A dressmaker needs to cut 18-inch pieces of ribbon from rolls of ribbon that are 9 feet in length. How many 18-inch pieces can the dressmaker cut from 5 of these rolls of ribbon? Before you try that problem, answer the question below. How many inches of ribbon does the dressmaker have, in total?

Answer:

447 6/7

Step-by-step explanation:

The total elevation if The submarine is at an elevation of -355 2/7 feet, the explorers spot a humpback whale and dive downward an additional 92 4/7 feet, is 447 6 / 7 feet

A mixed fraction is a fraction that is created by fusing a fraction with a whole number. For instance, 8 1 / 2 is a mixed fraction if 8 is a whole number and 1/2 is a fraction.

Given:

The submarine is at an elevation of -355 2/7 feet, the explorers spot a humpback whale and dive downward an additional 92 4/7 feet,

Calculate the total elevation as shown below,

Total elevation = -355 2 / 7 +  (-92 4 / 7)

Total elevation = -2485 + 2 / 7 - 644 + 4 / 7

Total elevation = -2487 - 648 / 7

Total elevation = 3135 / 7

Thus, the total elevation is -447 6 / 7 feet.

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Answer:

The distance is approximately 3.6

Step-by-step explanation:

The distance from a point (xo, yo) to a line ax+by+c=0 is the shortest distance from the given point to any point on the line.

It can be calculated with the formula:

\(\displaystyle d={\frac {\mid ax_{0}+by_{0}+c\mid}{\sqrt {a^{2}+b^{2}}}}\)

The coordinates of point A are (1,-2). The equation of the line must be found by knowing two clear points it passes through.

These points are (0,3) and (6,-1). First, we calculate the slope:

\(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)

\(\displaystyle m=\frac{-1-3}{6-0}=\frac{-4}{6}=-\frac{2}{3}\)

The equation of the line in slope-point form is:

\(y=m(x-x_o)+y_o\)

Taking the point (0,3) and the slope above:

\(\displaystyle y=-\frac{2}{3}(x-0)+3\)

Multiply by 3:

\(3y=-2x+9\)

Moving all terms to the left side:

\(2x+3y-9=0\)

We now have all the required values to calculate the distance:

a=2, b=3, c=-9, xo=1, yo=-2

\(\displaystyle d={\frac {\mid 2\cdot 1+3\cdot (-2)+(-9)\mid}{\sqrt {2^{2}+3^{2}}}}\)

\(\displaystyle d={\frac {\mid 2-6-9\mid}{\sqrt {13}}}\approx 3.61\)

The distance is approximately 3.6

The acceleration produced by a car will decrease as its mass rises. Less acceleration will be recorded by the computer system, which will cause a drop in the acceleration value on the graph.

Graph:

An organized visual representation of any data in mathematics is called a graph. The graph shows the correlation between the variable values. In graph theory, a graph is used to represent the collection of objects that are somehow connected to one another. In essence, the objects' vertices or nodes are mathematical concepts, and the connections between the nodes are represented by the edges. Different types of graphs are used in mathematics and statistics to visually display data. The discipline of graph theory is the study of points and lines. It is a field of mathematics that specializes in the study of graphs. This image visually illustrates the mathematical truth. The graph theory is used to study relationships.

Complete question:

Use the image to answer the question. Students are using the experimental setup shown in the image in which the two ends of a string are attached to a car and to a hanger. The students conduct three trials in which they place metal discs on the hanger to manipulate the force applied to the car. As a result, the car accelerates along the table while two photogate probes collect motion data. On the fourth trial of this experiment, a student places some discs on the car by mistake. In 1-2 sentences, explain how this mistake will affect the graphs produced by the computer.

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Answer:

4.432 * 10^-1

Step-by-step explanation:

move your decimal so that you have less than 10 before the decimal.

Then count the number of spaces moved (1) and put that in the 10^x (10^-1)

Answer:

T1. Evaluate the area between the curves: y = 1 - x^2, y = |x - 1|.

T2. Solve the initial value problem: y' = 3y^2 sin(x) cos(x), y(0) = 1.

T3. Sketch on the complex plane: {z ∈ C: 9((2 - 1)) < 0 < 1}.

T4. Evaluate (1 - 3)^(2022).

T5. Evaluate: 2^1 + 0^1 + 3^1 + 0^1 + 1^3 + 2^1 + 3^1 = 2 + 0 + 3 + 0 + 1 + 2 + 3 = 11.

T6. Solve the system of equations.

