I’ll give the Brainliest to who answers this question with a reasonable explanation.

If Jan can buy 12 copies of a certain book for $40, what is the unit rate for cost per copy? How much would it cost her to buy 18 copies at the same rate?

Thank you!

Answer:

27i^3x

Step-by-step explanation:

a = x          b = 3i

ab^3 = x * 3i^3 = x * 27i^3 = 27i^3x

I hope this is correct and please mark me as brainliest if it is!

Answer:

Hi

Step-by-step explanation:

Answer:

7dm is longer than 7mm

Step-by-step explanation:

Answer:

1 rectangle

Step-by-step explanation

Area= lxb

So 7.7 x 11 = 84.7

3 trapezoid

Area =(a+b/2)

Base a=13

Base b = 6

Height = 5

By 2

Answer= 47.5

4 Right angled triangle

Ab/2

Axb

Multiply each legs of the right angle triangle

So 3 1by4 x 4

By 2

Answer: See explanation

Step-by-step explanation:

1. That's a rectangle, the area of a rectangle is l (length) × w (width)

l = 11 cm

w = 7.7 cm

11 × 7.7 = 84.7

Area = 84.7 cm²

2. That is a triangle, the area of a triangle is 1/2 × b (base) × h (height)

b = 12 ft

h = 4ft

1/2 × 12 × 4 = 1/2 × 48 = 24

Area = 24 cm²

3. That is a trapezoid, the area of a trapezoid is \(\frac{a (base) + b(base)}{2} h(height)\)

a = 6 cm

b = 13 cm

h = 5cm

((6 + 13) ÷ 2) x 5

(19 ÷ 2) x 5 = 9.5 × 5 = 47.5

Area = 47.5 cm²

4. Same formula: 1/2 × b × h

b = 3 1/4 in

h = 4 in

1/2 × 3 1/4 × 4 = 1/2 × 13/4 × 4

1/2 × 13 = 6.5

Area = 6.5 in²

Hope I helped!

Adding a derivational suffix to a word often changes the part of speech is true.

What is derivational suffix ?

A derivational suffix is a type of affix that is added to the end of a base word to create a new word with a different meaning, often a different part of speech.

For example, adding the derivational suffix "-ness" to the base word "kind" creates the new word "kindness," which is a noun that refers to the quality or state of being kind. Similarly, adding the derivational suffix "-able" to the base word "value" creates the new word "valuable," which is an adjective that describes something that is worth a lot.

Derivational suffixes can change the meaning and function of a word, and they are often used to create new words in English. Some common derivational suffixes include "-er," "-able," "-ness," "-ful," "-ish," and "-ize."

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Complete question is: Adding a derivational suffix to a word often changes the part of speech is true.

Answer:

Step-by-step explanation:

Answer:

17x+4=123(alternate angle)

17x=123-4

17x=119

x=7

You should pay approximately $10,117.09 initially to secure the annuity and receive annual payments of $1500 over the 9-year period.

To find the cost of the annuity, we need to calculate the present value of the future payments. The present value represents the current worth of future cash flows, taking into account the interest earned or charged over time. In this case, we'll calculate the present value of the $1500 payments using compound interest.

The formula to calculate the present value of an annuity is:

PV = PMT × [1 - (1 + r)⁻ⁿ] / r

Where:

PV is the present value of the annuity (the amount you should pay initially)

PMT is the payment amount received annually ($1500 in this case)

r is the interest rate per period (6.28% or 0.0628)

n is the total number of periods (9 years)

Let's substitute the values into the formula:

PV = $1500 × [1 - (1 + 0.0628)⁻⁹] / 0.0628

Calculating this expression:

PV = $1500 × [1 - 1.0628⁻⁹] / 0.0628

PV = $1500 × [1 - 0.575255] / 0.0628

PV = $1500 × 0.424745 / 0.0628

PV ≈ $10117.09

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a. To solve for the correct value of the expression : (2)/(3) + (1)/(2)(8 + 3(1)/(4)) `=` 2/3 + 1/2(8 + 3/4) `=` 2/3 + 1/2(33/4) `=` 2/3 + 33/8 To add these fractions, we need to find the lowest common denominator which is 24.2/3 * 8/8 = 16/24 ; 33/8 * 3/3 = 99/24

So, 16/24 + 99/24 = 115/24 Therefore, the correct value of the expression is 115/24.

b. Josiah likely made the error of forgetting to convert the mixed number (1)/(4) to an improper fraction before multiplying 3 by it. Instead, he may have multiplied 3 by the whole number 1.

This would result in the incorrect value of 13(1)/(8).

