There are 5 questions on a math exam. Each question is worth twice as much as the question before it. The fifth question is worth 16 points. How much is the first question worth?

Ayana's sandcastle is 1/8 foot taller than her sister's.

Fractions in Math, represent a numerical value that expresses a part of a whole. The whole can be any number, specific value, or a thing.

Given,

Ayana's sandcastle was 1/2 of a foot tall

Her sister's was 3/8 of a foot tall.

Difference between the height of the both sandcastle

= 1/2 - 3/8

= (4 - 3)/8

= 1/8

Hence, Ayana's sandcastle is taller than her sister's by 1/8 foot.

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The average value of a function over the interval to be -π/4 + C/3π.

In this case, we need to calculate the average value of y=xsin(x) over the interval [0,3π/2]. To calculate this, we must first calculate the integral of the function over the interval. This is done by finding the antiderivative of the function and then evaluating the antiderivative at the upper and lower limits of the interval. The antiderivative of the function is -cos(x) + sin(x)x + C. Evaluating this at the lower and upper limits of the interval, we get 0-0 + 0 + C = C. To calculate the average value of the function, we divide the integral by the length of the interval. The length of the interval is 3π/2, so the average value of the function over the interval is the integral divided by 3π/2. Evaluating the integral, we get -cos(3π/2) + sin(3π/2)(3π/2) + C. Substituting in the values, we get -(-1) + 1(3π/2) + C = -π/2 + C. Finally, dividing this by 3π/2, we get the average value of the function over the interval to be -π/4 + C/3π.

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According to the triangle proportionality theorem, the drawings where DE is parallel to AC is: C.

The Triangle Proportionality Theorem states that in any triangle, the ratio of the length of a side to the length of the segment from its endpoint to the line containing the opposite side is constant, and equal to the ratio of the lengths of the other two sides. If the ratios are equal, then the segment that joins two sides is parallel to the third side.

In figure C, we have the following:

AD/DB = CE/EB

Substitute

22.5/15 = 24/16 = 1.5

Therefore, the correct drawing is: C.

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Answer:

b+52<72

Step-by-step explanation:

Answer:

375

Step-by-step explanation:

Formula+ Number x 100/percent= 345x100/92=375

Marissa will earn $ 1678.41 more if she chooses the Lumpsum amount of money.

The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. A = P(1 + r/n)^nt, where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, which is the formula for compound interest.

Given, Marisa has just won a contest. She must decide between two prize options:

Option A: Collect a lump-sum payment of $50 000.

Option B: Receive $800 at the end of every quarter for 10 years from an investment. The investment earns 8%/annum, compounded quarterly.

We must calculate how much the future value has an 800$ quarterly payment for 10 years at 8%.

R = 800

rate = 0.08

Compounded quarterly

i = 0.08/4 = 0.02

t = 10 years

m = 10 *4

From the formula of the present value of Annuity:

FV = R. ((1 + i)^m - 1)/i

FV = 48321.59

Since the lump sum payment is 50,000$

The difference in payments = 50,000 - 48321.59

The difference in payments = 1678.41

Therefore, Marissa will earn $ 1678.41 more if she chooses the Lumpsum amount of money.

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Number C₃ = 5 is written in the center.

Matrices are the arrangement of numbers, variables, symbols, or expressions in the rectangular format, in the form of rows and columns.

Square matrix is a matrix with the same number of rows and columns.

Given,

Sum of neighbors of 6 and 8  is 10.

By the figure,

If C₁ = 6

then, 1 + C₃ + 2 = 10 ⇒ C₃ = 7

But if C₃ = 7, then sum for neighbors of any unknown column cannot be 10.

Now, C₂ = 5

then, 1 + C₃ + 4 = 10 ⇒ C₃ = 5

Considering

C₃ + 2 + 3 = 10 that are neighbors to C₄

5 + 2 + 3 = 10

Thus, C₄ = 8

Hence, C₃ = 5 is the number written in center.

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all sets are equal because all the sets contains only three elements in it that elements are 6,7,8

What is a set?