T7. Evaluate the volume of the tetrahedron ABCD if A(1, -1, 1), B(4, 7, 1), C(2, 2, 2), D(2, -4, 2).

T8. Find the distance between the point P(-3, 5, 4) and the plane: 2x - y - z + 3 = 0.

T1. To evaluate the area between the curves y = 1 - x^2 and y = |x - 1|, we need to find the points of intersection between the two curves. Setting the equations equal to each other, we have 1 - x^2 = |x - 1|.

Solving this equation gives us x = -1, x = 0, and x = 1. We can evaluate the integral of the absolute difference between the curves over the interval [-1, 1] to find the area between them.

T2. To solve the initial value problem y' = 3y^2 sin(x) cos(x), y(0) = 1, we need to find the function y(x) that satisfies the differential equation and the initial condition.

This is a separable differential equation, so we can separate the variables and integrate both sides to find the solution.

T3. Sketching the set {z ∈ C: 9((2 - 1)) < 0 < 1} on the complex plane involves finding the complex numbers z that satisfy the given inequality. By simplifying the inequality, we have 9 < 0 < 1, which is a contradiction since 9 is not less than 0. Therefore, there are no complex numbers that satisfy this inequality.

T4. Evaluating (1 - 3)^(2022) involves calculating the result of raising the number 1 minus 3 to the power of 2022.

T5. Evaluating the given expression involves performing the operations of addition and exponentiation according to the given sequence of numbers and operations.

T6. Solving the system of equations requires writing down the equations and finding values for the variables that satisfy all of the equations simultaneously.

T7. To find the volume of the tetrahedron ABCD with given vertices A(1, -1, 1), B(4, 7, 1), C(2, 2, 2), and D(2, -4, 2), we can use the formula for the volume of a tetrahedron in terms of the coordinates of its vertices.

T8. Finding the distance between the point P(-3, 5, 4) and the plane 2x - y - z + 3 = 0 involves using the formula for the distance between a point and a plane. This formula requires finding the perpendicular

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Answer:

She is about 14.765 miles (\(\sqrt{218}\) miles) from where she started

Step-by-step explanation:

There is a relation between the three sides of the right triangle

∵ Jennifer bikes 7 miles south

∵ She turns to bike 13 miles east

∵ South and East are perpendicular

→ That means the distance from her start point to end point represents

   a hypotenuse of a right triangle, whose legs are 7 and 13

∴  (hypotenuse)² =  (leg1)² + (leg2)², where

∵ Leg1 = 7 miles

∵ leg 2 = 13 miles

∴ (hypotenuse)² =  (7)² + (13)²

∴ (hypotenuse)² = 49 + 169

∴ (hypotenuse)² = 218

→ Take √  for both sides

∴ hypotenuse = \(\sqrt{218}\)

∴ hypotenuse ≅ 14.76482306

∴ She is about 14.765 miles (\(\sqrt{218}\) miles) from where she started.

Answer:

r = 152/55

Step-by-step explanation:

122 - 44r = - 30 + 11r

122 - 44r - 11r = - 30

- 44r - 11r = - 30 - 122

- 55r = - 30 - 122

- 55r = - 152

Polynomials are  closed under the operations of addition, subtraction, and multiplication, polynomials constitute a system similar to that of integers.

Polynomial exponents are whole numbers.

The fact that addition is closed for the whole numbers ensures that the resultant exponents will also be whole numbers. Polynomials are hence closed under addition.

Polynomials will be closed under an operation if the operation produces another polynomial.

If we subtract 2 polynomials, the result is a polynomial. Therefore, they are also closed under subtraction.

Polynomials are an algebraic equation that has more than two terms, particularly the accumulation of numerous phrases that each include a different power of the same variable (s).

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Answer:

a

Step-by-step explanation:

the graph would continue on both sides; no asymptote

Range is set of y values

And it tends to -infinity with increase in x .

So

RAnge

Option D

In scenario three, we explore additional options e and f, each with their own unique probabilities and potential outcomes.

Option e introduces a 50% chance of winning $0 or an unspecified amount, while option f offers a 50% chance of winning either $20 or $60.

These options introduce different potential outcomes and associated probabilities compared to the original scenarios. In option e, there is an equal chance of winning nothing or winning an unspecified amount of money.

The introduction of these options expands the range of possible outcomes and probabilities in scenario three, providing different risk-reward trade-offs for the decision-maker.

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Based on Transformation of functions the transformed equation is  \(y=x^3\) is \(y=\frac{-1}{7}(x+8)^3\).

