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Answer:

The vector that describes their hike from their starting position to their final destination is \(\vec r = 7\,\hat{i}+1\,\hat{j}\,\,\,[mi]\).

Step-by-step explanation:

In this problem we assume that orthogonal axes coincide with the north and east. We proceed to translate each sentence from statement into vectorial equations:

(i) A group of hikers walks 3 miles east and then 1 mile north:

\(\vec r_{A} = 3\,\hat{i}+1\,\hat{j}\,\,\,[mi]\)

(ii) After taking a break, they then hike 4 miles east to their final destination:

\(\vec r_{B} = 4\,\hat{i}\,\,\,[mi]\)

The vector that describes their hike from their starting position to their final destination is the sum of the vectors deducted above. That is:

\(\vec r = \vec r_{A}+\vec r_{B}\)  (1)

\(\vec r = (3\,\hat{i}+1\,\hat{j})+4\,\hat{i}\,\,\,[mi]\)

\(\vec r = 7\,\hat{i}+1\,\hat{j}\,\,\,[mi]\)

The vector that describes their hike from their starting position to their final destination is \(\vec r = 7\,\hat{i}+1\,\hat{j}\,\,\,[mi]\).

The additional information that would have to be true for the parallelogram to also be a rhombus is D. Opposite angles congruent

All rhombuses are parallelograms, but not all parallelograms are rhombuses. In a rhombus, all four sides are equal and the diagonals intersect at 90 degrees. In a parallelogram, the opposite sides are equal and the diagonals bisect each other.

Because its sides are parallel to one another, a rhombus can also be referred to as a particular kind of parallelogram. 360° is the total number of angles in a rhombus. Angles on either side of one another are equal, and adjacent angles are supplementary angles.

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Barbara draws a parallelogram. Jason thought it might be a rhombus. What additional information would have to be true for the parallelogram to also be a rhombus?a. Opposite sides congruent.b. Diagonals are perpendicular.c. Consecutive angles supplementary.d. Opposite angles congruent.

Answer:

(2, 5 )

Step-by-step explanation:

y = 2x + 1 → (1)

3y = 4x + 7  → (2)

substitute y = 2x + 1 into (2)

3(2x + 1) = 4x + 7 ← distribute parenthesis on left side

6x + 3 = 4x + 7 ( subtract 4x from both sides )

2x + 3 = 7 ( subtract 3 from both sides )

2x = 4 ( divide both sides by 2 )

x = 2

substitute x = 2 into (1) for corresponding value of y

y = 2(2) + 1 = 4 + 1 = 5

solution is (2, 5 )

If the material used for the half-spheres are three times more expensive than the material used for the part cylindrical, then the radius of the cylindrical part should be (125/3π)^(1/3) meters and the length of the cylindrical part should be 11.99 meters.

The radius and length of the cylindrical part that will minimize the cost of building the tank, can be determined by considering the cost of the materials used for the half-spheres and the cylindrical part.

Let's start by finding the volume of the cylindrical part. The volume of a cylinder is given by the formula

V = πr²h, where r is the radius and h is the height or length of the cylindrical part.

In this case, we want the volume to be 1000m³, so we can write the equation as:

1000 = πr²h ...(1)

Next, let's find the surface area of the two half-spheres. The surface area of a sphere is given by the formula:

A = 4πr².

Since we have two half-spheres, the total surface area of the half-spheres is:

2(4πr²) = 8πr².

The cost of the half-spheres is three times more expensive than the cost of the cylindrical part. Let's say the cost per unit area of the cylindrical part is x, then the cost per unit area of the half-spheres is 3x.

