Three numbers form a gp. If the first and third numbers are 5 and 245 respectively, find two possible values for the middle number. Showing the workings

The ferry travels at constant rate is 7/18 miles/hour

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

As per the data given in the question we have to find the ferry travels at a constant rate.

As per the question it is given that a ferry traveled 1/6 of the distance between two ports in 3/7 hour.

Now, Ferry travelled 1/6 miles of distance between two ports in 3/7 hours  

Hence, Rate of Ferry is equal to distance travelled over time taken.  

Rate of ferry = 1/6 ÷ 3/7

Now we calculate it.  

Rate of ferry = 1/6 × 7 / 3 miles/hour

Rate of Ferry = 7/18 miles/hour

Hence, The ferry travels at constant rate is, 7/18 miles/hour.

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The match of the terms and correct locations are:

1. A - Amplitude

2. B is compression

3. C is rarefaction

A longitudinal wave is a form of wave in which its direction of propagation is similar to the direction of vibration of the particles of the medium through which the wave is travelling. The waves generated by a stretched or compressed spiral spring produces longitudinal waves.

When a spiral spring is streched or compressed, on removal of the force a series of compression and rarefactions of the sections of the spring are produced. This sections vibrates in the direction of propagation of the waves produced.

Thus the match of the terms and correct locations are:

i. A - Amplitude

ii. B is compression

iii. C is rarefaction

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If Cindy bought 7/8 yards of ribbon, then the length of Ribbon that Jacob bought is 7/10 yard.

The length of ribbon which Cindy bought is = 7/8 yard;

Jacob bought 4/5 the length as Cindy,

Which means that he bought, (4/5) × (7/8) yards of ribbon,

On multiplying these two fractions,

We get,

⇒ (4/5) × (7/8) = (4×7)/(5×8) = 28/40;

On simplifying this fraction, we divide both the numerator and denominator by their greatest common factor, which is 4,

We get,

⇒ 28/40 = 7/10,

Therefore, Jacob bought 7/10 yard of ribbon.

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The vector representing D = A - B has following values,

1. x- component of vector D = 9 and y- component of vector D = 9.

2. Magnitude and direction of vector D is equal to 12.73 and 45° above the positive x-axis.

Here, Vector D= A-B  __(1)

Components of vector A are,

Ax=5

Ay=5

Components of vector B are,

Bx= -4,

By= -4

1. Subtract the x- and y-components of vector B from vector A, respectively by substituting in (1) we get,

Dx = Ax - Bx

    = 5 - (-4)

    = 5 + 4

    = 9

Dy = Ay - By

     = 5 - (-4)

     = 5 + 4

     = 9

2. Magnitude of vector D, use the Pythagorean theorem,

|D| = √(Dx² + Dy²)

    = √(9² + 9²)

    = √(162)

     ≈ 12.73

Direction of vector D, use trigonometry.

Angle θ represents vector D makes angle with positive x-axis is ,

θ = tan⁻¹(Dy / Dx)

   = tan⁻¹(9 / 9)

   = tan⁻¹(1)

    = 45°

Therefore, required value of the vectors are,

1. x- and y-components of vector D are 9 and 9, respectively.

2. Magnitude of vector D is 12.73, and direction is 45° above the positive x-axis.

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The above question is incomplete , the complete question is:

Suppose D= A-B where vector A has components Ax=5, and Ay=5 and vector B has components Bx= -4, By= -4.

1. What are the x- and y- components of vector D?

2. What are the magnitude and direction of vector D?

The reason that should be used to complete statement 2 "∠2 and ∠3 are supplementary" is linear pair postulate.

In Mathematics, the linear pair theorem is sometimes referred to as linear pair postulate and it states that the measure of two angles would add up to 180° provided that they both form a linear pair.

This ultimately implies that, the measure of the sum of two adjacent angles would be equal to 180° when two parallel lines are cut through by a transversal.

