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The value of the fractions in the mixed fraction form is 3(⁷/₉), 4(⁷/₉), and 6(²/₅) respectively.

A mixed fraction is a fraction that is created by fusing a fraction with a whole number. The fraction is defined as the division of the whole part into an equal number of parts.

The given fractions 34/9, 43/9, and 32/5 can be written in the form of the mixed fraction as below:-

To write the fractions in the form of the mixed fraction first divide the fraction by the complete number and put the remainder on the numerator.

34/9 = 3(⁷/₉)

43/9 = 4(⁷/₉)

32/5 = 6(²/₅)

Therefore, the value of the fractions in the mixed fraction form is 3(⁷/₉), 4(⁷/₉), and 6(²/₅) respectively.

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The n-ary rule for linear sequences is 7n - 1. The given sequence is an arithmetic sequence.

What is Arithmetic Progression?

Any two consecutive integers in a sequence are in "arithmetic progression" (AP) if their difference is constant.

The formula is given by Tn = a + (n - 1) d. where,

a, first term = 6 n, number of terms

d, binomial tolerance = 13 - 6 = 7

So substitute the value into the equations. It will be as follows.

Tn = a + (n - 1)d

= 6 + (n - 1)7

= 6 + 7n - 7

= 7n - 1

So the n term of this sequence is 7n - 1. 

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Answer:

The answer is to the question A

Answer:

Its B 100%

i took the test and got it right

k bye :):):):):):):)

Step-by-step explanation:

Answer:

You use the formula (y to the second power minus y to the first power minus the same formula with the two different points

Step-by-step explanation:

Solution:

Given:

The radius and tangent to a circle at the point of intersection are perpendicular to each other.

Hence, considering the right triangle;

Hence, the length of the missing side can be gotten using the Pythagorean theorem.

Therefore, to the nearest tenth, the length of the missing side is 6.3

Blank 1: Corresponding because All angles that are either exterior angles, interior angles, alternate angles or corresponding angles are all congruent.

Blank 2:

Blank 3: x= 46 as 180-134 = 46

Answer:

Step-by-step explanation:

An inequality has two solutions, we have to figure out if x is greater than a number or less. There are a few special rules when solving inequalities.

1. When we divide by a negative number, we must reverse the inequality sign.

2. When we check the solution of an inequality, we need to try two numbers to ensure that we have the sign in the correct direction.

Let's solve!

-3x - 5 > 10

-3x - 5 + 5 > 15

-3x > 15

-3x/-3 > 15/-3

Remember: When we divide by negative numbers, we must reverse the sign as seen below, so greater than becomes less than.

x < -5

Now we will check two different numbers from our solution set to ensure that we have the correct answer.

-3(-6) - 5 > 10

18 - 5 > 10

13 > 10 ✔️

Remember: When we check inequalities, we need to check two solutions, so we will go with -8 for the second check, since it is also less than -5.

-3(-8) - 5 > 10

24 - 5 > 10

19 > 10 ✔️

The solution set for this inequality is any number less than -5 or x < -5 (not including -5)

Answer:

Hi! The answer is B!

I would suggest using a graphing calculator to compare all the lines. You can use this free one called Desmos, sorry i was not able to attach a link :)

By rational number algebra, the mixed number 3 5 / 11 is equivalent to the decimal expansion 3.\(\overline {45}\).

According to the statement, we find a mixed number, that is, a notation to represent rational numbers that combines both integers and fractions. The procedure to obtain the decimal form of a mixed number is:

Then, the decimal expansion of the mixed number 3 5 / 11 is:

3 5 / 11 = (3 · 11) / 11 + 5 / 11 = 33 / 11 + 5 / 11 = 38 / 11 = 3.\(\overline {45}\)

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Answer:

I just finished taking the test and the answer is 15s + 25c ≤ 1500

The speed of the faster cyclist is 14\ miles/hr.

What is speed?

