-30}, 30 \leq X \leq 40[/tex]

And using this we got:

[tex]P(34< X <38) = F(38) -F(34)= \frac{38-30}{10} -\frac{34-30}{10}= 0.8-0.4=0.4[/tex]

Final answer:

The probability density function, expected price, standard deviation, and the probability of the stock price being between $34 and $38 are calculated.

Explanation:

To find the probability density function, f(x), for the price of the stock, we need to determine the range of the variable x, and then divide the range by the total probability. In this case, the range of x is from $30 to $40, and the total probability is equal to 1. So, the probability density function is:

f(x) = 1 / (40 - 30) = 1/10 = 0.1

To determine the expected price of the stock, we can calculate the average of the range of x:

Expected price = (30 + 40) / 2 = $35

To determine the standard deviation for the stock, we can use the formula:

Standard deviation = (40 - 30) / sqrt(12) = 10 / sqrt(12) ≈ 2.8879

To find the probability that the stock price will be between $34 and $38, we need to find the area under the probability density function curve between these two prices. Since the probability density function is a uniform distribution, the probability is equal to the width of the range divided by the total width of the distribution:

Probability = (38 - 34) / (40 - 30) = 4 / 10 = 0.4

Answer:

Systems of linear equations are used in the real world by economists and entrepreneurs to find out when supply equals demand.It's all about the mullah, and if you don't know the numbers when you have a business, it might fail.

Step-by-step explanation: