In the rectangle ABCD given in the figure, AB = 3x + 2 cm and AD=x+3 cm. It is given that APQD is a square. Show that PB=2x-1 cm and It is given that AB/AD=PQ/PB Show that 5x²-5x-11-0.​

The errors that may have occurred in the student's measurements are random errors. These types of errors can arise from various sources, such as slight variations in measurement techniques or environmental factors.

Since the measured values are slightly different, it suggests that random errors affected the measurements rather than systematic errors, which would result in consistently incorrect measurements.

To minimize the impact of random errors during data analysis, the student can calculate the average of the three measured values. The average value can serve as the best estimate of the true value of the mass of the rock. Additionally, the student can calculate the standard deviation of the measured values to determine the precision of the measurements. The smaller the standard deviation, the more precise the measurements.

The student can further minimize random errors by taking multiple measurements and averaging them to obtain a more accurate value. Additionally, using a digital balance instead of an analog one may reduce random errors as digital balances have greater precision and accuracy.

It is also important for the student to use proper measurement techniques such as ensuring that the balance is calibrated and zeroed correctly before each measurement. The student should also avoid applying excessive force on the balance and ensure that the rock is stable and level during measurement.

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The estimated probability  that Roger runs less than 5 km in his next tennis match is  33%.

The dot plot summarizes the distance Roger ran in his recent tennis matches. To estimate the probability that he will run less than 5 km in the next match, we can use the data from the dot plot.

So according to question, there are kilometres as :

3 km, 4 km, 5 km, 6 km, and 7 km.

Total matches he played

for 3 km- 1 match , for 4 km- 2 matches , for 5 km- 4 matches, for 6 km- 0 matches, and for 7 km- 2 matches.

Out of 9 matches, he ran less than 5 km in 3 matches.

So the probability that Roger runs less than 5 km in his next tennis match is: 3/9  = 1/3

So the percentage will be : 33.33%   ≈ 33%

Therefore, the estimated probabilityrobability that Roger runs less than 5 km in his next tennis match is 1/3 or about 33%.

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Answer: 33%

Step-by-step explanation:

The ordered pairs that are solution to the system are (15, -1) (0,4) (10, 30) (5, 5) (1, 10)​

From the question, we have the following parameters that can be used in our computation:

2x + 3y>10

y≥ -3x + 2

Represent properly

2x + 3y > 10

y ≥ -3x + 2

Next, we make a plot of the system to determine the solution

The shaded area in the plot represent the solution to the inequality

In this case, the coordinates in the shaded area are

(15, -1) (0,4) (10, 30) (5, 5) (1, 10)​

None of the options represent the shaded area (see attachment)

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The standard form of the polynomial is given as follows:

-13m^4 - m² + 12m + 7.

Hence the degree of the polynomial is of:

4th degree.

The leading coefficient is of:

-13.

The standard form of the polynomial is obtained writing the polynomial in decreasing order of the exponents, hence:

-13m^4 - m² + 12m + 7.

Then the degree and the leading coefficient are given as follows:

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The information from the given set have the following solutions for:

a) X ∪ Y = {1, 3, 5, 6, 7, 9}

b) X ∩ Z = {1, 9}

c) X' = {2, 4, 6, 8}

In mathematics, a set is a collection of distinct objects, called elements or members, that share a common property or are grouped together for some reason. A set can be finite or infinite.

For the universal set S = {1, 2, 3, 4, 5, 6, 7, 8, 9}

Z = {1, 2, 4, 6, 8, 9}

X = {1, 3, 5, 7, 9}

Y = {1, 5, 6, 7}

we shall evaluate for the following:

X ∪ Y = {1, 3, 5, 6, 7, 9} {all the elements in X and Y}

X ∩ Z = {1, 9} {the elements common to X and Z}

X' = {2, 4, 6, 8} {all the elements in the universal set not in X}

Therefore, the information from the given set have the following solutions for:

a) X ∪ Y = {1, 3, 5, 6, 7, 9}

b) X ∩ Z = {1, 9}

c) X' = {2, 4, 6, 8}

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The final count of integers between 3 and 89 that cannot be written as the sum of exactly two elements of the set is 39.

