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The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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Answer: y=-6.4

Step-by-step explanation:

The length of unknown side x is 58.

The correct answer is option D.

To find the unknown side length, x, in a right triangle with the base measuring 42 and the perpendicular measuring 40, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Let x be the hypotenuse. Applying the Pythagorean theorem, we have:

\(x^2 = 42^2 + 40^2\)

Simplifying:

\(x^2\) = 1764 + 1600

\(x^2\)= 3364

Taking the square root of both sides to solve for x:

x = \(\sqrt{3364}\)

Simplifying the square root:

x = (\(\sqrt{4 * 841)}\)

Since 841 is a perfect square (\(29^2\)), we can further simplify:

x = 2 * 29

x = 58

Therefore, the unknown side length, x, is equal to 58.

From the options provided the correct option is D.

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Answer:

C. The items have different y-intercepts and different rates of change

Step-by-step explanation:

Figure I shows a linear equation in the form y = mx + b, where "m" is the rate of change and "b" is the y-intercept. That means for y = 1/4 * x - 1/2, 1/4 is the slope and 1/2 is the y-intercept.

Figure II shows a table. The y-intercept is when x = 0, so look at where x = 0 is in the table and see the y-value which corresponds to it. The y-value in this case would be -0.25. To find the rate of change, assuming Table II is changing at a constant rate, subtract the subsequent y-value from a proceeding y-value and divide that by subtracting the corresponding x-values (any two sets of x and y-values should work): (3.75 - 7.75)/(-1 - -2) = -4/(-1 + 2) = -4/-1 = 4.

Thus, we know that the rates of change are different and the y-intercepts are different for both functions.

The length of the arc defined by the central angle of 312 degrees is 26π cm.

The formula for the arc length of a circle is given by:

L = (θ/360) × 2πr

where L is the length of the arc, θ is the central angle in degrees, and r is the radius of the circle.

Substituting the given values, we get:

L = (312/360) × 2π(30)

L = (26/30) × π × 30

L = 26π cm

Therefore, the length of the arc defined by the central angle of 312 degrees is 26π cm.

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Answer:45

Step-by-step explanation:

9x5=45

15x3=45

4x5=20

4+5=9

Step-by-step explanation:

8x +20 = 6x -18

8x -6x = -18 -20

2x = -38

x = -19

Answer:

x=-19

Step by step:

I did the quiz and got it right

Answer:

10%

Step-by-step explanation:

Answer:

she starts with $25

every three games she spends $1.50 (.50 per game)

Step-by-step explanation:

i mean i cant really explain it, its kinda self explanatory

Answer:

ΔACB ≅ ΔQPR ( SAS congruence )

Step-by-step explanation:

What is SAS congruence ?

Two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the other triangle, according to the SAS (Side Angle Side) rule.

In triangle ΔACB and ΔQPR

                    AC  =     PQ  ( equal sides )

                 ∠ACB  =   ∠QPR ( equal angles between the sides )

                    BC  =   RP      ( equal sides )

Hence         ΔACB ≅ ΔQPR ( SAS congruence )

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Least time required to reach the point Q as per the distance and the speed rate is equal to 2 hours.

As given in the question,

Nearest point on the coast is 2 miles far away

rate of the row = 1mile per hour

Walk at the rate of 3 miles per hour

Let 'x' hours be the least time to reach point Q.

Time = distance / speed

Time taken to reach the point Q = [√ 1 + ( 3 - x)² ]/ 3

Time taken to reach the coast = (√ 4 + x² ) / 1

Total  time taken 't' = (√ 4 + x² ) / 1 + [√ 1 + ( 3 - x)² ]/ 3

To find least time dt/dx = 0

t  = (√ 4 + x² ) / 1 + [√ 1 + ( 3 - x)² ]/ 3

⇒dt/dx = [ x / √ 4 + x² ] + ( 3 - x) / √( 10 -6x + x² )

⇒x / √ 4 + x² = ( x - 3) / √( 10 -6x + x² )

Squaring both the side we get,

x² / (4 + x²) = ( x - 3)² / ( 10 -6x + x² )

⇒3x² -24x +36 =0

⇒ x² -8x + 12 = 0

⇒ x = 2 or 6 hours

Therefore , the least time taken to reach the point Q is equal to 2 hours.

