nearly a quarter of the texas gulf coast is national seashore or state park. At 372 miles long, it is undergoing a seaward advance at the rate of about .0095 mile per year. find the length of the texas shoreline in km. 1 mile = 1.61 km

The equation of sphere is (x -1 )^{2}  + (y - 2 )^{2}  + (z+3 )^{2}  = 14.

According to the statement

we have to find the equation of the sphere which passes through the a(1,2,-3), with center b (2,4,0).

So, For this purpose, we know that the

Sphere is In analytical geometry, if “r” is the radius, (x, y, z) is the locus of all points and \((x_{0} , y_{0} , z_{0})\)

is the center of a sphere, then the equation of a sphere is given by: \((x -x_{0} )^{2} + (y - y_{0} )^{2} + (z-z_{0} )^{2} = r^{2}\).

So, Here from given equation

The sphere that passes through a(1,2,-3), with center b (2,4,0).

here the locus point is a(1,2,-3).

The radius of sphere is

\(Radius = \sqrt{(1-2)^{2} + (2-4)^{2} + (-3-0)^{2} } \\Radius = \sqrt{(1 + 4 +9 }\)

So, radius is square root 14.

And then the equation of sphere become

\((x -1 )^{2} + (y - 2 )^{2} + (z+3 )^{2} = 14\).

So, The equation of sphere is (x -1 )^{2}  + (y - 2 )^{2}  + (z+3 )^{2}  = 14.

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Answer:

1/4

Step-by-step explanation:

The amount of interest earned on a deposit of $60.00 at a rate of 9% per annum for 2 years is $108.

As per the given problem:

Amount deposited = $60.00

Interest rate per year = 9%

The formula for calculating the interest is given by:

Interest = (Principal × Rate × Time)/100

Where Principal is the initial amount invested or deposited

Rate is the percentage of interest that you earn per annum

Time is the duration for which you want to calculate the interest

Putting the values in the above formula, we get:

Interest = (60 × 9 × 2)/100= (108 × 1)/1= $108

So, the amount of interest earned on a deposit of $60.00 at a rate of 9% per annum for 2 years is $108.

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The correct answer is d. 0.37.

To find the probability that the person's highest level of education is an undergraduate degree, we need to consider both the cases where they take and do not take supplements. We can calculate this by adding the probabilities for these two scenarios:

Probability = P(Undergraduate Degree & Takes Supplements) + P(Undergraduate Degree & Does Not Take Supplements)

Probability = 0.09 + 0.28

Probability = 0.37

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The producer's surplus if the supply function for pork bellies is s(q)=q^(5/2)+ 3q^(3/2)+50 by assuming supply and demand are in equilibrium at q = 9 is approximately $18.20.

To find the producer's surplus, we need to first determine the market price at the equilibrium quantity of 9 units.

At equilibrium, the quantity demanded is equal to the quantity supplied:

d(q) = s(q)

q^(3/2) = 9^(5/2) / (3*50)

q^(3/2) = 81/2

q = (81/2)^(2/3)

q ≈ 7.55

The equilibrium quantity is approximately 7.55 units. To find the equilibrium price, we can substitute this value into either the demand or supply function:

p = d(7.55) = s(7.55)

p = (9^(5/2)) / (3*(7.55^(3/2)) * 50)

p ≈ $1.71 per unit

Now we can find the producer's surplus. The area of the triangle formed by the supply curve and the equilibrium price is equal to the producer's surplus:

Producer's surplus = (1/2) * (9^5/2) * (1/50) * (1.71 - 0)

Producer's surplus ≈ $18.20

Therefore, the producer's surplus is approximately $18.20.

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The fourth ordered pair using the two

sequences is ( 7/3 ,106) .

The first sequence is constructed by first multiplying the terms by 2 and then adding one-third starting from zero. So, sequence starts from 0.

First term of first sequence, a₁ = 0

a₂ = (2x0) + 1/3 = 1/3

a₃ = (2x1/3) + 1/3 = 2/3 + 1/3 = 1

a₄ = (2x1) + 1/3 = 2 + 1/3 = 7/3

Hence, the sequence is 0, 1/3, 1, 7/3, ...