The total cost, C, is the sum of the cost of the cylindrical part and the cost of the half-spheres. It can be expressed as:

C = x(2πrh) + 3x(8πr²) ...(2)

Now, we can minimize the cost by differentiating equation (2) with respect to either r or h and setting it equal to zero. This will help us find the values of r and h that minimize the cost. To simplify the calculations, we can rewrite equation (2) in terms of h using equation (1):

C = x(2πr(1000/πr²)) + 3x(8πr²) C = 2x(1000/r) + 24xπr² ...(3)

Now, differentiating equation (3) with respect to r:

dC/dr = -2000x/r² + 48xπr

Setting dC/dr equal to zero:

0 = -2000x/r² + 48xπr

Simplifying the equation:

2000x/r² = 48xπr

Dividing both sides by 4x: 500/r² = 12πr

Multiplying both sides by r²: 500 = 12πr³

Dividing both sides by 12π: 500/(12π) = r³

Simplifying: 125/3π = r³

Taking the cube root of both sides: r = (125/3π)^(1/3)

Now, we can substitute this value of r back into equation (1) to find the value of h:

1000 = π((125/3π)^(1/3))^2h

Simplifying: 1000 = (125/3π)^(2/3)πh

Dividing both sides by π and simplifying:

1000/π = (125/3π)^(2/3)h

Simplifying further:

1000/π = (125/3)^(2/3)h

Now we can solve for h: h = (1000/π) / ( (125/3)^(2/3) )

Simplifying: h = 11.99 m

To summarize, to minimize the cost of building the tank, the radius of the cylindrical part should be (125/3π)^(1/3) meters and the length of the cylindrical part should be approximately 11.99 meters.

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Answer:

3(8)-4= 24-4= 20 your answer is 20

Step-by-step explanation:

\(\bold{H \: e \: y \: o \: !}\)

__________________

\(\mathtt{\sqrt{\frac{9x^3}{4y^2}}}\)

__________________

Apply radical rule: \(\mathtt{=\sqrt{\frac{a}{b}}} \: = \: \mathtt{\sqrt{\frac{a}{b}}},\) assuming \(\mathtt{a \geq 0, \: b \: \leq 0}\)

\(\mathtt{=\sqrt{\frac{9x^3}{4y^2}}}\)

__________________

Simplify: \(\mathtt{\sqrt{9x^3}} \: : \: \mathtt{3x\sqrt{x}}}\)

\(\mathtt{=\sqrt{\frac{3x\sqrt{x}}{4y^2}}}\)

__________________

Simplify: \(\mathtt{\sqrt{4y^2}} \: : \: \mathtt{2y}\)

\(\mathtt{\frac{3x\sqrt{x}}{2y}}\)

Hope It Helps!

A n s w e r e d : -  ᴀᴅʀɪᴀɴɴᴏɪʀ

Step-by-step explanation:

equality have the same values where as inequality have different values

Answer:

using the properties of equality on any equation will not change the solution set. When multiplying or dividing an any quality by a negative number, you must reverse the inequality symbol or he will not get the correct solution set.

Step-by-step explanation:

As a result, an experiment entails randomly selecting one of two urns and then drawing a marble from that urn. The probability that a green marble was picked is 0.524.

We are informed from the question that

Urn 1 has the following number of green marbles \(Ng=14\)

Urn 1 has the following number of yellow marbles \(Ny=15\)

Urn 2 has the following number of green marbles: \(n_{g} =11\)

Urn 2 has the following number of yellow marbles:\(n_{y}=8\)

The likelihood of selecting Urn 1 is \(P(U1) = 0.57\)

The likelihood of selecting Urn 2 is \(P (U2)= 1-0.57\)

                                                           \(P(U2)= 0.43\)

Let \(Nt\) be the total number of marbles in urn 1. Then,

Typically, Urn 1's total marble is \(Nt=Ng+Ny\)

                                                   \(Nt=14+15\)

                                                   \(Nt=29\)

Let \(nt\) be the total number of marbles in urn 1

Typically, Urn 2's total marble is n \(n_{t} = n_{g} +n_{y}\)

                                                     \(n_{t} =11+8\)

                                                     \(n_{t}=19\)

The likelihood of selecting green marble is typically

\(P(Ng)=P(U1)* \frac{Ng}{Nt} + [P(U2)*\frac{n_{g} }{n_{t} }]\)

\(P(Ng)=0.57*\frac{14}{29} + [0.43*\frac{11}{19} ]\)

\(P(Ng)=0.57*0.483+[0.43*0.579]\)

\(P(Ng)= 0.275+0.249\)

\(P(Ng)= 0.524\)

The probability that a green marble was picked is 0.524.