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The ship started at the Position 0.14 units.

To determine the starting position of the ship, we can consider the distance sailed to the left and the distance to the treasure.

Given that you sailed 0.055 units to the left and found the treasure at 0.085 units, we can represent this situation mathematically as follows:

Starting position + Distance sailed to the left = Distance to the treasure

Let's assign a variable, "x," to represent the starting position of the ship.

The equation becomes:

x - 0.055 = 0.085

To find the value of x, we can solve this equation by isolating x on one side:

x = 0.085 + 0.055

x = 0.14

Therefore, the ship started at the position 0.14 units.

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Using the formula X=μ+Zσ, the baby kitten's weight corresponds to the z-scores Z=1.98 and Z=2.87 are 16.656 and 18.614.

In a normal distribution, data points are referred to as x, whereas in a z distribution, they are referred to as z or z scores. A z score is a standard score that indicates how many standard deviations an individual statistic is from the mean (x). The formula used to calculate this z-score is Z= (X-μ)/σ where x is the raw score, σ is the population standard deviation, and μ is the population means. From this formula, X can be calculated as X=μ+Zσ.

For the first z-score, Z = 1.98, σ = 2.2 and μ = 12.3, then

X = 12.3+1.98(2.2) = 16.656

For the second z-score, Z = 2.87, σ = 2.2 and μ = 12.3, then

X = 12.3+2.87(2.2) = 18.614

The answers are 16.656 and 18.614.

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Answer: 4

Step-by-step explanation:

1 third of 30 is 10 and 2/5s of 10 is 4

Answer:

true

Step-by-step explanation:

a. Category with the greatest frequency is 20 - 24

b. 14 students

c. The percentage is 7%

Frequency is simply described as the number of times an event or observation happened in a given study or experiment that is carried out.

From the information given, we have that;

a. The category with the greatest frequency is the one with most words spelt, we have;

20 - 24

b. The number of students that spelt 35 - 39 words is traceable to

14 students

c. If the total number of students is 200

Then, the percent of students in the 35 - 39 category is;

14/200 × 100/1

Multiply the values

7%

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Answer:

99.75

Step-by-step explanation:

The answer for blanks in statements are, an x-intercept of 1 , -3, x>1 , increasing , 7.5.

Many mathematical and real-world phenomena are described by functions. Modeling real-world occurrences like population increase, interest rates, or physical motion is frequently done using them. There are many distinct features that functions can have, including continuity, differentiability, and periodicity. Functions can also be linear or nonlinear.

The domain and range of functions are crucial components. The set of all potential input values makes up the domain of a function, whereas the set of all possible output values makes up the range. The behaviour of a function, such as whether it is increasing, decreasing, or constant, can also be used to categorize it. A function's graph shows the relationship between its input and output values graphically.

Function h has an x-intercept of 1 and a y-intercept of -3.  The function is positive for x>1 and increasing on all intervals of x. The average rate of change for the function on the interval [0, 2] is 7.5

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A possible starting point:

Split up the limit as

\(\displaystyle \lim_{n\to\infty} \frac{1 + \sqrt[3]{2} + \cdots + \sqrt[3]{n}}{n^{4/3}} \times \lim_{n\to\infty} \frac1{n \left(\frac1{(an+1)^2} + \frac1{(an+2)^2} + \cdots + \frac1{(an+n)^2}\right)} = 54\)

Consider the first limit,

\(\displaystyle \lim_{n\to\infty} \frac{1 + \sqrt[3]{2} + \cdots + \sqrt[3]{n}}{n^{4/3}}\)

Refer to the Stolz-Cesàro theorem, which says

\(\displaystyle \lim_{n\to\infty} \frac{a_n}{b_n} = \lim_{n\to\infty}\frac{a_{n+1}-a_n}{b_{n+1}-b_n}\)

where \(a_n\) and \(b_n\) are two real sequences, with \(b_n\) monotone and divergent. In this case,

