The average distance a swimmer swims
can be described by the equation
d= 30t, where d is the
horizontal
distance in meters and tis the time
in minutes. Find the distances the
swimmer swims at the times of 7, 10, 14,
and 20 minutes.

Given:

The expression is

\(\dfrac{x-5}{3x^2-10x-25}\)

To find:

The restricted value of given expression.

Solution:

We have,

\(\dfrac{x-5}{3x^2-10x-25}\)

Equate the denominate equal to 0, to find the restricted value.

\(3x^2-10x-25=0\)

\(3x^2-15x+5x-25=0\)

\(3x(x-5)+5(x-5)=0\)

\((x-5)(3x+5)=0\)

Using zero product property, we get

\(x-5=0\text{ and }3x+5=0\)

\(x=5\text{ and }x=-\dfrac{5}{3}\)

Therefore, the restricted values are \(x=5\text{ and }x=-\dfrac{5}{3}\).

Answer:

4.2 you should use a calculator for these

Step-by-step explanation:

Answer:

B = 160°

Step-by-step explanation:

This is how I solved it (I hope the explanation isn't too confusing):

Since L and K are parallel, I drew a straight line from A to B. By doing this, I'm making a triangle: ΔABC

Then I solved for the angles of the triangle. First, we are given that ∠C = 80° and ∠A = 120°. Although, when I drew the vertical line from A to B, it made a 90° (see attachment).

So what we basically did was break ∠A into two parts: an angle inside ΔABC and one outside. To find the interior angle, simply subtract 90° from 120° to get 30°.

There are 180° in a triangle, so add the two interior angles you know:

30° + 80° = 110°

Then subtract 110° from 180° to find the final interior angle which is:

180° - 110° = 70°.

To find the measure of angle B, you must add all of the parts together, so the 90° outside angle and the 70° interior angle:

90° + 70° = 160°

There are 7920 ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

In this problem, we want to find the number of ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

Since every man must be diametrically opposite a woman, we can pair each man with one woman. There are 5 men and 9 women, so there are 5 pairs. We need to find the number of ways to seat these 5 pairs of people in a circle.

To do this, we can first seat one pair in any position. Then, we can seat the second pair anywhere but opposite the first pair. This gives us 11 positions for the second pair. Continuing in this way, we see that there are 11 * 6 * 5 * 4 * 3 = 7920 ways to seat the 5 pairs of people in a circle.

So, there are 7920 ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

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Assuming 14 people, 5 men and 9 women, how many ways can they sit in a circle such that every man is diametrically opposite a woman?

The probability that a student scored greater than 69 is 0.943746.

Using continuity correction we would know that a score of 69 would correspond to values between 68.5 and 69.5 , a score of 70 would correspond to values between 68.5 and 69.5, etc…

Lets, the mean of the scores as  X . Since we are taking the mean of scores, to have a mean greater than 69, at minimum, we would have to have scores that are 69, and one score that is 70, the average of  values of 68.5 and 1 value of 70 , that means we want to know:

Now,

Z= m - x/ σ                          -------------------------------- (1)

where, m is the upper value

            X is the mean score

            σ is the standard deviation

Putting the values in equation (1),

Z = 70 - 69/ 7

   = 0.1428

Now,

P( 0.1428) = 0.056854

                 = 5.6855%

So, 5.6866% of students average scored 69 or less,

                P( > 69) = 1 - 0.056854

                              = 0.943746.

therefore the probability that a student scored greater than 69 is 0.943746.

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The total values between 99 and 999 which are multiples of 2 are 450.

A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms.

The number of multiple of 2 between 99 and 999.

Therefore, the first term is a = 100 as 100 is the multiple of 2, and we need to find the multiples of 2.

Therefore, the last term will be:

aₙ = 998

The common difference, d = 2

Using the formula for the arithmetic sequence:

aₙ = a + ( n - 1 )d

998 = 100 + ( n - 1 )2

( n - 1 )2 = 898

Dividing each side of the equation by 2,

n - 1 = 449

Adding 1 on each side of the equation,

n = 450

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The algebraic rule that best describes the translation of point A(3, 2) to point A'(-1, 5) in Quadrilateral ABCD is (x, y) → (x - 4, y + 3).