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The chocolate bar has a length of 10.5ft and width of 5.7ft

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

In the question, we were given the l is equal to 0.9 less than 2 times the width of the rectangle.

let;

A = l * w

l = 2w - 0.9

A = l * w

59.85 = w * (2w - 0.9)

59.85 = 2w² - 0.9w

2w² - 0.9w - 59.85 = 0

Solving for w

w = 5.7ft

The width of the bar is 5.7ft

The length will be (2 * 5.7) - 0.9

L = 10.5ft

The length and width of the bar is 10.5ft and 5.7ft respectively

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Answer:

44+

Step-by-step explanation:

just got it correct

Answer:

The answer is turtle

Step-by-step explanation:

When we analyze the Quadratic Equation Properly we will find that x belongs to R

What is Quadratic Equation?

The polynomial equation of degree 2 is called Quadratic Equation

Lets us take our equation

f(x) \(\geq\) g(x)

\(x^2+3x-1 \geq 2x-3\\\\x^2+x+2\geq 0\\\\\)

Here if we calculate discriminant for this Quadratic equation

it is -ve means whenever Discriminant is negative then quadratic equation is always +ve

Hence for all values of x this inequality will hold True

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There are two main subtypes of quantitative data, which are discrete data and continuous data. Each subtype has different techniques for analysis.

1. Discrete data: This type of data represents whole numbers or counts that can only take specific values. Examples include the number of students in a class or the number of cars in a parking lot. Techniques used to analyze discrete data include:
  a. Frequency distribution: A summary of the number of times each value appears in the dataset.

 b. Measures of central tendency: Calculating the mean, median, and mode of the dataset to understand its central point.

 c. Measures of dispersion: Assessing the range, variance, and standard deviation to understand the spread of the data.

2. Continuous data: This type of data represents measurements that can take any value within a range, such as height, weight, or temperature. Techniques used to analyze continuous data include:

 a. Histogram: A graphical representation of the distribution of the data, using bars to represent the frequency of values within specific intervals.

  b. Probability density function: A mathematical function that describes the probability of a continuous random variable falling within a specific range.

  c. Regression analysis: A statistical method for analyzing the relationship between a dependent variable and one or more independent variables.

Both discrete and continuous data can also be analyzed using inferential statistics, such as hypothesis testing and confidence intervals, to make inferences about a population based on a sample of the data.

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Answer:

f=8

Step-by-step explanation:

0.62(f+(-6)+6.96=8.2

0.62(f-6)+6.96=8.2

multiply both sides by 100

0.62(f-6)*100+6.96*100=8.2*100

Refine

62(f-6)+696=820

Subtract 696 from both sides

62(f-6)+696-696=820-696

Simplify

62(f-6)=124

Divide both sides by 62

62(f-6)/62 = 124/62

Simplify

f-6=2

add 6 to both sides

f-6+6=2+6

simplify

f=8

Answer:

8

Step-by-step explanation:

1. Distribute 0.62 to each term in the parenthesis:

0.62(f) + 0.62(-6)

0.62f - 3.72 + 6.96 = 8.2

2. Add 3.72 and 6.96:

0.62f - 3.72 + 6.96 = 8.2

0.62f + 3.24 = 8.2

3. Subtract 3.24 from both sides of the equation:

0.62f + 3.24-3.24 = 8.2-3.24

0.62f = 4.96

4. Divide 0.62 by both sides to isolate f:

0.62f/0.62 = 4.96/0.62

f = 8

hope this helps!

About 57 red pens were sold

According to the information given:

number of packs of black pens sold: number of packs of red pens sold: number of packs of green pens sold = 7:3:4

Number of red pens sold = 3/14 * 268

Number of red pens sold = 57 pens

Hence about 57 red pens were sold

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The state that has the standard of Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction, and limits dividing decimals to specific cases is not specified in the given question.