\(a_n = 1+\sqrt[3]{2}+\sqrt[3]{3}+\cdots+\sqrt[3]{n}\)

\(b_n = n^{4/3}\)

Applying S-C, we get

\(\displaystyle \lim_{n\to\infty} \frac{\sqrt[3]{n+1}}{(n+1)^{4/3} - n^{4/3}} = \lim_{n\to\infty} \frac{(n+1)^{1/3}}{(n+1)^{4/3} - n^{4/3}}\)

Recalling the difference of cubes identity,

\(a^3 - b^3 = (a - b) (a^2 + ab + b^2)\)

we can rewrite the limit as

\(\displaystyle \lim_{n\to\infty} \frac{(n+1)^3 + (n+1)^{5/3} n^{4/3} + (n+1)^{1/3} n^{8/3}}{(n+1)^4 - n^4}\)

and dividing uniformly through the limand by (n + 1)³ yields

\(\displaystyle \lim_{n\to\infty} \frac{1 + \left(\frac n{n+1}\right)^{4/3} + \left(\frac n{n+1}\right)^{8/3}}{(n+1) - \frac{n^4}{(n+1)^3}}\)

Now,

\(n^4 = (n+1)^4 - 4n^3 - 6n^2 - 4n - 1\)

\(\implies \dfrac{n^4}{(n+1)^3} = (n+1) - \dfrac{4n^3+6n^2+4n+1}{(n+1)^3}\)

so the denominator in the limit reduces to a degree-1 polynomial with leading coefficient +4. The numerator converges to 1 + 1 + 1 = 3, so this first limit evaluates to

\(\displaystyle \lim_{n\to\infty} \frac{1 + \sqrt[3]{2} + \cdots + \sqrt[3]{n}}{n^{4/3}} = \frac34\)

It remains to determine the value of a such that

\(\displaystyle \lim_{n\to\infty} \frac1{n \left(\frac1{(an+1)^2} + \frac1{(an+2)^2} + \cdots + \frac1{(an+n)^2}\right)} = \frac43\times54 = 72\)

We have a natural choice of lower and upper bounds for the sum in the denominator:

\(\displaystyle \frac1{(an+n)^2} + \cdots + \frac1{(an+n)^2} \\\\ ~ ~ ~ ~ \le \frac1{(an+1)^2} + \cdots + \frac1{(an+n)^2} \\\\ ~ ~ ~ ~ ~ ~ ~ ~ \le \frac1{(an+1)^2} + \cdots + \frac1{(an+1)^2}\)

\(\implies \displaystyle \frac{n}{(an+n)^2} \le \frac1{(an+1)^2} + \cdots + \frac1{(an+n)^2} \le \frac{n}{(an+1)^2}\)

and

\(\displaystyle \lim_{n\to\infty} n\times\frac{n}{(an+n)^2} = \frac1{(a+1)^2}\)

\(\displaystyle \lim_{n\to\infty} n\times\frac{n}{(an+1)^2} = \frac1{a^2}\)

so that by the squeeze/sandwich theorem,

\(\displaystyle \frac1{(a+1)^2} \le \lim_{n\to\infty} n \left(\frac1{(an+1)^2} + \frac1{(an+2)^2} + \cdots + \frac1{(an+n)^2}\right) \le \frac1{a^2}\)

\(\implies \displaystyle a^2 \le \lim_{n\to\infty} \frac1{n \left(\frac1{(an+1)^2} + \frac1{(an+2)^2} + \cdots + \frac1{(an+n)^2}\right)} \le (a+1)^2\)

and if the middle limit is supposed to evaluate to 72, solving the inequality for a puts it in the interval [6√2 - 1, 6√2] ≈ [7.48528, 8.48528].

Checking against a computer, the solution appears to be a = 8, which agrees with the analysis above. Just not sure how to bridge the gap yet...

Using the normal distribution, it is found that a student has to score 0.6433 standard deviations above the mean to be publicly recognized.

In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The top 26% of the scores are given by scores above the 74th percentile, which corresponds to Z = 0.6433, hence, a student has to score 0.6433 standard deviations above the mean to be publicly recognized.

