on a line segment of length 1, chooses two points independently at random. what is the probability the distance between them is more than 1/3?

With α = 0.05, 1.761 is the critical t value for a one-tailed test with n = 15 for a single-sample t-test.

Given that,

We have to find with α = 0.05, what is the critical t value for a one-tailed test with n = 15 for a single-sample t-test.

We know that,

α = 0.05

n = 15

One tailed t test for single sample.

We know from t-table

α = 0.05 (corresponding one -tail) and corresponding d.f = n - 1.

For sample t-test

d.f = 15 - 1 = 14

tα (0.05,14) for tail = 1.761       (from t-table)

Therefore, with α = 0.05, 1.761 is the critical t value for a one-tailed test with n = 15 for a single-sample t-test.

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Answer:

use the way I told u down

Step-by-step explanation:

Angle ABC is a straight angle.

Angles ABD and DBC are right angles.

Angles CBE and DBE are acute angles.

Angle ABE is an obtuse angle.

Angles

The sum of the three angles in any triangle is always 180°.

a + b + c = 180°

Knowing that the sum of the angles of triangle is 180° can help you to solve problems about triangles.

Angles

In this triangle, angle b is a right angle and angle c = 40°. What is the measure of angle a?

a + b + c = 180°

Since b is a right angle, b = 90°.

The problem states that c = 40°.

Therefore, a + 90° + 40° = 180°

a + 130° = 180°

a + 130° − 130° = 180° − 130°

a = 50°

Angle a measures 50°.

Angles

Click on the figure that matches this description.

An obtuse angle

Question 1 of 8

This is an acute angle. It measures less than 90°. Try again

This is a right angle. The square in the corner shows that it measures 90°. Try again

This is a straight angle. It measures 180°. Try again.

This angle is obtuse. It is greater than 90° and less than 180°.

One of these figures is an obtuse angle. Try again.

An obtuse angle is larger then a right angle and smaller then a straight angle.

Angles

Click on the figure that matches this description.

An acute angle

Question 2 of 8

This is an acute angle. It measures less than 90°.

This is a right angle. The square in the corner shows that it measures 90°. Try again

This is a straight angle. It measures 180°. Try again.

This angle is obtuse. It is greater than 90° and less than 180°. Try again.

One of these figures is an acute angle. Try again.

An acute angle is smaller then a right angle.

Angles

Click on the figure that matches this description.

A right angle

Question 3 of 8

This is an acute angle. It measures less than 90°. Try again

This is a straight angle. It measures 180°. Try again.

This angle is an obtuse angle. It measures more than 90° and less than 180°. Try again.

This is an acute angle. It measures less than 90°. Try again.

A right angle looks like a square corner and measures 90°.

A right angle measures 90°.

Angles

There are five question remaining. In each of these question, you will be asked to find the size of a missing angle.

Angles

Click on the correct answer.

Angle ABC is a right angle. If angle n is 40°, how large is angle m?

50°

140°

90°

60°

None of these

Question 4 of 8

90° − 40° = 50°

Angle m is 50°.

Angle ABC is 90° , and angle m is only part of this right angle. It is less than 90°. Try again.

Angle ABC is 90°, and angle m is only part of this right angle. Try again.

Angle m and n together from a 90° angle. Subtract 40° from 90° .Try again.

One of these is size of angle m. Try again.

Since angle ABC is a straight angle, angle m + angle n = 90°.

The value x is 28. By using Pythagorean theorem on the given triangle.

What is the meaning of the nearest tenth?

To write a decimal number up to one decimal place, round it to the nearest tenth. This is done in a way that leaves one digit after the decimal point after rounding.

Given that,

DC = 28

BC = 32

Assume that, AB = a and AD = b

Applying Pythagorean theorem on △BCD:

BC² = DC² + DB²

Putting BC = 32 and DC = 28 in the above equation:

32² = 28² + DB²

DB² = 32² - 28²

DB² = 32² - 28²

DB² = 240

The length of AC is CD + DA = 28 + b.

Now applying Pythagorean theorem on △ABC:

BC² = AB² + AC²

32² = a² + (28 + b)²

a² = 32² - (28 + b)²   .....(i)

Now applying Pythagorean theorem on △ABD:

AB² = AD² + BD²

a² = b² + 240  ....(ii)

Now comparing equation (i) and equation (ii)

32² - (28 + b)² = b² + 240

1024 - (28² + 56b + b²) = b² + 240

1024 - 784 - 56b - b² = b² + 240

b² + 240 - 1024 + 784 + 56b + b² = 0

2b² + 56b = 0

2b(b + 28) = 0

Either,

2b = 0,  b + 28 =0

b = 0, b = -28

Since the value of b can't be negative. Thus b = 0.