There are two different translations we can apply to a function graph. In addition, they are scaling. If you count reflections, there are three, but reflections are really a specific instance of the second translation.

Transformations:

Reflecting a function on X-axis  : Change y in function to -y.

Reflecting aa function on Y-axis : Change x in function to -x.

Shifting right by a:  Replace x by (x-a)

Shifting left by a:  Replace x by (x+a).

Shifting up by a: Replace y by (y-a).

Shifting down by a: Replace y by (y+a).

Scaling up by  n times: Multiply n

Step1: Vertical compression by a factor of  \(\frac{1}{7}\), we need to multiply the function by \(\frac{1}{7}\) .

So, we have:

\(y=\frac{1}{7}x^3\);

Step2:Horizontal shift by 8 units to the left, we need to add 8 to x.

So, we have:

\(y=\frac{1}{7}(x+8)^3\);

Step3:Reflection over the x-axis, we need to Replace y by -y.

So, we have:

\(y=-\frac{1}{7}(x+8)^3\)

Based on Transformation of functions the transformed equation is  \(y=x^3\) is \(y=\frac{-1}{7}(x+8)^3\).

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Answer:

B: Ellipse

Step-by-step explanation:

Just put in the equation on desmos. An ellipse will pop-up

The conic section is represented by the following equation –5x^2 + 9xy + 5y^2 + 6x – 4y + 11 = 0 is  circle.

We have given that the equation of the equation is,

–5x^2 + 9xy + 5y^2 + 6x – 4y + 11 = 0

The general formula of the circle is

\(ax^2+2xy+by^2+2fx+2gy+c=0\)

Compare the given equation with the general formula of the circle so we get the equation of the circle

Therefore the equation of the circle is  –5^+ 9xy + 5y^2 + 6x – 4y + 11 = 0

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We can either round off 11.75 to 12 or to 11, depending on whether we want to overestimate or underestimate the number of cups of coffee sold. In the former case, the solution is (12, 31), and in the latter case, the solution is (11, 32).

Let the number of cups of coffee sold be x and the number of cups of tea sold be y. The ordered pair representing the solution will be (x, y).Given, a total of 43 cups were sold. Therefore, we have:

x + y = 43 ..... (1)

Also, the money collected was $140. Since cups of coffee are sold for $5 and cups of tea are sold for $2, we can write the total amount of money as:

5x + 2y = 140 ..... (2)

We have two equations (1) and (2) in two unknowns x and y. We can solve them to find the values of x and y.

Subtracting equation (1) from twice equation (2), we get:

8x = 94 => x = 11.75

Substituting this value of x in equation (1), we get:

11.75 + y = 43 => y = 31.25

The solution is the ordered pair (x, y) = (11.75, 31.25).

However, we need to remember that the number of cups must be integers and not fractions. We can see that 11.75 is not an integer. Therefore, we need to adjust our solution by rounding off appropriately.

We can either round off 11.75 to 12 or to 11, depending on whether we want to overestimate or underestimate the number of cups of coffee sold. In the former case, the solution is (12, 31), and in the latter case, the solution is (11, 32).

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The area of the composite figure is equal to 60.75 m² square metres.

The composite figure is made up of a triangle and two rectangles, so we shall calculate for the areas of the three figures and then add the result to get the total area of the composite figure as follows:

area of the triangle = 1/2 × 7.5 m × 3 m

area of the triangle = 1/2 × 22.5 m²

area of the triangle = 11.25 m²

area of smaller rectangle = 4.5 m × 3 m

area of smaller rectangle = 13.5 m²

area of the bigger rectangle = 12 m × 3 m

area of the bigger rectangle = 36 m²

total area of the composite figure = 11.25 m² + 13.5 m² + 36 m²

total area of the composite figure = 60.75 m²

Therefore, the area of the composite figure is equal to 60.75 m² square metres.

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Answer:

A, C, F

Step-by-step explanation:

JK is proportional to PQ, so that would be 8/x. Then, JL is proportional to PR, which would be 10/5. So, the answer is: 8/x = 10/5

Then, C would also be correct as KL is proportional to QR, and JK is proportional to PQ.

Finally, F is correct as JK to KL is proportional to PQ to QR, as JK is proportional to PQ, and KL is proportional to QR.

Answer:

3x+2=15

    -2=-2

3x/3=13/3

                  _

x=4 1/3 = 4.33

Therefore, the two equations that would be most appropriately solved by using the quadratic formula are: 0.25x² + 0.8x - 8 = 0 and -2x² + 5x = 7.

