find a rational number between 3 and 4​

Answer:

64 Nickels

Step-by-step explanation:

172 coins equal $14.00

It took time to figure this out, I just used a calculator to shimmy down the gap of possibilities, starting here;

100d = $10.00

72n = $3.60

I got closer here;

110d = $11.00

62n =$3.10

I subtracted 2 dimes and added 2 nickels from the previous to get the answer.

108d = $10.80

64n = $3.20

$10.80 + $3.20 = $14.00

The rate of change of the volume with respect to s when s = 15 centimeters is 3375 centimeters

The formula for volume of a cube is given as;

Volume = a³

Where:

a = length of its side

From the information given, we have;

V = s³

Where s = 15 centimeters

Substitute the value into the formula

v = (15)³

v = 3375 centimeters

Thus, the rate of change of the volume with respect to s when s = 15 centimeters is 3375 centimeters

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If using the method of completing the square to solve the quadratic equation number 1 be added to both side of the equation to be added to "complete the square".

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. The requirement that the coefficient of x² be a non-zero term (a 0) is necessary for an equation to qualify as a quadratic equation. The x² term is written first when constructing a quadratic equation in standard form, then the x term, and finally the constant term.

Add 1 to both sides of the equation to get:

\(x^2+4x+4=1\)

The left hand side is now a perfect square:

\(x^2+4x+4=(x+2)^2\)

So we have:

\((x+2)^2=1\)

Hence:

\(x+2=\pm\sqrt{1} =\pm1\)

Subtract 2 from both ends to get:

x = -2 ± 1

That is:

x = -3 or x = -1.

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Answer:

22

Step-by-step explanation:

1/2x + 6 = 17

subtract 6 from each side of the equation:

1/2x = 11

multiply both sides by 2:

x = 22

Answer

\(2\sqrt{42} +7\sqrt{x2}-6-\sqrt{21}\)

Answer:

x = 6

y = 3

6 twenty-five paisa coin

3 fifty-paisa coins

Step-by-step explanation:

x -----> twenty-five paisa coin

y -----> fifty-paisa coins

0.25x + 0.5y = 3.00        per 100

x = 2y

25x + 50y = 300

x = 2y

25(2y) + 50y = 300

50y + 50y = 300

100y = 300

y = 300/100

y = 3

x = 2y

x = 2(3)

x = 6

(a) The limit of f(x) as x approaches a = -2 does not exist.
(b) The limit of f(x) as x approaches a = 0 is 1.
(c) The limit of f(x) as x approaches a = 0 is 0.
(d) The limit of f(x) as x approaches a = 0 is 3/2.

(a) To determine the limit of f(x) = (x+2) / (√(6+x) - 2) as x approaches -2, we substitute -2 into the function: f(-2) = (-2+2) / (√(6-2) - 2) = 0/0, which is an indeterminate form. Taking the limit as x approaches -2 from the left and right sides yields different results, so the limit does not exist.

(b) For f(x) = 2x+1, if x is rational, we can see that regardless of whether x is rational or irrational, the function f(x) = 2x+1 is continuous everywhere. Thus, the limit of f(x) as x approaches 0 is the same as the function value at a = 0, which is f(0) = 2(0)+1 = 1.

(c) Considering the function f(x) = x² * cos(1/(sin(x))^4, we need to evaluate the limit as x approaches 0. As x approaches 0, the term 1/(sin(x))^4 approaches infinity. Since the cosine function oscillates between -1 and 1, the term x² will be multiplied by values between -1 and 1, resulting in the entire function f(x) oscillating between -x² and x². Therefore, the limit of f(x) as x approaches 0 is 0.