The length of AC is CD + DA = 28 + b = 28.

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To prove that AC = BD, we can use the symmetric property. The symmetric property states that if two quantities are equal, then their opposites are also equal.

In this case, we are given that AB = CD. Since AB and CD are opposite quantities (they are the lengths of the diagonals of a rectangle), we can use the symmetric property to conclude that AC = BD.

Therefore, the reason that can be used to justify statement 4 in the proof is the symmetric property.

Answer:

c

Step-by-step explanation:

Samantha was receiving an interest rate of 12% on her account.

Present value is the present value of future cash flows discounted at a certain rate. Present value is based on the concept of the time value of money, where a dollar today is worth more than a dollar in the future.

PV = FV /(1 + r )ⁿ

Information provided to us ,

time period , n = 6 years

let " $x " be the present value of Samantha's account money.

After 6 years it becomes double that is

future value, F = $2x

let "r" be rate of interest was Samantha receiving on her account.

plugging all known values in above formula,

$x = $2x /(1+r)⁶

=> (1+r)^6 = 2

=> 1 + r = (2)^1/6 = 1.122

=> r = 1.122 - 1 = 0.122

=> r = 12%

So, rate of interest is 12% .

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The area of the shaded region in the rectangle is given as follows:

42 units squared.

The area of a rectangle of base b and height h is given by the multiplication of these dimensions, as follows:

Area = base x height.

For the shaded region in this problem, given by the image shown at the end of the answer, the area can be obtained as the subtraction of the area of the entire rectangle by the area of the non-shaded region.

The entire rectangle has base 11 and height 12, hence it's area is given as follows:

Ar = 11 x 12 = 132 units².

The non-shaded region has base of 9 units and height of 10 units, hence it's area is given as follows:

An = 9 x 10 = 90 units².

Then the area of the shaded region on the rectangle is calculated as follows:

As = Ar - An = 132 - 90 = 42 units².

The rectangle is given by the image shown at the end of the answer.

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Answer: [tex]12x^{2} -18x-12[/tex]

Step-by-step explanation:

(6x-12)(2x+1)

Foil method

6x*2x

6x*1

-12*2x

-12*1

add them up

[tex]12x^{2} -18x-12[/tex]

Answer:

[tex] \sf \: -2x² + 6x + 4 [/tex]

Step-by-step explanation:

Given problem,

→ (3x² + 8x - 7) - (5x² + 2x - 11)

Let's solve the problem,

→ (3x² + 8x - 7) - (5x² + 2x - 11)

→ 3x² + 8x - 7 - 5x² - 2x + 11

→ (3x² - 5x²) + (8x - 2x) + (-7 + 11)

→ (3 - 5)x² + (8 - 2)x + 4

→ -2x² + 6x + 4

Hence, answer is -2x² + 6x + 4.

Answer:

Step-by-step explanation:

The graph of the parent function f(x) = |x|

transformed function g(x) = |x – h|

To Find : How does changing the value of h affect the vertex?

Positive values of h shift the graph

Negative values of h shift the graph

Solution:

f(x) = |x|

is f(x) = x  for  x ≥ 0

 f(x) = -x   for  x < 0

g(x) = |x – h|

Positive values of h shift the graph  to the right  

f(x)  = x  - h   for x  ≥ 0

f(x)  = h - x   for x  < h

As values of h increase graph keep shifting to right

Vertex is ( h , 0)   Vertex keep shifting to right with increases value of h

g(x) = |x – h|

Negative value of h shift the graph  to the left

f(x)  = x  - h   for x  ≥ 0

f(x)  = h - x   for x  < h

Vertex is ( h , 0)   Vertex keep shifting to left with increases magnitude of negative h

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The linear functions f(x) and g(x) are represented on the graph ...

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The linear functions f(x) and g(x) are represented on the graph ...

Answer:

See below

Step-by-step explanation:

5z/(z-2) = - 1/z

1)  z [tex]\neq[/tex] 2  the expression (z-2) in 5z/(z-2) would be 0, leaving 5/0.  Division by 0 is undefined.