To determine the number of integers between 3 and 89 that cannot be written as the sum of exactly two elements of the set {1, 2, 3, 5, 8, 13, 21, 34, 55}, we can use a process of elimination.

First, we can list all the possible sums of two distinct elements of the set. This gives us a total of 28 sums.

Next, we can identify all the integers between 3 and 89 that can be expressed as the sum of two distinct elements of the set. We can do this by checking each integer between 3 and 89 to see if it can be written as a sum of two elements of the set. If an integer can be written as a sum of two elements of the set, we can cross it off the list.

After eliminating all the integers that can be written as a sum of two elements of the set, we are left with the integers that cannot be expressed as such.

In summary, we can determine the number of integers between 3 and 89 that cannot be written as the sum of exactly two elements of the set by listing all possible sums, identifying the integers that can be expressed as such sums, and eliminating them from the list.

The remaining integers are those that cannot be expressed as the sum of exactly two elements of the set.

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The statement "if written backwards, the number, one thousand, one hundred twenty-five, would be written five thousand, two hundred eleven " is true

The given statement is

If written backwards, the number, one thousand, one hundred twenty-five, would be written five thousand, two hundred eleven

We have to check the given statement is true or false

The given number is

One thousand one hundred and twenty five

Write the number in numeric terms

One thousand one hundred and twenty five = 1125

Write the number in backwards

= 5211

Then the number will be

Five thousand two hundred and eleven

Therefore, the given statement is true

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If Mark and jada share 5 yards of ribbon equally, then each one will get 2.5 yards of ribbon using division method.

When Mark and Jada share 5 yards of ribbon equally, it means that they will divide the total amount of ribbon equally between the two of them. This is a common type of problem in mathematics that involves dividing a given quantity equally among a certain number of people or objects.

To solve this problem, we used the division operation to divide the total amount of ribbon (5 yards) by the number of people who are sharing it (2). The resulting quotient (2.5 yards) represents the amount of ribbon that each person will receive.

Using the division operation, we can write,

5 yards ÷ 2 = 2.5 yards

This problem illustrates an important concept in mathematics: the division of quantities into equal parts. This concept is used in many real-world applications, such as dividing up a pizza among a group of people or allocating resources in a company among different departments or teams.

Understanding how to divide quantities into equal parts is an important skill that can be applied in many different contexts, making it a valuable mathematical concept to learn and understand.

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a)The energy stored when the extension is 5 cm is given by A = 675 Joules

b) The extension when the energy is 36 Joules is x = ( 2/√3 ) cm

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The energy E stored in an elastic band varies as the square of the energy stored extension x

So , the equation is E = kx²

And , when x = 3 cm , E = 243 Joules

Substituting the values in the equation , we get

243 = k ( 3 )²

9k = 243

k = 27

a)

Now , when the extension x = 5 cm

The energy stored when the extension is E = kx²

On simplifying , we get

E = 27 ( 5 )²

E = 27 x 25

E = 675 Joules

b)

When the energy is E = 36 Joules

E = kx²

36 = 27 ( x )²

On simplifying , we get

x² = ( 36 / 27 )

Taking square roots on both sides , we get

x = ( 6/3√3 ) cm

x = ( 2/√3 ) cm

Hence , the equation is E = kx²

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Answer: The number of blue marbles in the sample is 11, so the proportion of blue marbles in the sample is 11/20. If the sample is representative, we can use this proportion to estimate the proportion of blue marbles in the whole bag of 950 marbles. So, our estimate of the number of blue marbles in the whole bag is:

950 * (11/20) = 477.5

So, we can estimate that about 478 marbles out of 950 are blue.

Step-by-step explanation:

The width in miles, of the park is equal to 5/6 miles.

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

Where:

Substituting the given points into the area of rectangle formula, we have the following;

25/54 = 5/9 × W

Width, W = 25/54 × 9/5

Width, W = 5/6 miles.