Explanation: To translate a point (x,y) to (x+a,y+b), the algebraic rule is given by (x,y) → (x + a, y + b), where 'a' and 'b' are the horizontal and vertical translations respectively. In this case, point A is being translated to A'(-1, 5). The horizontal translation is from 3 to -1, which is a decrease of 4 units. The vertical translation is from 2 to 5, which is an increase of 3 units. Therefore, the algebraic rule that best describes this translation is (x, y) → (x - 4, y + 3).

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Answer:

r=3.399

Step-by-step explanation:

82.3=1/2(4/3pir^3)

164.6=4/3pir^3

164.6*(3/4) = 123.45=pir^3

123.45/pi=39.2953554494=r^3

cube root of 39.2953554494 =3.399

r= around3.4

Answer:

The range of the function is [0 , ∞) ⇒ answer B. Step-by-step explanation: * lets revise the meaning of the domain and the range - The domain is the values of x - The domain is all the values of x which make the function is defined - If there are some values of x make the function undefined, we exclude these values from the domain

Step-by-step explanation:

Step-by-step explanation:

Area=b×h

= (x+5)×(x+6)

=x^2+6x+5x+30

=x^2+11x+30

If u simplify u will get (x+5)(x+6) as answer.

Keep smiling and hope u are satisfied with my answer.Have a good day :)

The density of the given metal is 19.3g/cm³ . Then, the correct answer to this given question is Option E.

The given mass of  the metal is 611 g  and it is kept in a elevated cylinder that contains 25.1 mL of water,
Now, let us increase the water level to 56.7 mL. The metal  volume can be evaluated by subtracting the initial volume  from the final volume of water released by the metal.

Hence,
Metal volume = final volume - initial volume
= 56.7 mL - 25.1 mL
= 31.6 mL

Therefore,
Density = Mass / Volume
= 611 g/31.6 mL
= 19.3 g/cm³

The density of the given metal is 19.3g/cm³ . Then, the correct answer to this given question is Option E.


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It is cheaper to buy the games console in the UK.

Measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.

Given that;

A games console costs £255 in the UK.

And, The same one costs 300 euros in France.

Here, The exchange rate is,

⇒ £1 = €1.16

Hence, The cost of games console in UK is,

⇒ £1 = €1.16

⇒ £255 = €1.16 × 255

              = €295.8

Thus, It is cheaper to buy the games console in the UK.

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Camilla have total of 7 dogs.

acc to our question-

hence,Camilla have total of 7 dogs.

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Answer:

a

Step-by-step explanation:

Razorback's acceleration is 1.25 m/sec².

In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities.

Now it is given that,

Distance ran by Razorback, S = 40 m

Time taken, t = 8 seconds

Since the equation of motion is given as,

S = ut + 1/2at²

Now Razorback was at rest, therefore u = 0

⇒ 40 = 0 + 1/2a(8)²

⇒ 64a = 80

⇒ a = 80/64

⇒ a = 1.25 m/sec²

Thus, Razorback's acceleration is 1.25 m/sec².

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Answer:

30

Step-by-step explanation:

2a +4

Let a = 13

2*13 +4

Multiply

26 +4

Add

30

Answer: the answer is d

Step-by-step explanation:

The probability that "average-thickness" of 10 wafers is either greater than 12 or less than 8 micrometers is 0.

The thickness of the photoresist is normally distributed with a mean of 10 micrometers and a standard deviation of 1 micrometer.

We need to find probability that average thickness of 10 wafers is either "greater than 12" or "less than 8" micrometers.

Let X = thickness of a single wafer. Then the mean of the sample means  is also μ = 10 micrometers, and

the standard deviation of sample means is = σ/√n = 1/√10 micrometers, where n = 10 is the sample size.