The given question does not mention a specific state that has the mentioned standard for decimal operations.

However, this standard aligns with the mathematics curriculum in many states across the United States. It focuses on developing students' understanding of decimal operations and their ability to apply various strategies and models to solve problems involving addition, subtraction, multiplication, and division of decimals.

To meet this standard, students are encouraged to use concrete models or drawings that represent the place value and properties of decimal numbers. They learn to relate these models to written methods, such as the standard algorithm, and explain their reasoning behind the chosen strategies.

The emphasis is on understanding the concepts behind decimal operations, rather than solely relying on rote memorization of procedures.

The standard also specifies that dividing decimals is limited to specific cases, including a whole number dividend with a decimal divisor or a decimal dividend with a whole number divisor.

Students are expected to compare the value of the quotient based on the values of the dividend and divisor, considering the relationship between the two numbers.

By mastering these skills and concepts, students develop a strong foundation in decimal operations, which are essential for real-world applications involving money, measurements, and other quantitative situations.

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Answer:

a=56/11

Step-by-step explanation:

Answer:

You are calculating the constant speed

A hypothesis that there is some sort of relationship between the variables is where scientists start their inquiry. The alternative, or null hypothesis, asserts that there is no such relationship. Although the null hypothesis may not appear fascinating, it is a crucial component of research.

The claim can be supported by either the null hypothesis or the alternative hypothesis. The null hypothesis states that the population proportion is the same as the value specified in the claim. If the null hypothesis is the assertion, then the alternative hypothesis statement is the antithesis of the null hypothesis. A hypothesis is a well-informed, logically-supported guess about the answer to a scientific question. Although it is the experiment's anticipated outcome, it does not constitute experimental proof. The information obtained may or may not be supported, depending on the information received. Simple hypotheses simply state the relationship between two independent and dependent variables. Examples: If you stay up late, you will feel fatigued the next day.

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Answer:

a = 7 , b = 9 , c = 4

Step-by-step explanation:

using the rule of exponents/ radicals

\(a^{\frac{b}{c} }\) = \(\sqrt[c]{a^{b} }\)

then

\(7^{\frac{9}{4} }\) = \(\sqrt[4]{7^{9} }\) ← in the form \(\sqrt[c]{a^{b} }\)

with a = 7 , b = 9 , c = 4

Answer:

46.80

Step-by-step explanation:

because 45/4%=1.80 and 45+1.80=46.80

Step-by-step explanation:

1 kg = 1000 g

1.5 kg = 1500 g

1500 g : 350 g

= 150 : 35

= 30 : 7

Answer:

3.3 pounds

Step-by-step explanation:

Answer:

Terrence made $30 more than Teresa.

Step-by-step explanation:

Giving the following information:

Terrence earns $450 per week.

Teresa earns $300 per week plus a 6% commission on the total sales of books she sells.

First, we need to structure the total income formula for each:

Terrence= 450

Teresa= 300 + 0.06*x

x= sales

Now, for $2,000 sales of books:

Terrence= $450

Teresa= 300 + 0.06*2,000= $420

The lengths of line segments PS and WS are both equal to 9. Thus, the sum of the lengths of PS and WS is 18.

To find the sum of the lengths of PS and WS, we need to determine the lengths of these line segments based on the given information.

Given that line segment WX is six times the length of line segment YS, we can write the equation WX = 6 * YS.

We also know that line segment QR has a length of 7 and line segment XY has a length of 18.

Since line segment QR intersects circle C2 at points Q and R, we can say that the lengths of line segments QW and RX are equal to 7.

Similarly, since line segment XY intersects circle C2 at points X and Y, the lengths of line segments YS and XW are equal to 18.

Now, let's calculate the lengths of line segments PS and WS.

We can start by finding the length of line segment PQ. Since line segment PQ intersects circle C1 at point P and line segment QR intersects circle C1 at point Q, we can say that the lengths of line segments QP and QR are equal. So, QP = QR = 7.

Similarly, since line segment RS intersects circle C1 at point R and line segment PS intersects circle C1 at point S, the lengths of line segments RS and PS are equal. So, RS = PS = 9.