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Answer:

Step-by-step explanation:

Wee

Using the piecewise function graphed in this problem, we have that:

1. The x-axis represents the time in hours.

2. The y-axis represents the distance in miles.

3. The person traveled 30 miles in those 4 hours.

4. The person traveled at a rate of 7.5 miles per hour in Section A.

5. In section B, the person remained stopped 30 miles from her starting point for 2 hours.

6. The velocity for Section B was of 0 miles per hour.

7. The person traveled 30 miles in Section C.

8. 8. The speed in Section D was of 20 miles per hour.

9. The person was moving at the highest speed in Section C, at a rate of 30 miles per hour.

10. The farthest distance traveled was of 60 miles in Section D.

11. A person had an appointment 30 miles away from their home, and due to slow traffic had to leave early. Then the appointment lasted 2 hours, then the person went to another place 30 miles away to do something then came back home.

A piecewise-defined function is a function that has different definitions, depending on the input of the function.

From the graph, the function has four different definitions, in intervals, A, B, C and D.

From the axis of the graph, we have that:

1. The x-axis represents the time in hours.

2. The y-axis represents the distance in miles.

Considering that the graph has points (0,0) and (4,30), we have that:

3. The person traveled 30 miles in those 4 hours.

The velocity is given by distance divided by time, hence:

30/4 = 7.5.

4. The person traveled at a rate of 7.5 miles per hour in Section A.

In Section B, the person remains at the same position, hence:

5. In section B, the person remained stopped 30 miles from her starting point for 2 hours.

The distance was of 0, hence:

6. The velocity for Section B was of 0 miles per hour.

In Section C, from the y-axis of the graph, the distance traveled was:

60 - 30 = 30 miles.

7. The person traveled 30 miles in Section C.

For Section D, the person traveled 60 miles in 10 - 7 = 3 hours, hence:

60/3 = 20.

8. The speed in Section D was of 20 miles per hour.

10. The farthest distance traveled was of 60 miles in Section D.

In Section C, the person traveled 30 miles in one hour = 30 miles per hour, hence:

9. The person was moving at the highest speed in Section C, at a rate of 30 miles per hour.

For item 11, a situation that can be modeled is:

A person had an appointment 30 miles away from their home, and due to slow traffic had to leave early. Then the appointment lasted 2 hours, then the person went to another place 30 miles away to do something then came back home.

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Answer:

substitute the -3 in the equation.

f(x)=-3

f(x)= -5(-3)+2

f(x)= +15 +2

f(x)= 17

Answer:

f(-3) = 17

Step-by-step explanation:

f(x) = -5(x) + 2

we want to find f(-3)

to do so, we simply substitute -3 for x

f(-3) = -5(-3) + 2

multiply -5 and -3

f(-3) = 15 + 2

add 15 and 2

f(-3) = 17

The 2nd and 3rd terms of the sequence will be 38.5 and 37, respectively.

A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.

Let a₁ be the first term and d be a common difference.

Then the nth term of the arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

The first term is 40 and the fourth term is 35.5. Then the common difference is given as,

35.5 = 40 + (4 - 1)d

- 4.5 = 3d

d = - 1.5

Then the second term is given as,

a₂ = a₁ + d

a₂ = 40 - 1.5

a₂ = 38.5

Then the third term is given as,

a₃ = a₂ + d

a₃ = 38.5 - 1.5

a₃ = 37

The 2nd and 3rd terms of the sequence will be 38.5 and 37, respectively.

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Answer: X + (X + 2) + (X + 4) + (X + 6) = 0

Step-by-step explanation:

We were already given the sum of four consecutive integers. Consecutive means coming after another. Let's first define our first consecutive odd number as X. Since it says consecutive odd integers, there is a difference of 2   between two odd numbers. We keep on adding 2 to the value of X, since they asked for four consecutive odd integers, so we get the 4 values of X,  (X+2), (X+4), and (X+6). Once we put this in an equation, we get X + (X + 2) + (X + 4) + (X + 6) = 0.

The equation that models the sentence is :  x + (x + 2) + (x + 4) + + (x + 6)  = 0.

An odd number is a number that cannot be divided into half without any remainders. Examples of odd numbers are 1,3, 7, 11.

For example when 11 is divided in half, its value is 5.5

Consecutive odd numbers are odd numbers that follow each other. Examples are 1, 3, 5.

Consecutive odd numbers increase by 2

In order to model the sentence, let x represent the first odd number

Second odd number = x + 2

Third odd number = x + 4

Fourth odd number = x + 6

The equation is: x + (x + 2) + (x + 4) + + (x + 6)  = 0

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Answer:

I solved it for u!