According to the linear pair theorem, we have the following supplementary angles:

∠2 + ∠3 = 180°

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The solution for the inequality in this problem is problem is given as follows:

v ≤ 81.

The four inequality symbols, along with their meaning, are presented as follows:

The inequality is given as follows:

5v/9 ≤ 45.

v ≤ 45 x 9/5

v ≤ 9 x 9

v ≤ 81.

Hence the solution is composed by the numbers to the left of 81, with a closed interval at x = 81.

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Answer: 20

Step-by-step explanation:

49 ÷ 245 %

convert the percentage to decimals

49 ÷ 2.455

calculate the product or quotient

20

                   Please give me brainliest

Answer:20

Step-by-step explanation:

Let's denote the number we are looking for as "x".

We can set up the equation:

245% of x = 49

We can convert 245% to the decimal form by dividing by 100:

2.45 * x = 49

To solve for x, we can divide both sides of the equation by 2.45:

x = 49 / 2.45

x = 20

Therefore, 245% of 20 is equal to 49.

Answer:

The argument of the logarithmic function should be greater than zero.

Thus, for y = log(-x + 3) - 1 to be real-valued, we need:

-x + 3 > 0

or

x < 3

So, the domain of the function is all real numbers less than 3.

To find the range, let's consider the behavior of the logarithmic function.

As x approaches 3 from the left, the argument of the logarithm approaches zero from the negative side, which means the logarithm approaches negative infinity.

As x approaches negative infinity, the argument of the logarithm becomes very large and negative, which means the logarithm approaches negative infinity.

Therefore, the range of the function y = log(-x + 3) - 1 is all real numbers.

Step-by-step explanation:

The frequency and cumulative frequency distribution tables for the given data are below in the solution part.

Cumulative frequency is used to calculate the number of observations in a data collection that is above (or below) a specific value.

The data is provided for 62 students in a certain class in terms of their maths marks out of 100.

55, 60, 81, 90, 45, 65,  45, 52, 30,  85,  20, 10, 75, 95, 09, 20, 25, 39,  45, 50, 78,  70,  46, 64, 42, 58, 31, 82, 27, 11,  78, 97, 07,  22,  2  36, 35, 40, 75, 80, 47, 69,  48, 59, 32,  83,  23, 17, 77, 45, 05, 23, 37, 38,  35, 25, 46,  57,  68, 45, 47, 49.

The frequency distribution table for the given data is as follows:

       Class                               Frequency

(Marks obtained)                 (No. of students)

0 - 10                                              4

10 - 20                                             3

20 - 30                                            8

30 - 40                                             9

40 - 50                                            13

50 - 60                                            6

60 - 70                                            5

70 - 80                                            6

80 - 90                                            5

90 - 100                                          3

                                                  N = 62

The cumulative frequency table more than or equal to the type for the given data is as follows:

       Class                               Frequency             Cumulative frequency

(Marks obtained)                 (No. of students)  

0 - 10                                               4                          62

10 - 20                                             3                          58

20 - 30                                            8                          55

30 - 40                                             9                          47

40 - 50                                            13                          38

50 - 60                                            6                           25                    

60 - 70                                            5                            19

70 - 80                                            6                            14

80 - 90                                            5                            8

90 - 100                                          3                             3

                                                  N = 62

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we have proved that H ◃ G ↔ N(H) = G.

Given G = (G;*) is a group and H ≤ G, and given set N(H) = {g ∈ G | gHg^-1 = H}, we need to prove that H ◃ G ↔ N(H) = G.

First, let's assume that H ◃ G. This means that H is a normal subgroup of G. By definition, a normal subgroup is a subgroup that is invariant under conjugation by any element of the group. In other words, for any g ∈ G and h ∈ H, we have gHg^-1 = H. This is exactly the condition for an element to be in N(H), so we can conclude that N(H) = G.