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Complete Question:

The area of a rectangular city park is 25/54 square miles. The length if the park is 5/9 of a mile. What is the width in miles, of the park?

Answer:

6 is not the solution.  7 is the solution.

Step-by-step explanation:

5(x -3) = x + 13  Substitute 6 for x

5(6 -3) = 6 + 13

5(3) = 19

15 ≠ 19

6 is not a solution because it results in a false statement.  The two sides do not equal each other.

5(x - 3) = x + 13   Distribute the 5

5x -15 = x + 13  Subtract x from both sides

5x - x - 15 = x - x + 13

4x - 15 = 13  Add 15 to both sides

4x - 15 + 15 = 15 + 13

4x = 28  Divide both sides by 4

x = 7

7 is the solution to the equaion.

1. 121 degree. 2. 15 degree. The side of the dilated triangle increases by scale factor. Here, 1.5, thus: 3. LM = (20)(1.5) = 30 4. MN = 26(1.5) = 39 5. RT = 57/1.5 = 38. 6. Triangle RST is congruent to triangle LMN.

Transformations involve the reflection, refraction, or translation of forms on a coordinate plane. Felix Klein put forth a novel perspective on geometry in the 19th century called transfinite geometry. The majority of geometric principles depend on the transmissions of objects.

Transfrmatiions enable the modification of any image in a coordinate plane. You can better understand the graphics in video games by using the mathematical laws of transmission.

As a result, the red triangle is a dilation of the blue triangle.

When triangle is dilated the angles remain the same. Thus,

1. 121 degree.

2. 15 degree.

The side of the dilated triangle increases by scale factor. Here, 1.5, thus:

3. LM = (20)(1.5) = 30

4. MN = 26(1.5) = 39

5. RT = 57/1.5 = 38

6. Triangle RST is congruent to triangle LMN.

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120 calories make up one cup amount of calories. Three cups of the cereal have 360 calories in them.

1. Determine how many calories are in a cup: 120 calories are in 3/4 cup; 3/4 cup is 120 calories.

2. Determine how many calories are in 3 cups: 3 cups at 120 calories each equals 360 calories.

You must divide the total amount of calories in a serving of 3/4 cup by 3/4 cup to determine the unit rate for calories per cup of a certain cereal. In this instance, a serving of the cereal that is 3/4 cup in size has 120 calories. As a result, 120 calories are the number of calories in a cup. You must multiply the unit rate for calories per cup (120 calories) by 3 cups to see how many calories are in 3 cups of cereal. This indicates that there are 360 calories in 3 cups of the cereal. In summary, there are 360 calories in 3 cups of cereal, or 120 calories per cup, at the unit rate.

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The measurements required to provide a 95% confidence interval in the true mean to within plus minus 0.28v  are 2 measurements and they are 1.24v and 1.8v .

Given that, based on 51 measurements of time-dependent electrical signal, the standard deviation is 1.52 v

The 95 confidence interval in its true mean value is 0.28 and the measurements required to provide a 95% confidence interval in the true mean to within plus minus 0.28v  are 2 measurements and they are 1.24v and 1.8v

A Standard Deviation of the R.V.(random variable), a sample, and a statistical population, the data set, or the probability distribution is the square root of the its variance

A True Mean refers to a population mean. It actually would not have a population mean, because since it is the either impossible to get and probably the time consuming and too much expensive to get it.

Therefore, the 95 confidence interval in its true mean value is 0.28 and the measurements required to provide a 95% confidence interval in the true mean to within plus minus 0.28v  are 2 measurements and they are 1.24v and 1.8v

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Step-by-step explanation:

let's write this properly that we are not confusing ourselves :

s = ½×a×t²

a = 30 ft/sec²

t = 6 sec

so,

s = ½ × 30 ft/sec² × (6 sec)² = ½ × 30 ft/sec² × 36 sec² =

= ½ × 30 ft × 36 = 15 ft × 36 = 540 ft

s = 540 ft

There are 20 different combinations of committees that can be formed since no person can serve on more than one committee.