(d) For f(x) = 3 * (tan(2x))^2 / (2x²), we substitute a = 0 into the function: f(0) = 3 * (tan(2(0)))^2 / (2(0))^2 = 0/0, which is an indeterminate form. By applying L'Hôpital's rule, we differentiate the numerator and denominator with respect to x. Differentiating the numerator gives 6tan(2x)sec²(2x), and differentiating the denominator gives 4x. Substituting a = 0 into the derivatives yields 6(0)sec²(2(0))/4(0) = 0/0. Applying L'Hôpital's rule again, we differentiate once more, resulting in 12sec²(2x)tan(2x)sec²(2x) / 4 = 12(1)(0)(1) / 4 = 0/0. Applying L'Hôpital's rule repeatedly, we find that the limit of f(x) as x approaches 0 is 3/2.

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Answer:

120 1 062 = × P . giving P = ÷ 120 1 062 . = 106 799

Answer:

not enough info

Step-by-step explanation:

Answer:

91 squares

Step-by-step explanation:

It is adding on by 2, 4, 6, 8... So in the next figure (5), they would add on 8 squares. Now you have 13+8=21.

Then Figure 6. Add on 10. You have 31.

Figure 7. Add 12. You have 43.

8. Add 14. 57.

9. 16. 73.

Figure 10. Add 18. You get 91.

A sampling is a subset of an unit that is tested or examined in to make inferences about the larger population, whereas a census refers to the entire population, things, or information we're interested in analyzing.

Population pyramids that are expansive, constrictive, or stationary can be created using age-sex distributions.

The term "population" in the context of statistics means the whole set of individuals, objects, or metrics we're interested in investigating.

A sample, on the other hand, is a portion of a population that is actually measured or observed in order to draw conclusions about the full population.

Before we can determine the sample and population of a math issue, we must first select the topic we're interested in finding out.

For instance, if we were to look at worldwide average heights, the population would be made up of everyone alive today.

Choosing whether to investigate the whole population or simply a subset of it is the next stage.

If we are studying the overall community, no sample is necessary.

Hence, even if we are only looking at a small section of the population, we must collect a sample.

For instance, if we were to study the heights the people there, the population would be the whole of the United States.

We might measure the elevations of 1000 people randomly selected from the population, drawn from different regions of the United States, if we wished to sample this population.

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Answer

LINE OF REFLECTION

Step-by-step explanation:

In geometry, reflection basically just means flipping things over a line.

Answer:

$350 - $180 = $170

$180 = T

$170 = F

T = Tatiana

F = Family

Step-by-step explanation:

Answer:

Equation to express how much Tatiana spent on her family

= $(350-180)

Answer: \(x^{10}\)

If I Helped, Please Mark Me As Brainliest, Have A Great Day :D

Therefore, the answer is D. Block 1 IQR: 20; Block 2 IQR: 5. Therefore, the answer is B. Block One: 25, Block Two: 100. Therefore, the answer is B. Block 1 is skewed right, Block 2 is skewed left. Therefore, the answer is option A: mean: 76.5, standard deviation: 21.6.

In statistics, the mean (or arithmetic mean) is a measure of central tendency of a set of numerical data. It is calculated by adding all the values in the dataset and dividing by the number of values. The mean is often used as a representative value for a dataset, as it provides a single value that summarizes the entire dataset. However, it can be affected by extreme values (outliers) in the dataset.

Here,

1. To find the interquartile range (IQR) for each block, we first need to determine the quartiles. We can do this by finding the median (Q2) of each block, and then finding the median of the lower half (Q1) and upper half (Q3) of the data.

For Block 1:

Q1: median of {25, 60, 70, 75, 80} = 70

Q2: median of {85, 85, 90, 95, 100} = 90

Q3: median of {70, 75, 80, 85, 90} = 80

IQR = Q3 - Q1 = 80 - 70 = 10

For Block 2:

Q1: median of {70, 70, 75, 75, 75} = 75

Q2: median of {75, 75, 80, 80, 85} = 80

Q3: median of {80, 85, 100, 75, 75} = 82.5

2. To identify outliers, we can use the 1.5 x IQR rule. Any data point that is more than 1.5 x IQR above Q3 or below Q1 is considered an outlier.