Now, let's assume that N(H) = G. This means that every element of G is in N(H), which means that for any g ∈ G and h ∈ H, we have gHg^-1 = H. This is the definition of a normal subgroup, so we can conclude that H ◃ G.

Therefore, we have proved that H ◃ G ↔ N(H) = G.

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Therefore, the correct answer is C. Log 65/177 y = x.

The correct answer is C. Log 65/177 y = x.

To solve the equation in exponential form, we need to use the properties of logarithms. The equation Y^x = 65 / 177 can be rewritten in logarithmic form as Log Y (65/177) = x. Using the property of logarithms, Log a^b = b Log a, we can rewrite the equation as Log (65/177) Y = x. This is the same as option C, Log 65/177 y = x.

Therefore, the correct answer is C. Log 65/177 y = x.

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The values of F(x), h(x), and g(x) when x=3 are 42, -230, and 6, respectively.

The given functions are F(x)=−529, F(x)=x^2+33, h(x)=∣x∣−233, and g(x)=2x.

To find the value of F(x) when x=3, we can substitute x=3 into the equation F(x)=x^2+33 and solve for F(x):
F(x)=x^2+33
F(3)=3^2+33
F(3)=9+33
F(3)=42

Similarly, to find the value of h(x) when x=3, we can substitute x=3 into the equation h(x)=∣x∣−233 and solve for h(x):
h(x)=∣x∣−233
h(3)=∣3∣−233
h(3)=3−233
h(3)=-230

And to find the value of g(x) when x=3, we can substitute x=3 into the equation g(x)=2x and solve for g(x):
g(x)=2x
g(3)=2(3)
g(3)=6

Therefore, the values of F(x), h(x), and g(x) when x=3 are 42, -230, and 6, respectively.

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The minimum cost per pupil is $7,500 when 250 students are enrolled.

To find the minimum cost per pupil, we need to find the vertex of the parabola C = 70,000 − 500n + n². The vertex of a parabola in the form y = ax² + bx + c is given by the formula x = -b/2a. In this case, a = 1, b = -500, and c = 70,000.

Plugging these values into the formula, we get:
x = -(-500)/2(1) = 500/2 = 250

So the minimum cost per pupil occurs when n = 250 students are enrolled.

To find the minimum cost, we can plug n = 250 back into the equation for C:
C = 70,000 − 500(250) + (250)² = 70,000 - 125,000 + 62,500 = 7,500

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Therefore , the solution of the given problem of unitary method comes out to be he only had a 19 gallon jug of petroleum, which was insufficient for both days.

To finish the job using the unitary method, multiply the subsets measures taken from this microsecond section by two. In a nutshell, when a wanted thing is present, the characterized by a variable group but also colour groups are both eliminated from the unit technique. For instance, 40 changeable-price pencils would cost Inr ($1.01). It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait.

Here,

Magnus had to fill up his skiff with 6 gallons and 3 quarts of gas on Monday. We can observe that 1 quart is equivalent to 0.25 gallons to express this in decimal form:

=> 6 gallons 3 quarts = 6 + 3/4 = 6.75 gallons

Magnus used 6.75 litres of fuel on Monday as a result.

He required twice as much petrol on Saturday as he did on Monday:

=> 13.5 gallons from

=> 2 (6.75" gallons).

So on Saturday, he consumed 13.5 litres of fuel.

Overall, he employed:

=> 6.75 gallons + 13.5 gallons = 20.25 gallons

He only had a 19 gallon jug of petroleum, which was insufficient for both days.

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The probability that clothing store have fewer than 12 customers in first 2 hours is 0.0003.

We know that, the store is open for 12 hours and gets an average of 120 customers per day, the expected number of customers in a 2-hour period can be calculated as:

The Expected number of customers in 2 hours = 120×(2/12) = 20 customers,

We, use the Poisson distribution to find the probability of having fewer than 12 customers in the first two hours.