It is the average distance coverd in unit time. It is also defined as the rate of change of distance with respect to time.

Since the speed of the first cyclist is double than the second cyclist hence, the first cyclist will cover the double distance than the second cyclist. Consider the first cyclist covers 2s distance and first cyclist covers s distance. The sum of these two distances should be 42 miles. Hence,

\(2s+s=42\\3s=42\\s=14\)

Now, distance coverd by the first cyclist is \(2s=2\times 14\\=28 \ $miles\).

Now, both the cyclists meet after 2 hr hence, time taken by the first cyclist is 2 hr.

\(Speed=\frac{Total\ distance}{Total\ time}\\=28\ miles/2 \ hr\\=14\ miles/hr\)

Hence, the speed of the faster cyclist is 14\ miles/hr.

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A chart or graph that presents grouped data with rectangular bars with lengths proportional to the values that they represent is known as a bar graph.

A bar graph is a way to visually represent data using rectangular bars with lengths proportional to the values that they represent.

The bars can be either vertical or horizontal, depending on the orientation of the graph. The vertical bars are known as a column graph, while the horizontal bars are known as a bar chart.

The purpose of a bar graph is to provide a clear and concise representation of data that is easy to understand and interpret. Bar graphs are commonly used to compare different sets of data or to track changes in data over time.

They can be used to show how a particular variable changes over time or to compare the values of different variables in a single graph.

Bar graphs are easy to read and interpret, making them a popular choice for both simple and complex data sets.

They are widely used in business, science, and education, among other fields, to present information in a clear and concise manner.

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Answer:

3 x 3 = 9 + 3 x 3 = 9 which would be 18, then add 7 and 3 which would be 10 then multiply it by 5 which would be 50 then divided by 2 and you would get 25 add 25 two times which would be 50 once you do, you add the 18 which would be 68 in square.

Step-by-step explanation:

we can say with 99% confidence that the true proportion of times the number cube would land with a six facing up is between 0.05 and 0.49.

To find the 99% confidence interval for the true proportion of times the number cube would land with a six facing up, we can use the formula:

CI = p ± zsqrt(p(1-p)/n)

where:

CI is the confidence interval

p is the sample proportion (number of times the cube landed with a six facing up divided by the total number of rolls)

z is the z-score corresponding to the desired confidence level (99% in this case)

n is the sample size (45 in this case)

First, let's calculate the sample proportion:

p = 12/45 = 0.27

Next, we need to find the z-score corresponding to a 99% confidence level. Using a standard normal distribution table or calculator, we find that the z-score is 2.58.

Now we can plug in the values and calculate the confidence interval:

CI = 0.27 ± 2.58sqrt(0.27(1-0.27)/45)

CI = 0.27 ± 0.22

CI = (0.05, 0.49)

The number cube would land with a six facing up between 0.05 and 0.49.

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(a) tangent line to the graph of f(x) = x^3 at the point (4,2).

(b) equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12).

(a) To find the equation of the tangent line to the graph of f(x) = x^3 at the point (4,2), we need to find the slope of the tangent line at that point. We can do this by taking the derivative of f(x) with respect to x and evaluating it at x = 4. The derivative of f(x) = x^3 is f'(x) = 3x^2. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Once we have the slope, we can use the point-slope form of a linear equation to write the equation of the tangent line.

(b) Similarly, to find the equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12), we differentiate f(x) to find the derivative f'(x). The derivative of f(x) = x^2 - x is f'(x) = 2x - 1. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Using the point-slope form, we can write the equation of the tangent line.

In both cases, the equations of the tangent lines will be in the form y = mx + b, where m is the slope and b is the y-intercept.

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Answer:

In 25 minutes, the monthly phone charges of both companies will be the same.