For Block 1:

Q1 = 70

Q3 = 80

IQR = 10

1.5 x IQR = 15

The only data point that is more than 15 above Q3 is 100, so it is an outlier.

For Block 2:

Q1 = 75

Q3 = 82.5

IQR = 8

1.5 x IQR = 12

There are no data points that are more than 12 above Q3 or below Q1, so there are no outliers.

3. To determine if each block's data is symmetric, skewed left, or skewed right, we can examine the shape of the distribution.

For Block 1, the data is:

Highest at 100, with several values clustered around the upper end of the range.

No values below 25, which suggests a lower boundary.

Median is 90.

No values are particularly isolated from the rest of the data.

This suggests that Block 1 is skewed right.

For Block 2, the data is:

Highest at 75, with several values clustered around the middle of the range.

No values below 70, which suggests a lower boundary.

Median is 80.

No values are particularly isolated from the rest of the data.

This suggests that Block 2 is skewed left.

4. To find the mean of Block 1, we add up all the scores and divide by the number of scores:

mean = (25 + 60 + 70 + 75 + 80 + 85 + 85 + 90 + 95 + 100) / 10

mean = 765 / 10

mean = 76.5

To find the standard deviation of Block 1, we need to first calculate the variance.

To do that, we can use the formula:

variance = (sum of (each score - mean)²) / (number of scores - 1)

First, we'll find the sum of (each score - mean)²:

(25 - 76.5)² = 2562.25

(60 - 76.5)² = 270.25

(70 - 76.5)² = 42.25

(75 - 76.5)² = 2.25

(80 - 76.5)² = 12.25

(85 - 76.5)² = 71.25

(85 - 76.5)² = 71.25

(90 - 76.5)² = 182.25

(95 - 76.5)² = 379.25

(100 - 76.5)² = 562.5

Next, we'll add up these values:

2562.25 + 270.25 + 42.25 + 2.25 + 12.25 + 71.25 + 71.25 + 182.25 + 379.25 + 562.5 = 3154.5

Now we can plug this into the variance formula:

variance = 3154.5 / 9

variance = 350.5

Finally, to get the standard deviation, we take the square root of the variance:

standard deviation = √(350.5)

standard deviation = 18.7 (rounded to one decimal place)

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Answer:

$ 30

$ 20

Step-by-step explanation:

Sea el costo fijo xy el costo por km sea y suponiendo que es el mismo para ambos taxis.

De la pregunta obtenemos las dos ecuaciones

\(x+8y=190\quad ...(i)\)

\(x+5y=130\quad ...(ii)\)

Aplicando \((i)-(ii)\)

\(8y-5y=190-130\\\Rightarrow 3y=60\\\Rightarrow y=\dfrac{60}{3}\\\Rightarrow y=20\)

Sustituyendo en \((ii)\)

\(x+5y=130\\\Rightarrow x+5\times 20=130\\\Rightarrow x=130-100\\\Rightarrow x=30\)

Entonces, el costo fijo es de $ 30 y el costo por km es de $ 20.

Answer:

1=1

Step-by-step explanation:

expand (cost - sint)²= cost² - 2costsint +sint²

(cost +sin t)² = cost² + 2sintcost+sint²

simplifying these = 2(cost²+sint²)= 2

2 will divide with 2 giving 1

çost²+sint²=1

substituting cost²= 1-sint² in above equation

1-sint²+sint²=1

giving us 1=1

Answer:

To divide £300 in the ratio of 10:20, we need to first add the two parts of the ratio to find the total number of parts:

10 + 20 = 30

This means that the ratio can be expressed as 10/30 and 20/30.

Next, we can use these ratios to find the amount of money for each part of the ratio:

10/30 x £300 = £100

20/30 x £300 = £200

Therefore, the amount of money for the parts of the ratio 10:20 would be £100 and £200 respectively.

The value of 'x' is 60.