2)  Similiarly, the expression - (1/z) requires that z [tex]\neq[/tex] 0, since division by 0 is not allowed (undefined).

Answer:

Step-by-step explanation:

Okay so you have to multiple 12 x 80 which gives you 960, then you  mulitply 960 x 4 to get your final answer which is 3840 cubic inches

ABDC is a quadrilateral with two non-parallel sides. It has two pairs of opposite sides which are parallel. It is also known as a trapezoid.

ABDC is a four-sided figure with two pairs of opposite sides that are parallel. This type of quadrilateral is also known as a trapezoid. A trapezoid has two non-parallel sides, while the other two sides are parallel to each other. In this case, the two parallel lines are L1 and L4, while L2 and L3 are the two non-parallel sides. We can see that the point C on L2 is a distance of 4cm from L1, and L4 is a line that is parallel to L1 and passes through C. Finally, L4 intersects L3 at the point D, which completes the trapezoid ABDC.

The length of AB can be determined by using the Pythagorean Theorem. We know that the length of L1 is 8 cm, so the length of AB is 3 cm.

example

AB = √(8^2 - 4^2) = √64 - 16 = √48 = 6 cm

The length of BD can also be determined by using the Pythagorean Theorem. We know that the length of L2 is 4 cm, so the length of BD is 3 cm.

BD = √(4^2 - 4^2) = √16 - 16 = 0 cm

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The exponent 1/5 meaning in the expression 64 1/5 is that a number that can be multiplied 5 times that will give 64.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4

It should be noted that the exponent 1/5 meaning in the expression 64 1/5 is that a number that can be multiplied 5 times that will give 64.

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Answer:

a) i) 6 numbers = 10^6=1000000

ii) 4 numbers followed by 2 letters= 10^4*26^2=6760000

iii)1 number followed by 5 letters : 10^1*26^5= 118,813,760

b)...

a) If Eddie repeat a digit or a letter:

i) The number of codes he can create with 6 numbers is 1,000,000.

ii) The number of codes he can create with 4 numbers followed by 2 letters is 67,600.

iii) The number of codes he can create with 1 number followed by 5 letters is 11,881,376.

b) If Eddie does not want to repeat a digit or a letter:

i) The number of codes he can create with 6 numbers is 15,120.

ii) The number of codes he can create with 4 numbers followed by 2 letters is 1,092,000.

iii) The number of codes he can create with 1 number followed by 5 letters is 7,893,600.

a) To calculate the number of codes Eddie can create for each scenario:

i) For a 6-digit code using only numbers, each digit can take on any value from 0 to 9 (10 options for each digit). So, the total number of codes is 10⁶ = 1,000,000.

ii) For a code with 4 numbers followed by 2 letters, there are 10 options for each digit and 26 options for each letter (assuming only uppercase letters). The total number of codes is 10⁴ * 26² = 67,600.

iii) For a code with 1 number followed by 5 letters, there are 10 options for the number and 26 options for each letter. The total number of codes is 10 * 26⁵ = 11,881,376.

b) If Eddie decides not to repeat a digit or a letter, the number of possibilities changes for each scenario:

i) Since he cannot repeat a digit, the first digit can be any of the 10 options. The second digit has only 9 options left, the third digit has 8 options, and so on. So, the total number of codes becomes 10 * 9 * 8 * 7 * 6 * 5 = 15,120.

ii) In this case, he cannot repeat any digit or letter. So, for the 4 numbers, there are 10 options for the first, 9 options for the second, 8 options for the third, and 7 options for the fourth. For the 2 letters, there are 26 options for the first and 25 options for the second (since no repetition is allowed). The total number of codes becomes 10 * 9 * 8 * 7 * 26 * 25 = 1,092,000.

iii) For the code with 1 number and 5 letters, the number has 10 options, and the first letter has 26 options. However, he cannot repeat any letter after the first, so the second letter has 25 options, the third has 24 options, and so on. The total number of codes becomes 10 * 26 * 25 * 24 * 23 * 22 = 7,893,600.

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The graph with the dilated line segment is given by the image shown at the end of the answer.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure, thus a dilation is classified as a non-rigid transformation.

The endpoints of the line segment in this problem are given as follows:

(0,0) and (5,5).

The scale factor of the dilation is given as follows:

k = 2.