To find probability that "average-thickness" of 10 wafers is either greater than 12 or less than 8 micrometers, we use central limit theorem,

⇒ z = (x - μ)/(σ/√n),

So, z₁ = (12 - 10)/(1/√10) ≈ 6.33,

and z₂ = (8 - 10)/(1/√10) ≈ -6.33,

The probability that the average thickness of 10 wafers is either greater than 12 or less than 8 micrometers can be calculated as the sum of the probabilities of z₁ and z₂, which is:

⇒ P(X < 8 or X > 12) = 1 - P(8 ≤ X ≤ 12);

and P(8 ≤ X ≤ 12) = P(-6.33 < Z  < 6.33)

= 1,

So, P(X < 8 or X > 12) = 1 - P(8 ≤ X ≤ 12) = 1 - 1 = 0,

Therefore, the required probability is 0, which means it is highly unlikely that the average thickness of 10 wafers will be either greater than 12 or less than 8 micrometers.

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The solution to the expression is -x² + 2ix²

From the question, we have the following parameters that can be used in our computation:

a = x

b = -1 + 2i

The expression to calculate is given as

a^2 * b

This can be properly expressed as

a² * b

Substitute the known values in the above equation, so, we have the following representation

a² * b = x² * (-1 + 2i)

Open the brackets

a² * b = -x² + 2ix²

Hence, the solution is -x² + 2ix²

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Answer:

Volume is the space occupied within the boundaries of an object in three-dimensional space, and is the capacity of an object.

Answer:

200/7

Step-by-step explanation:

(2 meters)/(7 centimeters) or (2m/7cm)

1 meter = 100 cm

(2m/7cm)*(100cm/1m) = 200/7 (or   28.57) scale factor.

Answer:

B

Step-by-step explanation:

Answer:

the answer B

Step-by-step explanation:

Answer:

Arc BC = 117°

Step-by-step explanation:

Angle D is an inscribed angle that intercepts arc ABC. According to the Inscribed angle theorem of a circle, m<D = ½ of arc ABC.

Thus,

104° = ½(AB + BC)

104° = ½(91° + BC)

Multiply both sides by 2

104*2 = 91 + BC

208 = 91 + BC

Subtract both sides by 91

208 - 91 = BC

117 = BC

Arc BC = 117°

The residential buildings' total assessed land value has the smallest standard deviation.

To determine the standard deviations for the commercial and residential buildings' total assessed land value and total assessed parcel value, we would need access to a specific dataset that includes these values. However, based on general trends and assumptions, residential buildings' total assessed land value is likely to have the smallest standard deviation.

Residential properties typically exhibit more homogeneity compared to commercial properties. Residential neighborhoods often consist of similar types of properties, with comparable land values within a specific area. As a result, the assessed land values for residential buildings are more likely to cluster around a mean value, resulting in a smaller standard deviation.

In contrast, commercial properties can vary significantly in terms of size, location, and intended use. They may be diverse in terms of their land value and parcel value. The assessed land values and parcel values for commercial buildings are more likely to have a wider range of values, leading to a larger standard deviation.  

Therefore, based on these general characteristics, the residential buildings' total assessed land value is expected to have the smallest standard deviation compared to the commercial buildings' total assessed land value and total assessed parcel value.

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Step-by-step explanation:

as the formula says for the acid of symmetry :

x = -b/2a

in the function m(x) = 2x² + 8x +3

we have

a = 2

b = 8

c = 3

the axis of symmetry is

x = -8/(2×2) = -8/4 = -2

the vertex is (h, k) out of the form

m(x) = a(x - h)² + k

we know already, a = 2

for the rest we do all the multiplications and then we compare it with the original function :

m(x) = a(x² - 2hx + h²) + k = ax² - 2ahx + ah² + k

a = 2

-2ah = 8

-2×2×h = 8

-4h = 8

h = -2

ah² + k = 3

2×(-2)² + k = 3

8 + k = 3

k = -5

so, the vertex is (-2, -5)

Answer:

4th term = 32, 10th term = 200

Step-by-step explanation:

basically you have to substitute in the values for n

2(4)² =  32

2(10)² = 200

The magnitude of the resulting velocity: sqrt(312.3^2 + 123.5^2) = 337.1 mph. Therefore, the plane's resulting velocity is 337.1 mph towards the northwest.