Step-by-step explanation:

If we allow m to represent the number of minutes, we can create two equations for C, the total cost of phone charges from both companies:

Phoenix equation:  C = 0.5m + 30

Nuphone equation: C - 0.10m + 40

Now, we can set the two equations equal to each other.  Solving for m will show us how many minutes must Abby use for the total cost at both companies to be the same:

0.5m + 30 = 0.10m + 40

Step 1:  Subtract 30 from both sides:

(0.5m + 30 = 0.10m + 40) - 30

0.5m = 0.10m + 10

Step 2:  Subtract 0.10m from both sides:

(0.5m = 0.10m + 10) - 0.10m

0.4m = 10

Step 3:  Divide both sides by 0.4 to solve for m (the number of minutes it takes for the total cost of both companies to be the same)

(0.4m = 10) / 0.4

m = 25

Thus, Abby would need to use 25 minutes for the total cost at both companies to be the same.

Optional Step 4: Check the validity of the answer by plugging in 25 for m in both equations and seeing if we get the same answer:

Checking m = 25 with Phoenix equation:

C = 0.5(25) + 30

C = 12.5 + 30

C = 42.5

Checking m = 25 with Nuphone equation:

C = 0.10(25) + 40

C = 2.5 + 40

C = 42.5

Thus, m = 25 is the correct answer.

The equations will be re-written such that the expression on one side can be graphed and the x-intercepts of the graph would indicate the solution.

A) 3X² = 81

Rewritten, we have  3X² - 81 = 0

This is also = 3(X² - 27) = 0

B) (X - 1)(X + 1) - 9 = 5X

Open the brackets and we have X² - 1 - 9 - 5x = 0

Simplified, we have X² - 5X - 10 = 0

C) X² - 9x + 10 = 32

Collect like terms and we have:
X² - 9X - 22 = 0

D) 6x(x - 8) = 29

Expand the bracket and collect like terms such that the equation is equal to zero and we have

6X² - 48x - 29 = 0

Using Desmos Graphing, the following results can be obtained showing that x intercepts at:

(a) (-5.196, 0) & (5.196, 0)

(b) (-1.531, 0) & (6.531, 0)

(c) (-2, 0) & (11, 0)

(d) (-0.564, 0) & (8.564, 0)

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Sarah's company started out with a $350 value and is currently changing at a rate of $100 annually.

The annual fee is expressed as an equation in slope-intercept form:

y = 100x + 350.

y = mx + b, where m is the line's slope and b is its y-intercept, is the formula for a straight line.

Given details:

The table displays the prices that Sarah charged each client during the course of her business's first two years:

Year                            Annual Dog-walking Fee

2010                            $350

2014                            $750

A.

Sarah has so increased the cost by $400 over the past four years.

For Sarah's company, its rate of change called slope will be,

m = 750 - 350 / 4

m = 100

Therefore, Sarah is raising the cost by $100 yearly.

Due to the payment she received for the first year, the calculated values of a business is $350.

B. Define x as the period of time that has passed since she began her business in 2010.

Consequently, the annual fee equation can be expressed in slope-intercept form as,

y = mx + c

where y stands for the cost she must pay after x years.

Her company's baseline value is therefore $350, and its rate of change is $100 annually.

The annual fee is expressed as an equation in slope-intercept form.: y = 100x + 350.

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Answer:

9x^2-12x+4=0

Step-by-step explanation:

you can use factorization method or Quadratic method (Almighty formular).

‍

The number of the solution of the equation is 2 and the solution is equal and real which is 2/3.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The quadratic equation is ax² + bx + c = 0. Then the discriminant is given as,

D = b² - 4ac

The equation is given below.

9x² - 12x + 4 = 0

The discriminant is given as,

D = (-12)² - 4 x 9 x 4

D = 144 - 144

D = 0

Then the roots of the equation is given as,

9x² - 12x + 4 = 0

(3x)² - 2 · 3x · 2 + (2)² = 0

(3x - 2)² = 0

x = 2/3

The number of the solution of the equation is 2 and the solution is equal and real which is 2/3.