In order to form committees of 4, 3, and 2 people, we must first determine how many combinations are possible. There are 9 people in total, so the first committee must consist of 4 people. That leaves 5 people. The second committee must consist of 3 people, leaving 2 people for the final committee. To calculate the total number of combinations, we must multiply the number of choices for each committee. For the first committee, there are 9C4 combinations, for the second committee there are 5C3 combinations, and for the third committee there are 2C2 combinations. Multiplying these together, we obtain 9C4 x 5C3 x 2C2 = 20 combinations. Therefore, there are 20 different combinations of committees that can be formed since no person can serve on more than one committee.

The complete question: A group of 9 people is going to be formed into committees of 4, 3, and 2 people. How many can be formed if no person can serve on more than one committee?

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All the angles of the given parallelogram found using the properties of the parallelogram are 38°,38°, 142° and 142°.

What is meant by a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size. On the same side of the transversal, the interior angles are supplementary. 360 degrees is the sum of all interior angles. The qualities of a parallelogram are shared by the shapes of a square and a rectangle.

Given the two opposite angles of parallelogram as (4x-50)° and

(60 - x)°.

We are asked to find all the angles of the parallelogram.

As said earlier, opposite angles of parallelogram are equal.

So,

4x-50 =  60 - x

5x = 110

x = 22

So the opposite angles are:

4x-50 = 4*22- 50 = 38°

Adjacent angles are supplementary. So,

38 + y = 180

y = 142°

Sum of all angles of parallelogram should be 360°.

38+38+142+142 = 360°.

Therefore all the angles of the parallelogram are 38°,38°, 142° and 142°.

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By empirical rule, 99.7% of the students have a grade point average which is between 1.38 and 3.84.

Suppose that the grade point average of undergraduate students at one university has a bell-shaped distribution with a mean of 2.61 and a standard deviation of 0.41.

Here, μ = 2.61 , σ = 0.41

Using the empirical rule :

The first part of the empirical rule states that 68% of the data values will fall within 1 standard deviation of the mean. To calculate "within 1 standard deviation," you need to subtract 1 standard deviation from the mean, then add 1 standard deviation to the mean. That will give you the range for 68% of the data values.

2.61 − 0.41 = 2.2

2.61 + 0.41 = 3.02

The range of numbers is 2.2 to 3.02

The second part of the empirical rule states that 95% of the data values will fall within 2 standard deviations of the mean. To calculate "within 2 standard deviations," you need to subtract 2 standard deviations from the mean, then add 2 standard deviations to the mean. That will give you the range for 95% of the data values.

2.61 − 2(0.41) = 1.79

2.61 + 2(0.41) = 3.43

The range of numbers is 1.79 to 3.43

Finally, the last part of the empirical rule states that 99.7% of the data values will fall within 3 standard deviations of the mean. To calculate "within 3 standard deviations," you need to subtract 3 standard deviations from the mean, then add 3 standard deviations to the mean. That will give you the range for 99.7% of the data values.

2.61 − 3(0.41) = 1.38

2.61+3(0.41) = 3.84

The range of numbers is 1.38 to 3.84.

Hence, 99.7% of the students have a grade point average which is between 1.38 and 3.84.  

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Zachariah has a higher ratio of American stamps than Khai because 7 over 12 is less than 15 over 24.

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Answer: obtuse scalene triangle

Step-by-step explanation:

A scalene triangle has three different sides.

An isosceles triangle has 2 of the same sides and 1 different side.

Answer:

Its a obtuse scalene triangle!

The distance between the candy store and the skate park is about 5.2 miles, with a hypotenuse of 6 miles and a leg of 9 miles, as computed using the Pythagorean theorem.

The candy shop is at the right angle of a triangle made up of Cindy's school, the skate park, and the candy store. Using the Pythagorean theorem, we can calculate the distance between the skate park and the candy shop.