To get the plane's resulting velocity, we need to use vector addition. The plane is traveling at a velocity of 360 mph towards the northwest (n20 w). The wind is blowing towards the east (due west + 180 degrees) at a velocity of 25 mph. We can break down these velocities into their x and y components.
The plane's velocity towards the northwest can be broken down into a velocity towards the west and a velocity towards the north. Using trigonometry, we can find that the plane's velocity towards the west is 360*cos(20) = 337.3 mph, and the plane's velocity towards the north is 360*sin(20) = 123.5 mph.
The wind's velocity towards the east can be broken down into a velocity towards the west and a velocity towards the north. Since the wind is blowing due west, its velocity towards the north is 0 mph, and its velocity towards the west is -25 mph.
To get the plane's resulting velocity, we need to add the x and y components of the plane's velocity and the wind's velocity. The resulting velocity towards the west is 337.3 - 25 = 312.3 mph, and the resulting velocity towards the north is 123.5 mph.
Using the Pythagorean theorem, we can get the magnitude of the resulting velocity: sqrt(312.3^2 + 123.5^2) = 337.1 mph. Therefore, the plane's resulting velocity is 337.1 mph towards the northwest.

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The average velocity of Gwen over the time interval 0 < t is zero. We need to solve the equation:250sin(πt/45) = 0Solving for t, we get:πt/45 = nπwhere n is an integer.

Given that Gwen runs back and forth along a straight track and her velocity, in feet per second, is modeled by the function v(t) during the time interval 0 < t < 45 seconds; We are to determine the first time at which Gwen changes direction and find her average velocity over the time interval 0 < t.Firstly, we know that velocity is a vector quantity and has both magnitude and direction.

Since she is running back and forth along a straight track, her displacement at any given time t is given by the function s(t), which is the integral of her velocity function v(t).That is, s(t) = ∫v(t)dtWe can find the displacement by taking the definite integral of v(t) from 0 to t. Since Gwen is running back and forth, her displacement will be zero at the times when she changes direction.

Therefore, we need to solve the equation:250sin(πt/45) = 0Solving for t, we get:πt/45 = nπwhere n is an integer. Therefore,t = 45n/πwhere n is an integer. Since we are looking for the first time at which Gwen changes direction, we need to take the smallest positive value of n, which is n = 1.

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The null hypothesis to test for instruments' relevance is option D) H0:π2=0 or π3=0 or π4=0.In order to test the relevance of the instrument, the first stage equation's null hypothesis should be stated as: H0: π2 = 0 or π3 = 0 or π4 = 0.The relevance requirement will be fulfilled if we can refute the null hypothesis.

The null hypothesis will not be rejected if the F-statistic is less than 10.0. However, if the F-statistic is greater than 10.0, the null hypothesis will be rejected, indicating that the variables are relevant and that the instrument satisfies the relevance requirement.In summary, to test for instruments' relevance in TSLS, the null hypothesis of the first stage equation is stated as H0: π2 = 0 or π3 = 0 or π4 = 0.

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The velocity of the particle at time t is given by v(t) = (2t² + 1)i + (3t² - 1)j + (tk + 1)k, where t is the time. It represents the motion of the particle in three-dimensional space.

To find the velocity of the particle at time t, we need to integrate the acceleration vector with respect to time.

To find the velocity vector v(t), we integrate each component of the acceleration vector:

∫a(t) dt = ∫(4ti + 6tj + k) dt

Integrating each component separately:

∫(4ti) dt = 2t²i + C₁

∫(6tj) dt = 3t²j + C₁

∫k dt = tk + C₃

where C₁, C₂, and C₃ are constants of integration.

Combining the integrals, we have:

v(t) = (2t² + C₁)i + (3t² + C₂)j + (tk + C₃)k

Given that v(0) = i - j + k, we can substitute t = 0 into the velocity equation:

v(0) = (2(0)² + C1)i + (3(0)² + C₂)j + (0k + C₃)k

i - j + k = C₁i + C₂j + C₃k

Comparing the coefficients, we get:

C₁ = 1

C₂ = -1

C₃ = 1

Substituting these values back into the velocity equation:

v(t) = (2t² + 1)i + (3t² - 1)j + (tk + 1)k

Therefore, the velocity of the particle at time t is given by:

v(t) = (2t² + 1)i + (3t² - 1)j + (tk + 1)k

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