Hope it helps

Step-by-step explanation:

Another way, it an isosceles triangle so the base will be same, so angle 3 and angle 1 will be same after u find angle 3, then angle 1 will be equal to it

So here angle 3 = 64°

So angle 1= 64°

Answer:

the answer that i found out was -5

Step-by-step explanation:

a - bc

= -2 - [ -1×(-3) ]

= -2 - 3

= -5

TRUE: A molecule can adopt a variety of geometries known as conformations by the rotation and bending of its bonds.

Conformational isomerism, often known as stereoisomerism, is a type of stereoisomerism in chemistry in which the isomers can be changed to one another simply by rotations about formally single bonds. Different conformations refer to any two arrangements of atoms in a molecule that differ by rotation about a single bond, whereas conformations that correspond to local minima on the potential energy surface are more specifically known as conformational isomers or conformers.

As a result, conformational isomers differ from other classes of stereoisomers (such as configurational isomers), where interconversion entails the necessary breaking and reformation of chemical bonds.

Thus, the statement, The different geometries that a molecule can attain by bond rotations and bends are called conformations is TRUE

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The system of equations that matches the given graph is:

A. 3x - 6y = 12

9x - 18y = 36

To determine which system of equations matches a given graph, we need to analyze the slope and intercepts of the lines in the graph.

Looking at the options provided:

A. 3x - 6y = 12

9x - 18y = 36

B. 3x + 6y = 12

9x + 18y = 36

Let's analyze the equations in each option:

For option A:

The first equation, 3x - 6y = 12, can be rearranged to slope-intercept form: y = (1/2)x - 2.

The second equation, 9x - 18y = 36, can be simplified to 3x - 6y = 12, which is the same as the first equation.

In option A, both equations represent the same line, as they are equivalent. Therefore, option A does not match the given graph.

For option B:

The first equation, 3x + 6y = 12, can be rearranged to slope-intercept form: y = (-1/2)x + 2.

The second equation, 9x + 18y = 36, can be simplified to 3x + 6y = 12, which is the same as the first equation.

In option B, both equations also represent the same line, as they are equivalent. Therefore, option B does not match the given graph.

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The volume of the cylindrical container on Venus can be calculated based on the given information.

To find the volume of the cylindrical container, we can use the formula for the volume of a cylinder: V = πr^2h, where V represents volume, r is the radius of the base, and h is the height of the cylinder. In this case, the diameter of the container is given as 4 feet, which means the radius (r) is half of that, or 2 feet. The height (h) of the container is given as 12 feet.

Using these values, we can calculate the volume as follows: V = π(2^2)(12) = 48π cubic feet.

However, we need to consider that the container is filled with an unknown liquid, and its weight is given as 160 pounds. The weight of the liquid is directly proportional to its volume, assuming the density remains constant. Since the fluid is 65% filled, we can calculate the total volume of the fluid by dividing the weight by the density and then multiplying by the percentage filled. However, without knowing the density of the liquid, we cannot determine the volume accurately. Therefore, the answer for the container volume is 48π cubic feet, assuming the density of the liquid remains constant throughout.

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Patrick received a total of approximately $6,785.97 over the course of 52 weeks.

To calculate the total amount of money Patrick received over the 52 weeks, we can use the concept of a geometric sequence. The first term of the sequence is $10, and each subsequent term is 10% more than the previous term.

To find the sum of a geometric sequence, we can use the formula:

Sn = a * (r^n - 1) / (r - 1),

where Sn is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = $10, r = 1 + 10% = 1.1 (common ratio), and n = 52 (number of weeks).

Plugging these values into the formula, we can calculate the sum of the sequence:

S52 = 10 * (1.1^52 - 1) / (1.1 - 1)

After evaluating this expression, we find that Patrick received approximately $6,785.97 over the 52 weeks.

As a result, Patrick collected about $6,785.97 in total over the course of 52 weeks.

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Answer:

PC = 14.42 cm

Step-by-step explanation:

If a tangent and secant are drawn from a point outside a circle, then the product of the lengths of the segments of the secant is equal to the square of the length of the tangent.

PC² = PB × BD

PC² = 4 × 52

PC² = 208

PC = \(\sqrt{208}\)

PC = 14.42 cm

The length of PC=14.42 cm.

when a tangent and secant are drawn from a point outside a circle, then the multiplication of the lengths of the segments of the secant is equal to the square of the length of the tangent.

PC² = PB × BD

Use the given value in above formula we get,

PC² = 4 × 52

PC² = 208

\(PC = \sqrt{208}\)

Therefore we get the value of PC is,PC = 14.42 cm.