Now, let's find the length of line segment WS. We know that line segment WX is six times the length of line segment YS. So, YS = WX / 6. Given that YS = 18, we can substitute this value into the equation to find the length of WX: WX = 6 * 18 = 108.

Since line segment PS and line segment WS are equal in length, we can conclude that PS = WS = 9.

Therefore, the sum of the lengths of PS and WS is: PS + WS = 9 + 9 = 18.

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Answer:

(1, 7)

Step-by-step explanation:

a = 2, b = -4, c = 9

x = -b/2a

x = 4/2(2)

x = 1

plug 1 in for 'x' into 2x² - 4x + 9 to get the y-value

2(1) - 4(1) + 9

2 - 4 + 9 = 7

The equation of the degree 6 polynomial with a root at 3, a double root at 2, and a triple root at -1, and y-intercept at y = 5 is given as follows:

y = -5/12(x - 3)(x - 2)²(x + 1)³.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

The zeros of the function, along with their multiplicities, are given as follows:

Then the linear factors of the function are given as follows:

The function is then defined as:

y = a(x - 3)(x - 2)²(x + 1)³.

In which a is the leading coefficient.

When x = 0, y = 5, due to the y-intercept, hence the leading coefficient a is obtained as follows:

5 = -12a

a = -5/12

Hence the polynomial is:

y = -5/12(x - 3)(x - 2)²(x + 1)³.

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The sides of the base of a triangular pyramid are 3, 4 and 5 feet and the altitude is 6 feet Therefore, the volume of the triangular pyramid is 12 cubic feet.

To find the volume of the triangular pyramid, we can use the formula:

Volume = (1/3) × Base Area × Height

First, let's find the base area of the pyramid. Since the sides of the base are given as 3, 4, and 5 feet, we can use Heron's formula to calculate the area of the triangle.

Let s be the semi-perimeter of the triangle, which is half the sum of the sides:

\(s = \frac{(3 + 4 + 5)}{2} = 6\)

Now, we can calculate the area (A) of the base using Heron's formula:

A = √(s × (s - 3) × (s - 4) × (s - 5))

= √(6 × (6 - 3) × (6 - 4) × (6 - 5))

= √(6 × 3 × 2 × 1)

= √36

= 6

Now that we have the base area (A = 6 square feet) and the height (h = 6 feet), we can calculate the volume:

Volume = (1/3) × Base Area × Height

= (1/3) × 6 × 6

= 12 cubic feet

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Protractor postulate: given any angle, we can express its measure as a unique real number from 0 to 180 degrees.

The protractor postulate is a fundamental concept in geometry that establishes a way to measure angles using a protractor. According to this postulate, every angle can be uniquely represented by a real number between 0 and 180 degrees.

A protractor is a geometric tool with a semicircular shape and marked degrees along its edge. To measure an angle using a protractor, we align the center of the protractor with the vertex of the angle and the baseline of the protractor with one side of the angle. We then read the degree measure where the other side of the angle intersects the protractor.

The protractor is divided into 180 degrees, with 0 degrees being the starting point at the baseline of the protractor, and 180 degrees being at the opposite end of the baseline. By aligning the protractor with an angle, we can determine its measure as a real number within this range.

For example, if we measure an angle using a protractor and find that the other side intersects the protractor at 45 degrees, we can express the measure of the angle as 45 degrees. Similarly, if the intersection point is at 90 degrees, the angle measure would be 90 degrees. The protractor postulate guarantees that these angle measures are unique within the range of 0 to 180 degrees.

It is important to note that the protractor postulate assumes that angles can be measured using a protractor and that the measurement is accurate and reliable. The postulate provides a consistent and standardized way to assign a numerical value to an angle, allowing for precise communication and comparison of angles in geometric contexts.

In summary, the protractor postulate establishes that the measure of any angle can be expressed as a unique real number between 0 and 180 degrees. This concept is fundamental in geometry and allows for the measurement, comparison, and communication of angles using a protractor.

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