Let's name the separation between the candy shop and the skate park "x" distance. The hypotenuse of the right triangle, the distance between Cindy's school and the candy store, is then 6 miles away, while one of the legs, the skate park, is 9 miles away.

Using the Pythagorean theorem, we can write:

6² = 9² + x²

Simplifying, we get:

x² = 27

Taking the square root of both sides, we get:

x ≈ 5.2

Therefore, The distance between the candy store and the skate park is about 5.2 miles, with a hypotenuse of 6 miles and a leg of 9 miles, as computed using the Pythagorean theorem.

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The total number of different sets using three points of the grid with three vertices of an isosceles triangle equal 36.

Number of points of 3 by 3 grid are spaced horizontally and vertically equally .

Total number of points present on 3 by 3 grid are 9.

To form an isosceles triangle with two of the equal sides .

Total number of different sets of isosceles triangle are given by :

⁹C₂

= 9! / ( 9 - 2)! 2!

= ( 9 × 8 × 7! ) / 7! 2!

= 36.

Therefore, the number of different sets of isosceles triangle with three vertices on 3 by 3 grid is equal to 36.

The above question is incomplete , the complete question is:

The points of this 3-by-3 grid are equally spaced horizontally and vertically. how many different sets of three points of this grid can be the three vertices of an isosceles triangle?

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Answer:

Student A is incorrect. Student b is correct.

Step-by-step explanation:

Yes, both students' evaluations of the expression are correct.

The product of a number by addition is equal to the total of the products of that number by each of the addends, according to the distribution property of multiplication.

Simplify the given expression 17(4 + 15) using the distributive property as:

17(4 + 15) = 17(19) = 323

Student A evaluates the expression by adding the product of 17 and 4 to the product of 17 and 15:

17(4) + 17(15) = 68 + 255 = 323

Thus, student A's evaluation is correct.

Student B evaluates the expression by determining the product of 17 and 19:

17(19) = 323

Thus, student B's evaluation is also correct.

Therefore, both students' evaluations are correct.

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The number of cups of mix that is needed to be used will be 12.8 cups.

Any value assigned to a variable that results in equal outcomes, i.e., tends to equalize the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal, is a solution to a formula. To solve a problem, you must find the formula's workable answer.

For every 2 cups of mix in a lemonade recipe, there should be 3 cups of water. Lemonade made with this recipe makes 5 cups.

Let 'W' be the amount of water in gallons and 'M' be the amount of mix in gallons.

Then the equations are given as,

W / M = 3 / 2            ...1

W + M = 2               ...2

From equations 1 and 2, then we have

(3/2)M + M = 2

(5/2)M = 2

M = 4/5

M = 0.80 gallons

We know that in one gallon, there are 16 cups. Then we have

M = 0.80 x 16

M = 12.8 cups

The number of cups of mix that is needed to be used will be 12.8 cups.

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nah I don't think I want to.

The volume of the rectangular prism will be 270 cm³. The correct option is B.

The volume of the rectangular prism is defined as the space in three-dimension covered by the rectangular prism having the sides Length, Width, and Height.

The volume of the rectangular prism will be the multiplication of the three parameters which are Length, Width, and Height of the prism.

The volume will be calculated by the formula:-

Volume = L x W x H
Volume = 2 x 9 x 15

Volume = 270 cubic cm

The volume of the rectangular prism will be 270 cm³.

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The complete question is given below and the missing image is attached with the answer below.

A ringtoss toy is composed of a rectangular prism on top of a cylinder.

The rectangular prism is completely filled with water.

The dimensions of the rectangular prism are shown in the diagram.

What is the volume of the rectangular prism in cubic centimeters?

A) 26 cm3

B) 270 cm3

C) 165 cm3

D) 348 cm3

Answer:

2y=9-3x. 2=(3-x)3y

2=(9-3x)/y......1 2= 3y(3-x)..........2

Combining equations 1 and 2;

9-3x=3y²(3-x)

3(3-x)=3y²(3-x)

y²=1

y=√1

y= ±1