Therefor the length of PC=14.42 cm.

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The cost of the least expensive box, with a volume of 420 cm3 and a base length three times the base width, is $300.

Let x be the width of the base. Then the length of the base is 3x. The height of the box is \(420/(3x^2) = 42/x^2.\)

The cost of the top and bottom is \(2(0.04)(42/x^2) = 8.4/x^2.\)

The cost of the sides is \(2(3x)(42/x^2) = 252/x.\)

The total cost is\(8.4/x^2 + 252/x.\)

To minimize the cost, we need to minimize \(8.4/x^2 + 252/x.\)

We can factor the expression as follows:

\(8.4/x^2 + 252/x = (8.4 + 252x)/(x^2)\)

We can see that the expression is minimized when x is as large as possible. The largest possible value of x is 6, because if x is greater than 6, then the volume of the box will be greater than 420 cm3.

When x = 6, the cost of the box is \((8.4 + 252*6)/(6^2) = 300\).

Therefore, the least expensive box costs $300.

Here is a table of the cost of the box for different values of x:

x | Cost

1 | 606

2 | 450

3 | 360

4 | 300

5 | 264

6 | 252

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The correct option regarding the 95% confidence interval for this problem is given as follows:

A. The confidence interval from the first simulation is (0.187, 0.237), and the confidence interval from the second simulation is (0.209, 0.261). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.187 and 0.237. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.209 and 0.261.

A confidence interval of proportions has the bounds given by the rule presented as follows:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value is z = 1.96.

The parameters for the first simulation are given as follows:

\(n = 1000, \pi = \frac{212}{1000} = 0.212\)

Hence the lower bound of the interval is of:

\(0.212 - 1.96\sqrt{\frac{0.212(0.788)}{1000}} = 0.187\)

The upper bound is of:

\(0.212 + 1.96\sqrt{\frac{0.212(0.788)}{1000}} = 0.237\)

For the second simulation, the parameters are given as follows:

\(n = 1000, \pi = \frac{235}{1000} = 0.235\)

Hence the lower bound of the interval is of:

\(0.235 - 1.96\sqrt{\frac{0.235(0.765)}{1000}} = 0.209\)

The upper bound is of:

\(0.235 + 1.96\sqrt{\frac{0.235(0.765)}{1000}} = 0.261\)

This means that option A is the correct option.

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The measure of the smaller interior angle is approximately 144 degrees.

The measure of the larger interior angle is 36 degrees.

Let's denote the measure of the smaller interior angle as x.

According to the given information, the measure of one interior angle (let's call it y) is 0.25 times the measure of the smaller angle. Therefore, we can write the equation:

y = 0.25x

Since a parallelogram has opposite angles congruent, we know that the sum of the measures of the smaller and larger angles is 180 degrees. Hence, we can write another equation:

x + y = 180

Substituting the value of y from the first equation into the second equation, we have:

x + 0.25x = 180

Combining like terms:

1.25x = 180

To find the measure of the smaller angle (x), we divide both sides of the equation by 1.25:

x = 180 / 1.25

x ≈ 144

Therefore, the measure of the smaller interior angle is approximately 144 degrees.

To find the measure of the larger interior angle, we substitute the value of x into the equation:

y = 0.25x

y = 0.25 * 144

y = 36

Hence, the measure of the larger interior angle is 36 degrees.

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Answer:

Y = 3

Step-by-step explanation:

Y = -3/2x +3

Y = -3/2 × 0 + 3

Y = 3

Answer:

\(y = \frac{-3}{2}x + 3\)

Step-by-step explanation:

Step 1 - Calculate slope first via the equation:

\(\frac{y2 - y1}{x2 - x1}\)

Where x1 and y1 are the coordinates of the first set whereas x2 and y2 are the second set. Plug the variables in:

\(\frac{6 - (-3)}{-2 - 4} \\\frac{6 + 3 )}{-2 - 4} \\\frac{9}{-6}\)

Which simplifies to:

\(\frac{3}{-2}\)

Now, in the line equation form we know x:

y = mx + c

y = \(\frac{3}{-2}\)x + c

Step 2 - Calculate y intercept

Plug the variables of one point into the above equation:

y = \(\frac{3}{-2}\)x + c

\(6 = \frac{3}{-2}(-2) + c\)

\(6 = \frac{3}{-2}(-2) + c \\6 = 3 + c\\6 - 3 = c\\c = 3\\\)

Meaning that the full line equation is:

\(y = \frac{-3}{2}x + 3\)

Hope this helps!