The Poisson distribution is given by : P(X = k) = (e^(-λ) × λ^k)/k! ;

where X = random variable (the number of customers), λ = expected value of X (in this case, λ = 20), k = number of customers we want to calculate the probability for, and k! is the factorial of k.

To find the probability of having fewer than 12 customers in the first 2 hours, we need to calculate the probability for k = 0, 1, 2, ..., 11 and add up the probabilities.

So, we have,

⇒ P(X < 12) = e⁻²⁰×(20⁰/0!) + e⁻²⁰×(20¹/1!) + ... + e⁻²⁰×(20¹¹/11!);

On solving, We get,

⇒ P(X < 12) = 0.0003,

Therefore, the required probability is 0.0003.

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Answer:

The given rectangle is not fully defined, as it is missing some measurements such as the length and width. Without this information, it is not possible to accurately calculate the perimeter of the rectangle.

However, assuming that the missing measurement is the width of the rectangle, then the expressions given by the five students would be:

2(3x + 4x + 3) = 14x + 6

2(6x + 6) + 2(4x + 6) = 20x + 24

2(3x + 3) + 2(4x + 3) = 14x + 12

2(6x + 3) + 2(4x + 3) = 20x + 12

2(6x + 3x) + 2(3 + 4x) = 18x + 10

Note that all expressions follow the formula for the perimeter of a rectangle, which is P = 2l + 2w, where l is the length and w is the width of the rectangle.

Answer:

-x + 6.5 > 1 Is true.

Step-by-step explanation:

The explaination is given in the Picture.

Answer:

[tex]y=\frac{2}{3}x+1[/tex]

Step-by-step explanation:

Slope-Intercept Line Equation:

[tex]y=mx+b[/tex]

Where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.

From the graph, we can see that the y-intercept is (0, 1). This means that the equation is currently:

[tex]y=mx+1[/tex]

To find the slope, we can use a point on the line to replace the x and y variables. The point that we use cannot have x equal to zero. If we use the x-intercept [tex](-1.5, 0)[/tex], the new equation will be:

[tex]0=m(-1.5)+1[/tex]

Then, we must find m:

[tex]0=m(-1.5)+1[/tex]

[tex]-1=m(-1.5)[/tex]

[tex]\frac{-1}{-1.5}=m[/tex]

[tex]m=\frac{2}{3}[/tex]

Now we can find the equation of the line:

[tex]y=\frac{2}{3}x+1[/tex]

There is no unit vector with a positive first component that is orthogonal to both u and v.

The unit vector we are looking for is (1/√14, √13/14, √15/14, -√12/14). To find this vector, we need to solve the equation 0 = u1 + v1, where u1 and v1 are the first components of u and v. From the given vectors, u1 = 1 and v1 = 6. So 0 = 1 + 6, which simplifies to -6 = 0, which is a contradiction, meaning there is no unit vector with a positive first component that is orthogonal to both u and v.

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Answer:

C is the answer

To write a quadratic function f whose zeros are -2 and 9 , we have to factor the function by (x+2) and (x-9).

A quadratic function is a second-degree mathematical function whose graph is a parabola. The general form of a quadratic function is given by f(x) = ax² + bx + c, where a, b and c are constants and a cannot be equal to zero. The variable x represents the input of the function and f(x) represents the output or result of the function. To find the quadratic function of f we first need to multiply these factors, like this:

So the quadratic function whose zeros are -2 and 9 is:

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The simplified form of the left side of the equation is $2 \tan x$.