The values of the unknown variable x that fulfil the quadratic equation are the solutions to the equation. Quadratic equations' roots or zeros are known as these answers.

Typical form: A quadratic equation is written in standard form as y = an x 2 + b x + c, where and are just integers. Factored form: A quadratic equation's factored form is denoted by the expression y = (a x + c) (b x + d), where a, b, c, and are just integers.

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Answer:

Question 1

Volume of a cylinder = πr²h

r= radius h= height

diameter = 2*radius

diameter = 2* 4cm= 8cm

Volume = π × 4² × 11

= 553.14cm³

The descriptive statistics for the above data is given as follows:
X = 12.5

A set of concise descriptive coefficients that describe a particular data set indicative of a whole or sample population is known as descriptive statistics.

For X (mean) = \({\displaystyle X={\frac {1}{n}}\sum _{i=1}^{n}X_{i}\)

= 300/24

= 12.5

For sample variance = \(s^2 = \frac{1}{n-1}\biggl[\, \sum_{i=1}^n X_i^2 - \frac{\Bigl(\,\sum\limits_{i=1}^n X_i\Bigr)^{\!2}}{n} \biggr]\)

= (1/(24-1) (4,900 - (300²/24)

= 50

Standard deviation s = √s²

= √50

= 7.0711

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The corresponding angles and sides of the two triangles need to be given in order to prove congruence by side-angle-side.

In order to prove congruence by side-angle-side, the corresponding angles and sides of the two triangles must be given. The sides must be proportional, which means that two sides of one triangle must be equal to two sides of the other triangle, and the angles between these two sides must also be equal. In other words, if two sides of one triangle are equal to two sides of the other triangle, and the angle between those two sides is also equal, then the two triangles are congruent. This can be expressed as “If two sides and the included angle of one triangle are equal to the corresponding sides and angle of a second triangle, then the two triangles are congruent.” In order to prove congruence by side-angle-side, all of the corresponding sides and angles must be given in order to show that they are equal.

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The additional information that is needed to prove the triangles are congruent by Side-Angle -Side us that the corresponding angles and sides of the two triangles need to be given .

What is Side-Angle-Side Congruence ?

The Two Triangles can be called as  Congruent by Side-Angle-Side rule  if any 2 sides and angle included between sides of one triangle is equivalent to corresponding 2 sides and angle between sides of second triangle .

In order to prove the Congruence by Side-Angle-Side, the corresponding angles and the sides of the 2 triangles must be given.

The sides must also be in proportional, that means that the two sides of one triangle must be equal to two sides of other triangle, and

the angles between these two sides of the triangle must  be equal.

So , In order to prove a triangle congruent by Side-Angle-Side, all of the corresponding sides and angles must be given in order to prove  that they are equal.

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The proposal during the Constitutional Convention that created a House proportionate to population along with a Senate in which all states were represented equally was called the Great Compromise.

The Great Compromise, also known as the Connecticut Compromise, was a pivotal agreement reached during the Constitutional Convention of 1787. It was proposed by Roger Sherman and Oliver Ellsworth of Connecticut. The compromise aimed to resolve the debate between the large and small states over the representation in the newly formed legislative body.

The compromise suggested a bicameral legislature consisting of two chambers: the House of Representatives and the Senate. The House would be proportionate to the population of each state, ensuring that more populous states had more representatives. On the other hand, the Senate would provide equal representation for all states, regardless of their size or population.

This compromise struck a delicate balance between the interests of large and small states, ensuring that both had a say in the legislative process. It ultimately became a key component of the United States Constitution, shaping the structure of the American government and fostering the principle of federalism.

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The ratio of cell A's length to cell B's length = 20

To find the ratio of cell A's length to cell B's length, we need to divide the length of cell A by the length of cell B:

Ratio of cell A's length to cell B's length = Length of cell A / Length of cell B

Ratio of cell A's length to cell B's length = (8×10^-5 m) / (0.000004 m)

= 0.00008 / 0.000004

Ratio of cell A's length to cell B's length = 20

Therefore, the ratio of cell A's length to cell B's length is 0.02.

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Using quantifiers; a) ∀ student ∈ this class, ∃ exactly 2 mathematics classes ∈ this school that the student has taken and b) ∃ person, ∀ country ∈ the world (country ≠ Libya), the person has visited that country.

a) "Every student in this class has taken exactly two mathematics classes at this school."