We are given with \(\frac{-5}{6}x-\frac{-7}{30}x+\frac{1}{5}x=-52\)

⇒ \(\frac{-25x-7x+6x}{30}=-52\)

⇒ \(\frac{-26x}{30}=-52\)

⇒ \(x = 2 \times 30\)

\(\therefore x=60\)

So the value of 'x' is 60.

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The expression is (3+4=5) Or (3+4≥5). The expression is false. The expression as (3+4=7) or(3+4>5). The number 7 is true.

Given that,

The expression is (3+4=5) Or (3+4≥5).

We have find the value and the expression is true or false.

The expression is false

3+4=5

7=5

The number 7 is not equal to 5.

Now

3+4≥5

7≥5

The number 7 is not equal to 5 but it is greater then 5.

So, we can write the expression as (3+4=7) or(3+4>5)

Therefore, The number 7 is not equal to 5 or The number 7 is not equal to 5 but it is greater then 5. The expression as (3+4=7) or(3+4>5).

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There are 384 ways to arrange these given letters as per the given situation.

A permutation is an orderly arrangement of things or numbers. Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.

Given, different ways can the 8 letters a, b, c, d, e, f, g, and h be arranged if the letters a and b must be next to one another, the letters c and d must be next to one another, the letters e and f must be next to one another, and the letters g and h must be next to one another.

In this question, we have 2 ways where A and B (AB, BA) are next to each other and 2 ways where C and D (CD, DC) are next to each other.  2 ways where g and h (gh, hg) are next to each other and 2 ways where e and f (ef, fe) are next to each other.

The total number of arrangements is = 4! * 2 * 2 *2*2

The total number of arrangements is = 24 * 16

The total number of arrangements is = 384

Therefore, the Different ways to arrange these letters are 384.

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A ray has only one endpoint. A segment has two endpoints.

What is a line?

A line is an object in geometry that is infinitely long and has neither width nor depth nor curvature. Since lines can exist in two, three, or higher-dimensional spaces, they are one-dimensional objects. In everyday language, a line segment with two points designating its ends is also referred to as a "line."

A ray and a segment are parts of a line.

This line segment has two fixed-length endpoints, A and B. The distance between this line segment's endpoints A and B is its length.

In other words, a line segment is a section or element of a line with two endpoints. A line segment, in contrast to a line, has a known length.

A line segment's length can be calculated using either metric units like millimeters or centimeters or conventional units like feet or inches.

Ray has only one endpoint and the other ends go infinity.

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It will be either Options A, D and E are correct.

When a plane cuts a solid, such as a cone, cylinder, or sphere, it creates a shape known as a cross-section. Depending on how the plane cuts the cone, the cross-section of a solid, such as a cone, can be a circle, a parabola, or a triangle.

Given:

A cone is intersected by a plane.

A cone that is crossed by a plane

When the cone intersects the plane, we must determine the shape of the cross-section.

When the Plane intersects the cone parallel to the base, the resulting cross-section is circular in shape.

When the plane intersects the cone at an angle, the resulting cross section is of parabola shape.

As a result, choices A, D, and E are correct.

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The volume of the solid whose base is a circle with radius 25 and cross-sections perpendicular to the x-axis that are squares is 1562500π/3 cubic units.

Let's consider a cross-section of the solid at a distance x from the center of the circle. This cross-section is a square with side length equal to the diameter of the circle minus 2x. Since the diameter of the circle is 50, the side length of the square can be expressed as 50 - 2x.

The volume of the solid can be found by integrating the area of each cross-section over the interval [0, 25]. The area of each cross-section is simply the square of the side length, which can be expressed as (50 - 2x)².