Answer:

C: (2,3)

Step-by-step explanation:

to solve this algebraically just plug in the x and y values of the points and see if they are true, but here is the graph to juse show you

Yes, the tangent constraint can be applied between a line and an arc in many CAD (Computer-Aided Design) software programs.

In CAD, a tangent constraint is a geometric constraint that forces two entities (lines, arcs, circles, etc.) to share a common tangent at their point of contact. When you apply a tangent constraint between a line and an arc, the software will ensure that the line and the arc are always tangent to each other at their point of intersection.

This constraint is useful for designing mechanical components, such as gears or cams, where you need to ensure that the contact between two parts is smooth and continuous. It is also commonly used in architecture, where a building's curved surfaces may need to be tangent to adjacent straight lines or walls.

In short, the tangent constraint can be applied between a line and an arc, and it is a useful tool in many different fields of design.

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Answer:

The equation of the perpendicular bisector is y =  \(\frac{-1}{2}\) x - 3

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

The rule of the slope is m = \(\frac{y2-y1}{x2-x1}\) , where

∵ A line passes through points (-1, 5) and (-7, -7)

∴ x1 = -1 ad y1 = 5

∴ x2 = -7 and y2 = -7

→ Use the rule of the slope above to find the slope of the line

∵ m = \(\frac{-7-5}{-7--1}\) = \(\frac{-12}{-7+1}\) = \(\frac{-12}{-6}\) = 2

∴ m = 2

→ Reciprocal the value of m and change its sign to find the slope of

  the line perpendicular line

∴ m⊥ = \(\frac{-1}{2}\)

→ Substitute in the form of the equation above

∵ y = \(\frac{-1}{2}\) x + b

∵ The ⊥ line is also the bisector of the given line, find the mid-point

   of the given line because it is also lying on the ⊥ line

∵ M = (\(\frac{-1+-7}{2},\frac{5+-7}{2}\)) =  (\(\frac{-8}{2},\frac{-2}{2}\)) = (-4, -1)

∴ M = (-4, -1)

→ Substitute the coordinates of M in the equation of the ⊥ line above

∵ x = -4 and y = -1

∴ -1 = \(\frac{-1}{2}\) (-4) + b

∴ -1 = 2 + b

→ Subtract 2 from both sides

∴ -3 = b

→ Substitute the value of b in the equation

∴  y =  \(\frac{-1}{2}\) x + -3

∴ y =  \(\frac{-1}{2}\) x - 3

∴ The equation of the perpendicular bisector is y =  \(\frac{-1}{2}\) x - 3

The value of x in the equation 1/4(4 + x) = 4/3 is x = 4/3.

Multiply both sides of the equation by 4 to eliminate the fraction on the left-hand side:

1/4(4 + x) = 4/3

4 * 1/4(4 + x) = 4 * 4/3

Simplifying:

4 + x = 16/3

Subtract 4 from both sides of the equation:

4 + x - 4 = 16/3 - 4

Simplifying:

x = 16/3 - 12/3

x = 4/3

A fraction is a mathematical concept used to represent a part of a whole or a ratio between two quantities. It is typically written in the form of a numerator (top number) over a denominator (bottom number), separated by a horizontal line. For example, the fraction 1/2 represents one out of two equal parts, or half of a whole. Similarly, the fraction 3/4 represents three out of four equal parts, or three-quarters of a whole.

Fractions are an essential part of mathematics and are used in a wide range of applications, including measurements, cooking, and financial calculations. They can be added, subtracted, multiplied, and divided just like whole numbers, but they require a bit more care in their manipulation due to their unique structure.

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We are 90% certain that the average number of  hamsters per litter is between 7.1077 and 8.3323.

A confidence interval is a range of values that includes a population value with a high degree of certainty. When a population mean falls between an upper and lower interval, it is frequently expressed as a percentage. The confidence level is the long-run proportion of corresponding CIs that contain the parameter's true value. For example, 95% of all intervals computed at the 95% level should contain the true value of the parameter.

Given, n=47

\(\bar{x}\)=7.72

s=2.5

c=90%=0.90

To find the t-value, look in the row that starts with degrees of freedom.

df=n-1

df=47-1

df=46>45 and in the column with c=90% in the table

=1.679

Now, the margin of error is then:

E=\(t_{\alpha/2}\times \dfrac{s}{\sqrt{n}}=1.679\times \dfrac{2.5}{\sqrt{47}}\approx 0.6123\)

The confidence interval's boundaries are thus:

\(\overline{x}-E\)=7.72-0.6123=7.1077

\(\overline{x}+E\)=7.72+0.6123= 8.3323

The average number of hamsters per litter is between 7.1077 and 8.3323, and we are 90% certain of this.

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