Then the endpoints of the dilated line segment will be obtained multiplying each of the coordinates of each of the endpoints by the scale factor of 2, as follows:

(0,0) and (10,10).

Then the dilated line segment, connecting the endpoints (0,0) and (10,10), is given by the image shown at the end of the answer.

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The predicted value of the car in 2009, to the nearest dollar, is $14,800.

The value of an exponentially depreciating asset can be calculated using the equation:

V = V_0 × [tex]e^{(-r*t)}[/tex]

where V is the current value of the asset, V_0 is the initial value of the asset, r is the rate of depreciation, and t is the time elapsed since the asset was purchased.

In this case, the initial value of the car was $27,600, the value in 2004 was $8,300, and the time elapsed since the car was purchased is 4 years.

To determine the predicted value of the car in 2009, we can set t equal to 9 years and solve for V:

V = 27,600 × [tex]e^{(-r*9)}[/tex] = 8,300

Solving for r gives us:

r = ln(8,300/27,600) / -9

= -0.069

To determine the predicted value of the car in 2009, we can plug the value for r into the equation and solve for V:

V = 27,600 × [tex]e^{(-0.069*9)}[/tex] = 14,800

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The total money received by madison was $ 21.6 from which she spent $13 when she went out.

We are given that -

Madison spent $13 in all when she went out.

Also, this was 3/5 of the amount that she had received.

Now let us find the total money she received as follows -

Money spent by madison = 3/5 of the total money received by madison

                              i.e.    13 = 3/5 x (total money received by madison)

or we can say that total money received by madison = (5/3) x 13

                                                                                        =  65/3

                                                                                        = 21.6

Hence, the total money received by madison was $ 21.6

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The number of miles Joseph traveled in one hour is calculated to be 20.25 miles

Since Joseph drove 27 miles in 1 1/3 hours, we first convert 1 1/3 into simpler form as follows;

1 1/3 hours = 4/3 hours

Now we can determine how far he traveled in one hour if he drove at a constant rate by cross multiplication as follows;

4/3 hours = 27 miles

1 hour = x

Here x represents the number of miles traveled in one hour;

1 × 27 = 4/3x

27 = 4/3x

x = 27/(4/3)

x = 27 × 3/4

x = 20.25 miles

Hence Joseph travels 20.25 miles in one hour.

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The function is called an if/else statement function lets you test if something is true or false and then do different things depending on which result you get.

An if/else statement is a type of control flow statement that allows a program to execute different instructions depending on the result of a logical expression. The statement begins with an if condition, followed by a set of instructions to be performed if the condition is true. If the condition is false, the program executes the instructions after the optional else statement. The syntax for an if/else statement looks like this: if (condition) { // Instructions to execute if condition is true } else { // Instructions to execute if condition is false } By using an if/else statement, a program can make decisions and perform different actions based on the results of a logical expression.

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Answer: x=1

Step-by-step explanation:

[tex][(-\frac{2}{5})^2] ^x*(-\frac{5}{2}) ^{-1}=-\frac{8}{125} \\\\(-\frac{2}{5})^{2*x}*(-\frac{2}{5})^1 =-\frac{2^3}{5^3} \\\\(-\frac{2}{5} )^{2x+1}=(-\frac{2}{5})^3 \\\\Hence,\\\\2x+1=3\\\\2x+1-1=3-1\\\\2x=2[/tex]

Divide both parts of the equation by 2:

[tex]x=1[/tex]

The probability of 20% or more of the sample owning Harleys is 0.95. It is likely that your sample will contain 20% or more who own Harleys.

1. First, calculate the mean number of Harley owners in your sample using the 14% rate of Harley ownership among all motorcycle owners in the US:

2. Next, calculate the standard deviation of the number of Harley owners in your sample using the 14% rate of Harley ownership:

3. Calculate the number of standard deviations that 20% (100 Harley owners) is from the mean of 70 Harley owners:

4. Using a standard normal distribution table, we find that the probability of obtaining 1.79 standard deviations or more from the mean is about 0.9643. Therefore, it is likely that your sample will contain 20% or more who own Harleys.

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The SS(residual) is - 301.19. Option (b) is the correct answer.

Given the table :

Source of Variation - - SS - - - df - - - MS - - - - F

Regression - - - - - -3177.17 - - -2 - - 1588.6

Residual - - - - - - - - ______ --17 - - -17.717

Total - - - - - - - - - - 3478.36 - - 19

Calculate the SSR, the Sum of the Square residual.