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The center of mass of the wire is (64/15, 0). To find the mass of the wire, we need to calculate its length first.

Since the wire is bent into the shape of a semicircle, its length is half the circumference of a circle with radius 8 units (since x>=0). Therefore, the length of the wire is πr = π(8) = 8π.

The linear density of the wire is given as k, which means that its mass per unit length is k. Thus, the mass of the wire is the product of its length and linear density: mass = k(8π) = 8kπ.

To find the center of mass, we need to locate the centroid of the semicircle. By symmetry, the centroid lies on the x-axis, and we only need to find its x-coordinate.

The x-coordinate of the centroid can be found using the formula:

x¯ = (1/M) ∫(x dM)

where M is the mass of the wire, and the integral is taken over the semicircle.

Using polar coordinates (x = rcosθ, y = rsinθ), we can rewrite the equation of the semicircle as y = (64-x^2)^0.5.

Then, we have:

dM = kds = k(sqrt(1+(dy/dx)^2))dx = k(1+(x^2/(64-x^2)))^(1/2) dx

Integrating from x=0 to x=8, we have:

x¯ = (1/M) ∫(x dM) = (1/8kπ) ∫(x (1+(x^2/(64-x^2)))^(1/2) dx) = 64/15

Therefore, the center of mass of the wire is (64/15, 0).

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39 subjects were tested in this simple one-way ANOVA.

The df for F distribution is (treatment df, error df)

Using given information

Treatment df = 7

Error df = 31

Total df= 7+31 = 38

Again, total df = N-1, N= number of subjects tested

Then, N-1 = 38

=> N= 39

One-way ANOVA is typically used when there is a single independent variable or factor and the goal is to see whether variation or different levels of that factor have a measurable effect on the dependent variable.

The t-test is a method of determining whether two populations are statistically different from each other, and ANOVA determines whether three or more populations are statistically different from each other.

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Answer:

6 gallons

Step-by-step explanation:

32/4=8

48/8=6

Answer: 6

Step-by-step explanation: If 4 gallons can take you 32 miles, divide 4 into 32 to get 8. That means 8 miles is 1 gallon. Now just do 48/8 to get 6.

The intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

To show that a1 ≤ a2 ≤ ... ≤ an ≤ ..., we need to use the fact that the sequence of intervals is nested, meaning that each interval is contained within the next one.

First, we know that I1 contains I2, so every point in I2 is also in I1. That means that a1 ≤ a2 and b1 ≥ b2.

Now consider I2 and I3. Again, every point in I3 is also in I2, so a2 ≤ a3 and b2 ≥ b3.

We can continue this process for all the intervals in the sequence, until we reach In. So we have:

a1 ≤ a2 ≤ ... ≤ an-1 ≤ an

and

b1 ≥ b2 ≥ ... ≥ bn-1 ≥ bn

This shows that the endpoints of the intervals are ordered in the same way.

Given that I₁ ⊇ I₂ ⊇ ... In ⊇ ... is a nested sequence of intervals and In = [an; bn], we can show that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... as follows:

Since the intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

Continuing this pattern for all intervals in the sequence, we can conclude that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... .

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Answer:

g(x)=x2-4

Step-by-step explanation:

The numerical of the graph g(x) = x² - 4 shifted 4 units down.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over y-axis, (-x, y).

-f(x) = Reflection over x-axis, (x, -y).

Given, The parent function is f(x) = x² which is a parabola that opens upwards and has a vertex at (0, 0).

Now, The transformed graph of f(x) which is g(x) = x² - 4 as the graph has shifted 4 units down along the y-axis.

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The probability that a student scored less than 55% on the exam is 0.134%.

It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.

We have:

Mean of the sample = 70

Standard deviation = 5

= P(X<55%)

Z = (55-70)/5

Z = -3

P(X < -3)

From the Z table:

P(x<-3) = 0.0013499

or

P(x<-3) = 0.134%  

Thus, the probability that a student scored less than 55% on the exam is 0.134%.