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Answer:

6/16

Step-by-step explanation:

Answer:

We can use the vector addition property to find the coordinates of the points M, N, and I.

Let

\(\bold{ A = (x_1, y_1), B = (x_2, y_2), C = (x_3, y_3), and\: D = (\frac{x_2+x_3}{2}, \frac{y_2+y_3}{2})}\)

To find M, we use the fact that MA + MB = 0. Therefore, we have:

MA = -MB

A - M = -(B - M)

A - M = -B + M

2M = A + B

M =\(\frac{A + B}{2}\)

So, the coordinates of point M are

\(\bold{(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})}\)

To find N, we use the fact that 3NA + NC = 0. Therefore, we have:

3NA = -NC

3A - N = -(C - N)

3A - N = -C + N

4N = 3A + C

N =\(\frac{ 3A + C}{4}\)

So, the coordinates of point N are \(\bold{(\frac{3x_1+x_3}{4},\frac{ 3y_1+y_3}{4})}\)

To find I, we use the fact that IM + 2IN = 0. Therefore, we have:

IM = -2IN

M - I = -2(N - I)

M - I = -2N + 2I

3I = M + 2N

I = \( \frac{(M + 2N)}{3} \)

Substituting the values of M and N that we found earlier, we get:

I = (A + B + 2(3A + C)/4)/3

Simplifying this expression, we get:

I = \(\frac{(7A + 2B + 2C)}{12}\)

So, the coordinates of a point I are\(\bold{(\frac{7x_1+2x_2+2x_3}{12}, \frac{7y_1+2y_2+2y_3}{12}).}\)

Answer:

y can only be greater than x if x has a variable less than y so the answers is ly- lx

Step-by-step explanation:

The sum of the fraction 74/10 + 42/5 is 15 4/5.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, the fraction will be illustrated as:

= 74/10 + 42/5

Change to mixed numbers

= 7 4/10 + 8 2/5

= 7 4/10 + 8 4/10

= 15 8/10

= 15 4/5

The value is 15 4/5.

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Answer:

3/2 or 1.5

Step-by-step explanation:

Hey there!

\(\huge\boxed{\mathsf{1\dfrac{1}{2}}}}\\\huge\boxed{\mathsf{\rightarrow \dfrac{1\times1+2}{2}}}\\\\\\\huge\boxed{{1\times1+2}}\\\huge\boxed{= 1+2}\\\huge\boxed{=3}\\\\\\\huge\boxed{\rightarrow \mathsf{\dfrac{3}{2}}}\\\\\\\huge\boxed{\textsf{Answer: }\bf \dfrac{3}{2}}\huge\checkmark\\\\\huge\text{Good luck on your assignment \& enjoy your day!}\\\\\\\\\\\huge\boxed{\frak{Amphitrite1040:)}}\)

Answer:

$18

Step-by-step explanation:

Buying the jeans for $27 leaves you with ($60 - $27), or $33.

Buying the shirt for s dollar leaves you with $15.  To find s, the price of the shirt, you subtract $15 from $33:  $18.

The shirt cost you $18.

A line segment that measures 92 millimeters in length can be drawn using scale.

Given that,

A line segment has to be drawn which has a measure of length 92 millimeters.

We know that,

10 millimeters = 1 centimeter

1 millimeter = 1/10 centimeters

92 millimeters = 92/10 = 9.2 centimeters

So it is enough to draw a line segment of length 9.2 centimeters.

In the scale, between a centimeter, there are 9 small lines which indicates the millimeters.

In between 9 and 10, there are 9 lines which indicates, 9.1, 9.2, 9.3, ....., 9.9 and after that is 10 cm.

So draw a line segment starting from 0 to 9.2.

Hence the line segment is drawn with scale.

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If you start at (0,-4) and you move left 1 unit and right 4 units, you end at (3, -4)

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

Start = (0, -4)

Also, we have

You move left 1 unit and right 4 units

Mathematically, this can be expressed as

(x, y) = (x - 1 + 4, y)

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

Endpoint = (0 - 1 + 4, -4)

Evaluate the expression

Endpoint = (3, -4)

Hence, the endpoint is (3, -4)

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