So, the volume of the solid can be found by integrating (50 - 2x)² with respect to x over the interval [0, 25]:

V = ∫[0,25] (50 - 2x)² dx

This integral can be evaluated using integration by substitution, with u = 50 - 2x:

du/dx = -2

dx = -1/2 du

When x = 0, u = 50, and when x = 25, u = 0. So, the integral becomes:

V = ∫[50,0] u² (-1/2) du

V = (-1/2) ∫[50,0] u² du

V = (-1/6) [u³]50_0

V = (-1/6) [(50³) - (0³)]

V = 1562500π/3

Therefore, the volume of the solid whose base is a circle with radius 25 and cross-sections perpendicular to the x-axis that are squares is 1562500π/3 cubic units.

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the area enclosed by the curves x = -2, x = 3, y = 3x² - 28, and y = 4x + 11 is -1014/27 square units.

To find the area enclosed by the curves x = -2, x = 3, y = 3x² - 28, and y = 4x + 11, we can integrate the difference between the upper and lower curves with respect to x.

First, let's find the points of intersection between the curves to determine the limits of integration.

Setting the two y-equations equal to each other:

3x² - 28 = 4x + 11

Rearranging the equation:

3x² - 4x - 39 = 0

We can solve this quadratic equation to find the x-values of the points of intersection. Factoring or using the quadratic formula, we find:

(x - 3)(3x + 13) = 0

This gives two solutions: x = 3 and x = -13/3.

Therefore, the limits of integration for the x-coordinate are -13/3 to 3.

To calculate the area, we integrate the difference between the upper curve (3x² - 28) and the lower curve (4x + 11) with respect to x:

A = ∫[-13/3, 3] [(3x² - 28) - (4x + 11)] dx

Simplifying:

A = ∫[-13/3, 3] (3x² - 4x - 39) dx

Integrating term by term:

A = [(x³ - 2x² - 39x)]|_[-13/3 to 3]

Evaluating the definite integral:

A = [(3³ - 2(3)² - 39(3)) - ((-13/3)³ - 2(-13/3)² - 39(-13/3))]

A = [(27 - 18 - 117) - ((-2197/27) - 2(169/9) + 507/3)]

A = [-108 - (-2197/27 + 338/9 + 507/3)]

A = [-108 - (-1902/27)]

A = [-108 + 1902/27]

A = (1902/27) - (2916/27)

A = -1014/27

Therefore, the area enclosed by the curves x = -2, x = 3, y = 3x² - 28, and y = 4x + 11 is -1014/27 square units.

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Answer: A

Step-by-step explanation:

I did the quiz

a) d/dt [√(289 - 8²)] = d/dt [√(255)] = d/dt [√(5²*17)] = 5/2√17 m/s.

b) The required value is the rate of change of x when the top of the ladder is 8 feet from the ground, then y = 15 feet.

a) Determine how fast the bottom of the ladder is sliding away when the top of the ladder is 8 feet from the ground. As the ladder leans against the side of the house, it makes a right angle with the ground. Using Pythagorean Theorem, the length of the ladder is given by.

Ladder length = √(hypotenuse)² - (height)²= √(17² - height²) meters. Taking the derivative of both sides of this equation, we get: dL/dt = [d/dt √(289 - h²)] meters/sec. Let h = 8 feet, dL/dt = -5 feet/sec.

Thus, the rate of change of the bottom of the ladder is d/dt [√(289 - h²)] meters/sec when the top of the ladder is 8 feet from the ground, and the bottom of the ladder is sliding away at a rate of 5 feet/sec.

b) At what rate is the angle o between the ladder and the ground changing then. Let y be the height of the ladder and the angle it makes with the ground be x. From the given values, y = 17 cos x.

Taking the derivative of both sides with respect to time: dy/dt = -17 sin x (dx/dt)In the given problem, dx/dt = -5/17sin x. Then, dy/dt = 5 sin x cos x= (5/2) sin 2x.

Solving this value of sin x by Pythagorean Theorem, sin x = 8/17. Substituting the value in the equation for the derivative, we get: dy/dt = (5/2) * sin 2x= (5/2) * sin 2(arc sin(8/17))= (5/2) * (2*8/17 * 15/17)= (600/289) ft/sec.

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