The Sum of Square RESIDUAL (SSR), Mean Square Residual (MSR), and Degree of Freedom RESIDUAL (DFR) are related by the formula :

MSR = SSR / DFR

Hence,

SSR = MSR × DFR

For the table ;

MSR = 17.717 ; DFR = 17

SSR = (17.717 × 17)

SSR = 301.19

So, the SS(residual) is - 301.19.

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keeping in mind that a function does not have any X-Repeats, that is, the 1st coordinate in every pair never repeats, Check the picture below.

The difference between the two numbers is the number of fewer people that would be predicted to be at the fair on a 100°F day than on a 75°F day.The answer will depend on the specific data from the catter plot.

1. Look at the catter plot and identify the points that correspond to the temperatures of 75°F and 100°F.

2. Note the number of people at the fair for each temperature.

3. Subtract the number of people at the fair in the 75°F point from the number of people at the fair in the 100°F point.

The difference between the two numbers is the number of fewer people that would be predicted to be at the fair on a 100°F day than on a 75°F day.

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im gussing you mean 5x+10=7x-6

if so

5x+10=7x-6

  -5x = -5x

     10=2x-6

     +6=+6

     16=2x

     /2=/2

      8=x

The value of x = 8

here, 5x+10 is the 1st Equation

and 7x-6 is the 2nd Equation

We have to form an equation

        5x+10=7x-6

To solve for x, we need to isolate it on one side of the equation. To do this, we need to use inverse operations.

put the variable term on one side and the numerical term on the other side of the equal to sign, and while doing this change the sign from

             plus with minus and vice versa

             multiply with divide and vice versa

5x+10=7x-6

5x-7x=10+6

2x=16

x=[tex]\frac{16}{2}[/tex]

x=8

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Approximately 795 newborn babies (88.3% of the 900 newborn babies) would be expected to weigh less than 7 pounds.

1. Approximately 728 newborn babies (81.3% of the 900 newborn babies) would be expected to weigh between 3 and 8 pounds.

2. Approximately 795 newborn babies (88.3% of the 900 newborn babies) would be expected to weigh less than 7 pounds.

3. Approximately 450 newborn babies (50% of the 900 newborn babies) would be expected to weigh more than 6 pounds.

4. Approximately 645 newborn babies (71.7% of the 900 newborn babies) would be expected to weigh between 6.6 and 9 pounds.

• Between 3 and 8 pounds: 0.6826*900 = 613.4 + 0.95*900 = 814.5 = 728

• Less than 7 pounds: 0.9545*900 = 859.05 = 795

• More than 6 pounds: 0.5*900 = 450

• Between 6.6 and 9 pounds: 0.6826*900 = 613.4 + 0.3413*900 = 306.17 = 64

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The value of function (f+g)(x) is x²-3x+7, (f-g)(x) is 3x²-3x+7, (fg)(x) is -2x⁴+3x³-7x² and (f/g)(x) is -2x²+3x-7/x²

A relation is a function if it has only One y-value for each x-value.

The given two functions are

f(x)=3x-2 and g(x)=4+x

at x=-1

f(-1)=-5, g(-1)=3

at x=2,

f(2)=4, g(2)=6

at x=5,

f(5)=13, g(5)=9

Now the functions are f(x)=2x²-3x+7  and g(x)=-x².

We need to find (f+g)(x)

f(x)+g(x)

2x²-3x+7-x².

x²-3x+7

(f-g)(x)

f(x)-g(x)

2x²-3x+7+x²

3x²-3x+7

(fg)(x)

(2x²-3x+7)(-x²)

-2x⁴+3x³-7x²

f/g(x)=-2x²+3x-7/x²

Hence, the functions (f+g)(x)=x²-3x+7, (f-g)(x)=3x²-3x+7, (fg)(x)=-2x⁴+3x³-7x² and (f/g)(x)=-2x²+3x-7/x²

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The distance Martin climbs in 60 minutes is 18 meters

From the question, we are to determine how many meters Martin can climb in 60 minutes

Let the distance he climbs in 60 minutes be x

From the given information,

Martin climbs 3 meters in the first 10 minutes

If Martin climbs 3 meters in 10 minutes

Then,

Martin will climb x meters in 60 minutes

Thus,

x × 10 = 3 × 60

Solve for x

10x = 180

x = 180/10

x = 18

Hence, the distance is 18 meters

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