In this statement, we have two main quantifiers:

Universal quantifier (∀): This quantifier denotes that we are making a statement about every individual student in the class. It indicates that the following condition applies to each and every student.

Existential quantifier (∃): This quantifier indicates the existence of something. In this case, it asserts that there exists exactly two mathematics classes at this school that each student has taken.

So, when we combine these quantifiers and their respective conditions, we get the statement: "For every student in this class, there exists exactly two mathematics classes at this school that the student has taken."

b) "Someone has visited every country in the world except Libya."

In this statement, we also have two main quantifiers:

Existential quantifier (∃): This quantifier signifies the existence of a person who satisfies a particular condition. It asserts that there is at least one person.

Universal quantifier (∀): This quantifier denotes that we are making a statement about every individual country in the world (excluding Libya). It indicates that the following condition applies to each and every country.

So, when we combine these quantifiers and their respective conditions, we get the statement: "There exists at least one person who has visited every country in the world (excluding Libya)."

In summary, quantifiers are used to express the scope of a statement and to indicate whether it applies to every element or if there is at least one element that satisfies the given condition.

Therefore, Using quantifiers; a) ∀ student ∈ this class, ∃ exactly 2 mathematics classes ∈ this school that the student has taken and b) ∃ person, ∀ country ∈ the world (country ≠ Libya), the person has visited that country.

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Answer:

600 students are from this graduating class.

Step-by-step explanation:

Set up an equation:

Variable x = total number of students

45/100 = 270/x

Cross multiply:

45 × x = 100 × 270

45x = 27,000

x = 600

Answer:

slope is undefined

Answer:

A. a two-column proof consist of a list of statements and the reasons the statements are true.

B. a flowchart proof gives a visual representation of the sequence of steps without justification.

D. a two-column proof list only the given information and what is to be proven.

Step-by-step explanation: This is the correct answer on Edge 2021, just took the quiz. Hope this helps. ^-^

The correct statements are:

In a paragraph proof, statements and their justifications are written in sentences in a logical order.

A two-column proof consists of a list of statements and the reasons the statements are true.

A flowchart proof is a visual way of describing the statements and reasons for a proof.

A flowchart is a graphical representation of a process, algorithm, or system that uses symbols, shapes, and arrows to depict the various steps and their interconnections.

We have,

In a two-column proof, each statement is listed in one column, and the justification for the statement is listed in a separate column.

A flowchart proof also provides a visual representation of the sequence of steps, but it includes justifications for each step.

So,

The following statements are incorrect:

A flowchart proof gives a visual representation of the sequence of steps without justifications.

A two-column proof lists only the given information and what is to be proven.

Thus,

The correct statements are:

In a paragraph proof, statements and their justifications are written in sentences in a logical order.

A two-column proof consists of a list of statements and the reasons the statements are true.

A flowchart proof is a visual way of describing the statements and reasons for a proof.

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The equation solved for w is:

w = A/l

The correct option is A.

A pair of algebraic equations with the equal symbol (=) in the center and the same value are referred to as an equation.

Starting with the equation:

A/l = lw/l

We can simplify it by multiplying both sides by l:

A = lw

To solve for w, we need to isolate it on one side of the equation.

We can do this by dividing both sides by l:

A/l = w

Therefore, the required equation is A/l = w.

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If you know that p = .7, then the value of q is 0.3 (option b)

If you know that p = .7, the value of q can be calculated using the complement rule of probability, which states that the probability of an event occurring is equal to one minus the probability of that event not occurring. In other words, q is equal to one minus p.

Therefore, q = 1 - p = 1 - 0.7 = 0.3.

It is important to note that the sum of p and q should always equal one, as there are only two possible outcomes in a given event. In this case, the sum of p and q is 0.7 + 0.3 = 1, which confirms that the values are correct.

Hence the correct option is (b).

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The decision for this test at a .05 level of significance is not enough information to make a decision the correct answer is (d).

To make a decision for a hypothesis test, we compare the obtained test statistic (in this case, z = 1.80) with the critical value(s) based on the chosen level of significance (in this case, α = 0.05).

For a one-sample z test, if the obtained test statistic falls in the rejection region (i.e., beyond the critical value(s)), we reject the null hypothesis. Otherwise, if the obtained test statistic does not fall in the rejection region, we fail to reject the null hypothesis.

Without knowing the critical value(s) corresponding to a significance level of 0.05 and the directionality of the test (one-tailed or two-tailed), we cannot determine the decision for this test. Therefore, the correct answer is (d) There is not enough information to make a decision.

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