The left side of the equation can be simplified using the quotient and reciprocal identities. The quotient identity states that $\tan x = \frac{\sin x}{\cos x}$ and the reciprocal identity states that $\sec x = \frac{1}{\cos x}$ and $\csc x = \frac{1}{\sin x}$. By substituting these identities into the equation, we can simplify the left side:

\[ \begin{aligned} \frac{\sec x+\tan x \csc x}{\csc x} & =\frac{\frac{1}{\cos x}+\frac{\sin x}{\cos x} \cdot \frac{1}{\sin x}}{\frac{1}{\sin x}} \\ & =\frac{\frac{1}{\cos x}+\frac{1}{\cos x}}{\frac{1}{\sin x}} \\ & =\frac{2 \cdot \frac{1}{\cos x}}{\frac{1}{\sin x}} \\ & =\frac{2}{\cos x} \cdot \frac{\sin x}{1} \\ & =\frac{2 \sin x}{\cos x} \\ & =2 \tan x \end{aligned} \]

Therefore, the simplified form of the left side of the equation is $2 \tan x$.

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Step-by-step explanation:

the perimeter of a rectangle is

2×length + 2×width

simply because the perimeter means to go along every side the shape has.

I don't see any answer options. you did not provide any. I can only give you the approach of how to solve this.

so, that means for us

2(6x + 5) + 2×3x = 100

12x + 10 + 6x = 100

18x = 90

x = 90/18 = 5

Answer:

1,254 - whole number; 0.13 - terminating; 0.123456789... - non-terminating/non-repetitive; 0.143143143... - repeating decimal

Step-by-step explanation:

A whole number is a number without any decimals or fractions. A terminating number is one that has an end. A non-terminating number is one that continues on forever. A repeating number is one that has the same pattern and continues on forever.

The function to represent the total charges for your hotel and car rental is C,) p(x) = 45 + 214x

In other terms, an equation is a mathematical statement stating that "this is equivalent to that." It appears to be a mathematical expression on the left, an equal sign in the center, and a mathematical expression on the right.

Given that hotel, you are going to stay at charge $135 per night. It can be represented by the function p(x) = 135x.

Also, car rental company charges a $45 insurance fee plus $79 per day.

It can be represented by the function p(x) = 45 + 79x.

Daily rental fee = $135 per night,

Write the equation for the total fees

p(x) = 45 + 214x

Thus, x represents the number of days.

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Answer:It will hit the ground when 84 - 16t^2 = 0

Step-by-step explanation:

16t^2 = 84

t^2 = 5.25

t = 2.29

About 71 % of the residents in a town say that they are making an effort to conserve water or electricity. 110 residents are randomly selected. The mean is 0.71. Standard Deviation is 0.043. The probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80% is 0.0183.

1) Mean:
The mean of a proportion is simply the proportion itself, so the mean is 0.71.

2) Standard Deviation:
The standard deviation of a proportion is given by the formula:
σ = √(p(1-p)/n)
where p is the proportion, and n is the sample size. Plugging in the values given in the question:
σ = √(0.71(1-0.71)/110)
σ = 0.043

3) To find this probability, we need to use the normal distribution. We will use the z-score formula:
z = (x - μ) / σ
where x is the proportion we are interested in (0.8), μ is the mean (0.71), and σ is the standard deviation (0.043). Plugging in the values:
z = (0.8 - 0.71) / 0.043
z = 2.09
Using a z-table, we find that the probability of getting a z-score greater than 2.09 is 0.0183. So the probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80% is 0.0183.

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The value for the quadratic equation is C(t) = t² + 3.

When two lines or rays intersect and cross at one endpoint or vertex, a vertex angle is created. This angle, which is expressed in degrees, is occasionally confused with face angle. Two intersecting lines at the corner of a 2D object, such a polygon, generate a vertex angle. In 3D forms, however, multiple angles are conceivable since there are more than two lines.

The standard form of the quadratic function is given as:

C(t) = at² + bt + c

Using different values of t from the table we have:

a(-2)² + b(-2) + c = 7

a(-1)² + b(-1) + c = 4

a(0)² + b(0) + c = 3

Simplifying the equations we have:

4a - 2b + c = 7

a - b + c = 4

c = 3

Substituting the value of c = 3 in equation 2:

a - b = 1

Further solving the equation for a and b we have:

a = 1

b = 0

Hence, the equation for the quadratic equation is C(t) = t² + 3.

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