The second sequence is constructed by first adding one half in terms and then multiplying by 4. The sequence starts from 1 ,

a₁ = 1

a₂ = (1 +1/2) × 4 = (3/2)4 = 6

a₃ = (6+1/2) x 4 = 13/2 x 4 = 26

a₄ = (26 + 1/2)× 4 = 53/2 x 4 = 106

Hence, the sequence is 1, 6, 26, se106, ...

Therefore, the fourth terms of the two sequences are the following, 7/3 and 106.

So, required ordered pairs is ( 7/3, 106).

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The femurs of the lower performer would stretch by approximately 0.176 meters (17.6 centimeters) due to the upward force from the upper performer.

The deformation of the femurs of the lower performer can be calculated using Hooke's law, which states that the deformation of a material is proportional to the force applied to it. Assuming that the femurs behave like linear springs, we can use the equation:

ΔL = F/k

where ΔL is the change in length of the femurs, F is the upward force on the lower performer's legs (3mg), and k is the spring constant of the femurs.

The spring constant of bone is difficult to determine, as it varies with bone density and structure. However, studies have found that the spring constant of femoral cortical bone (the outer layer of bone) ranges from 10,000 to 20,000 N/m.

Assuming a conservative estimate of k = 10,000 N/m, we can calculate the deformation of the femurs as follows:

ΔL = (3mg) / (10,000 N/m)

= (3 x 60 kg x 9.81 m/s^2) / (10,000 N/m)

= 0.176 m

Therefore, the femurs of the lower performer would stretch by approximately 0.176 meters (17.6 centimeters) due to the upward force from the upper performer.

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Answer:

The numerical limits for a B-grade is between 81 and 92

Step-by-step explanation:

Here in this question, our task is to find the numerical limits for B grade. This means the range between a test taker would be scored a B grade

Please check attachment for complete solution and explanation

Scaling transformation onto the x co ordinate by a factor of 5.

A co-ordinate system represents two points one for x axis and another for y axis in a ordered pair (x,y)

According the given question Point (w, z) is transformed by the rule (w5, z).

Here w represents x co-ordinate points and z represents y co-ordinate points.

We can observe that the x co-ordinate point have been scaled by a factor of 5.We can think of that after this transformation the line has become less steeper from origin.

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Answer:

In 15 years the final balance will be $632.15

Step-by-step explanation:

The final balance would be $632.15 and the total compound interest would be $332.15. If you have trouble with these kind of questions in the future I suggest using a compound interest calculator that can be found online :)

Answer:

150%

Step-by-step explanation:

4 * 1.5 = 6.

At the end of the fifth day, a bricklayer has laid 324 bricks on the job.

Multiplication is a mathematical arithmetic operation.

It is also a process of adding the same types of expression to some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given, a bricklayer lays 4 bricks on the first day on the job.

On each day thereafter, he lays three times the number of bricks he laid on the previous day.

And he continued his pattern.

Let x be the number of bricks he laid in the previous day.

Then according to the question,

The number of bricks in total is = 3x

For the second day, x =4

Number of the bricks he laid on the second day = 12

Now the x =12 for the third day.

Number of the bricks he laid on the third day = 36

Now x = 36 for the fourth day.

Number of the bricks he laid on the fourth day = 108

Now the x = 108 for the fifth day.

Number of the bricks he laid on the fifth day = 324

Therefore, 324 bricks he has laid at the end of the fifth day.

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The probability that the sample mean exceeds 135.4 millimeters is approximately 0.1446.  

You can use the central limit theorem to approximate the sample distribution of the sample mean.

The mean of the sample distribution is a rise to the population mean (135 mm)

 the standard deviation of the test distribution is a rise to the population standard deviation isolated by the square root of the test measure, which is \(5/√42\) ≈ 0.7689 mm.

To find the probability that the sample mean is greater than 135.4 millimeters, use the sample distribution to standardize the sample mean and use the standard normal distribution. That is,

\(z = (x - μ) / (σ / √n) = (135.4 - 135) / (5 / √42) ≒ 1.0607\)

where x = sample mean, μ = population mean, σ =population standard deviation, n=sample size, and z =standard value.

The probability that the sample mean exceeds 135.4 millimeters can be found by using a standard normal distribution table or calculator,

to find the area to the right of the Z value of 1.0607. This range is approximately 0.1446 or 14.46%.

Therefore, the probability that the sample mean exceeds 135.4 millimeters is approximately 0.1446.

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If the quadrilateral is a trapezoid , then the value of x is = (b) 5 .