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Answer:

9.7 miles

Step-by-step explanation:

The shortest distance between 2 points is a straight line

The distance from point A to point B is

d = sqrt( ( x2-x1)^2 + ( y2-y1) ^2)

d = sqrt( ( 3 - -3)^2 + ( 4-1) ^2)

d = sqrt( ( 6)^2 + ( 3) ^2)

d = sqrt(36+9)

d = sqrt(45)

d =6.7  to the nearest tenth

The distance from point B to point C is

d = sqrt( ( x2-x1)^2 + ( y2-y1) ^2)

d = sqrt( ( 3 - 3)^2 + ( -2-4) ^2)

d = sqrt( ( 0)^2 + ( -6) ^2)

d = sqrt(36)

d = 6

But They only made it half way so 1/2 (6) =3

Add the distances together

6.7+3 = 9.7 is the minimum distance

The sum of expression \(1.723 \times 10^{2}\) and \(7.38 \times 10^{3}\) is \(7.5523 \times 10^{3}\). The numbers in scientific notation are added by summing the coefficients while keeping the exponent unchanged.

In scientific notation, numbers are expressed as a coefficient multiplied by a power of 10. To add numbers in scientific notation, we need to ensure that the powers of 10 are the same.

In this case, both numbers are already in scientific notation with powers of 10. We can directly add the coefficients while keeping the exponent the same.

Adding \(1.723 \times 10^2\) and \(7.38 \times 10^3\) gives us a sum of \(7.5523 \times 10^3\). The coefficient represents the numerical value, and the power of 10 indicates the magnitude.

Thus, the expression \(1.723 \times 10^2 + 7.38 \times 10^3\) evaluates to \(7.5523 \times 10^3\), indicating a significant increase in magnitude compared to the individual numbers.

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20371.83 cm³ is the maximum volume of a cylinder.

The space occupied within an object's borders in three dimensions is referred to as its volume.

It is sometimes referred to as the object's capacity.

So, consider a cylinder with a radius of r and a height of h.

The cylinder's volume is: V = πr²h

Because its height plus circumference equals 120 cm.

h + 2πr

h = 120 - 2πr

Changing the value of h in the cylinder's volume equation:

V = πr² (120-2πr)

V = 120πr² - 2π²r³

To get the biggest volume, compare the above expression to r and equate it to zero:

dV/dx = 240πr - 6π²r² = 0

6πr(πr-0) = 0

r = 0, r = 40/π

The cylinder's radius is: r = 40/π

Now: h = 120 - 2π(40/π) = 80cm

Changing the values of r and h in the cylinder's volume formula:

V = π(40/π)²*40 = 20371.83 cm³

Value of π = 3.14

Therefore, 20371.83 cm³ is the maximum volume of a cylinder.

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To find the percentage, we can use the formula: (part/whole) x 100%. In this case, the part is 10.8 and the whole is 240. So, substituting these values in the formula, we get (10.8/240) x 100% = 4.5%. Therefore, 10.8 is 4.5% of 240. To round to four decimal places, we can keep the first four digits after the decimal point, which gives us 4.5000%.

To find what percent of 240 is 10.8, follow these steps:

Step 1: Write the problem as a proportion using the given values.
x% = (10.8 / 240)

Step 2: Convert the percentage to a decimal by dividing x by 100.
x/100 = (10.8 / 240)

Step 3: Solve for x by cross-multiplying.
100 * 10.8 = 240 * x

Step 4: Divide both sides by 240 to isolate x.
x = (100 * 10.8) / 240

Step 5: Calculate the value of x.
x = 1080 / 240

Step 6: Simplify the fraction and, if necessary, round to four decimal places.
x = 4.5000

Therefore, 10.8 is approximately 4.5000% of 240.

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