We know that the Midsegment of a trapezoid is parallel to each of the base and it's length is one half the sum of the lengths of the bases.

From the figure , we can observe that ⇒ side lengths are  21 units, 27 units , and the sides are parallel to each other.

From the given diagram of the trapezoid , the below expression is true:

that means : ⇒ 5x-1 = (21 + 27)/2  ;

⇒ 2(5x - 1) = 21 + 27 ;

⇒ 10x = 48 + 2 ;

⇒ 10x = 50

On Divide both sides by 10 ;

we have ;

⇒ x = 50/10  ;

⇒ x = 5  .

Therefore , for the quadrilateral the value of x is = 5 .

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The given question is incomplete , the complete question is

The quadrilateral in the below figure is a trapezoid. What is the value of x ?

(a) 4

(b) 5

(c) 48

(d) 25

The inequalities equation which will shade all the points except target point are, y >= 2, y >= -3.5x + 4.5 and y <= 1.25x - 1.5.

The line passing through P(-1,2) and P(-4,2) has a slope of 0 and a y-intercept of 2, so its equation is y = 2. The line passing through P(-1,2) and P(-2,0.5) has a slope of -3.5 and a y-intercept of 4.5, so its equation is y = -3.5x + 4.5. The line passing through P(-2,0.5) and P(-4,2) has a slope of 1.25 and a y-intercept of -1.5, so its equation is y = 1.25x - 1.5.

Now we can create a system of inequalities that will shade all of the points except for T(-2,2). We can do this by making sure that the inequality for each line is greater than or equal to the target point on one side of the line, and less than or equal to the target point on the other side of the line.

For the line y = 2, we can write the inequality y >= 2 on the side of the line that contains the target point T(-2,2). For the line y = -3.5x + 4.5, we can write the inequality y >= -3.5x + 4.5 on the side of the line that contains the point T(-2,2). For the line y = 1.25x - 1.5, we can write the inequality y <= 1.25x - 1.5 on the side of the line that contains the point T(-2,2).

Putting all of these inequalities together, we get:

y >= 2 (for the line passing through P(-1,2) and P(-4,2))

y >= -3.5x + 4.5 (for the line passing through P(-1,2) and P(-2,0.5))

y <= 1.25x - 1.5 (for the line passing through P(-2,0.5) and P(-4,2))

These inequalities should shade all of the points except for the target point T(-2,2), and they should do so with the fewest number of inequalities possible.

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--The complete question is, With the fewest inequalities, shade all the points but leave the targets exposed. Write the inequality equations to do this.

Points are P(-1,2), P(-4,2) and P(-2, 0.5)

T(-2,2)
Graph is show in the image.--

Answer:

=0.00004...x

Step-by-step explanation:

9514 1404 393

Answer:

  (x, y) = (0, -26)

Step-by-step explanation:

The y-intercept is the y-value that corresponds to x=0. Here, we have a table that has x-values that differ by 12 and 24. We want to find the y-value that corresponds to an x-value 24 less than the lowest one on the table:

  24 -24 = 0

We notice that when x-values differ by 24, the y-values differ by 10 -(-8) = 18. So, the y-value we want is 18 less than the lowest one in the table:

  y = -8 -18 = -26

The (x, y) coordinates of the y-intercept are (0, -26).

If a principal is invested at 5% compounded quarterly, it will take 14 years to double in value. If it is compounded continuously, it will take 13.9 years to double in value.

To find the time it takes to double an investment at 5% compounded quarterly, we can use the following formula:

t = (72 / r) / 4

where t is the number of years, r is the interest rate, and 4 is the number of compounding periods per year.

Plugging in the values, we get:

t = (72 / 5) / 4 = 14 years

To find the time it takes to double an investment at 5% compounded continuously, we can use the following formula:

t = ln(2) / r

where t is the number of years, r is the interest rate, and ln(2) is the natural logarithm of 2.

Plugging in the values, we get:

t = ln(2) / 0.05 = 13.9 years

As you can see, the time it takes to double an investment is slightly shorter when it is compounded continuously than when it is compounded quarterly.

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The probability that the mean annual precipitation of a sample of 49 randomly picked years will be less than 92.8 inches is, 0.9192

What is standard deviation?

The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.

Given: The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 90 inches, and a standard deviation of 14 inches.

z score is given by,

z = (x - μ)/(σ/√n) = (92.8 - 90)/(14/√49) = 2.8/2 = 1.4

The  required probability is,

p(z < 1.4) = 0.9192, by standard normal table.

Hence, the  probability that the mean annual precipitation of a sample of 49 randomly picked years will be less than 92.8 inches is,  0.9192.

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Answer:

25 cm

Step-by-step explanation:

a^2 + b^2 = c^2

7^2 + 24^2 = c^2

49 + 576 = c^2

c^2 = 625

c = 25

Answer: 25 cm

Given that the test's p-value is 0.0562>0.05, there is enough data to conclude that the machines' manufacturer should perform a new calibration.

A statistic employed in statistical hypothesis testing is known as a test statistic. A test statistic, which can be thought of as a numerical summary of a data set that condenses the data into a single value that can be used to conduct the hypothesis test, is how a hypothesis test is commonly expressed.

Here,

x=4.88 cm

μ=5 cm

σ=0.44 cm

n=49

The test statistic,

=(4.88-5)/(0.44/7)

z=-1.909

The p-value of the test is the probability that the sample mean is different by at least 4.88 - 5 = 0.12 from the target value, which is P(|z| > -1.909), which is 2 multiplied by the p-value of z = -1.909

At z=-1.909, p-value=0.0281

2*0.0281=0.0562

The test's p-value is 0.0562>0.05, indicating that there is enough data to conclude that the machines' manufacturer should perform a recalibration.

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Answer: 24

Step-by-step explanation:

We can use the pythagorean theorem to solve for the missing side.

Let the missing side be x.

Then, x^2 + 10^2 = 26^2.

x^2 + 100 = 676

Subtract 100 from both sides:

x^2 = 576

Square root both sides:

x = 24

Answer:

24

Step-by-step explanation:

~ Formula ~

a² + b² = c ²

Solve:

Let,

a² = 10

c² = 26

Thus,

a² + b² = c²

10² + b² = 26²                                 { ² means # × # Not # × 2 }

100 + b² = 676                                {Subtract both sides by 100}

b² = 576                                       {Square Root}

576 = 24²

= √24 ²

Apply radical rule - n √aⁿ = a

√24 ² = 24  

Answer = 24

Check Answer:

a² + b² = c²

10² + 24² = 26²

100 + 576= 676 ☑

Kavinsky

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

8 pounds.... 4hours

x pounds.... 3 hours

x=3 ×8 :4

x=24 :4

x=6 pounds of trash

The number of pounds of trash should the volunteers pick up this month is 6.

Since  Last month, the volunteers picked up 8 pounds of trash in 4 hours. This month, the same group of volunteers will spend 3 hours picking up trash.

So here we can do

x=3 ×8 :4

x=24 :4

x=6

Hence, The number of pounds of trash should the volunteers pick up this month is 6.

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Answer:

13.5%

Step-by-step explanation:

Answer:

22 sides total

Step-by-step explanation:

a hexagon has 6 sides, while a pentagon has 5 sides. In order to find out how many there are total, we would multiply each by two, and add them together.

\(2(6)+2(5)=\\12+10=22\)

Answer:

29

61

Step-by-step explanation:

x^2 - 20

x = 7 and 9

Evaluate

___________

We know the values of x, let's substitute them with the x in the problem :

(7)^2 - 20

49 - 20

29

(9)^2 - 20

81 - 20

61

The answer closest to the margin of error is option b: 4.2%.

To determine the margin of error at the 95% confidence level for the proportion of likely voters who prefer the incumbent candidate, we can use the formula:

Margin of Error = (Z * √(p*(1-p))/√n)

Where:

Z is the Z-score corresponding to the desired confidence level (95% corresponds to approximately 1.96)

p is the proportion of voters who prefer the incumbent candidate (42% or 0.42)

n is the sample size (350)

Calculating the margin of error:

Margin of Error = (1.96 * √(0.42*(1-0.42))/√350)

Using a calculator, the closest value to the margin of error is approximately 4.2%. Therefore, the answer closest to the margin of error is option b: 4.2%.

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The possible solution set for the system is (- 1, 4) and (4, - 1).

Given are the equations as -

x + y = 3

x² + y² = 17

Refer to the graph of the function attached. The points of intersection represents the possible solution set.

Therefore, the possible solution set for the system is (- 1, 4) and (4, - 1).

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