A set is a mathematical model for a collection of items; it comprises elements or members, which may be any mathematical object: numbers, symbols, points in space, lines, other geometrical structures, variables, or even other sets.

a = {6, 7, 8}

b = {x is in r| 5 ≤ x < 9}

c = {x is in r| 5 < x < 9}

d = {x is in z| 5 < x < 9}

e = {x is in z | 5 < x < 9}

Hence all sets are equal because all the sets contains only three elements in it that elements are 6,7,8

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So far they have painted 20% of the fence which is 70 feet long.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, It took Amair 2 hours to paint the first 14 feet of a 70-foot-long fence.

Therefore, The percentage of fences they have painted so far is,

= (14/70)×100%.

= 0.2×100%.

= 20%.

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The fraction value 3/8 of the total students 24 will be (students who rides the bus) 9.

What is a fraction?

In Maths, a fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator. The numerator defines the number of equal parts taken, whereas the denominator defines the total number of equal parts in a whole.

For example, 5/10 is a fraction.

Here, 5 is a numerator and 10 is a denominator.

There are four different types of fractions. They are:

Unit Fraction – In a fraction, the numerator with 1 is called a unit fraction. For example, ½, ¼

Proper Fraction – If a numerator value is less than the denominator value, it is called a proper fraction. Example: 7/9, 8/10

Improper Fraction – If a numerator value is greater than the denominator value, then it is called an improper fraction. Example: 6/5, 11/10

Mixed Fraction – If a fraction consists of a whole number with a proper fraction, it is called a mixed fraction. Example 5 ¾, 10 ½

Now,

Given

Total students=24

Fraction of students who rides the bus=3/8

So, no. of students who rides the bus=3/8*24

=3*3

=9

Hence,

       The no. of students who rides the bus is 9.

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The slopes of perpendicular lines are opposite reciprocals and hence option D is correct

The slope of the given line is 3/8, so its opposite reciprocal is -8/3. From the options we have to find a line with this slope.

In the given line, it was easy to find the slope because the equation is in slope-intercept form, but in the options the equations are in standard form,

If we solve this for y we get the slope-intercept form,

Thus the slope of a line whose equation is in standard form is,

• Option A: a = 3, b = 8. The slope is -3/8 → ,not perpendicular

• Option B: a = 3, b = -8. The slope is 3/8 → ,not perpendicular

• Option C: a = -8, b = 3. The slope is 8/3 → ,not perpendicular

• Option D,: a = 8, b = 3. The slope is -8/3 → ,this line is perpendicular, to the given line

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If marc r v = marc v u , the value of marc v u is given as 64°.

mArc R V = mArc V U, Angle S O R = 13 x degrees and angle T O U = 15 x - 8 degrees

∠SOR = ∠TOU  (Vertically opposite angles are equal). Therefore:

13 x = 15x - 8

solving by calculating the value of x to satisfy the equation: Subtracting 13x from both sides

13x - 13x = 15x - 8 - 13x

0 = 15x - 13x - 8

2x - 8 = 0

Adding 8 to both sides:

2x - 8 + 8 = 0 + 8

2x = 8

2x/2 = 8/2  

x = 4

∠SOR = 13x = 13(4) = 52°

∠TOU = 15x - 8 = 15(4) - 8 = 60 - 8 = 52°

Let a = mArc R V = mArc V U

Therefore:

mArc R V + mArc V U + ∠TOU = 180 (sum of angles on a straight line)

Substituting:

a + a + 52 = 180

2a = 180-52

2a = 128

a = 128/2

a= 64°

mArc R V = mArc V U = 64°

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Mike made 15/18 of his free throw attempts.

Lisa made 14/18 of her free throw attempts.

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

We have to given that;

Mike made 5/6 of his free throw attempts.

And, Lisa made 7/9 of her free throw attempts.

Now, We can solve as;

To bring the denominator, we need to take the LCM of the denominator, therefore,

⇒ 5/6, 7/9

We know that the LCM of 6 and 9 is 18.

⇒ 5×3/6×3, 7×2/9×2

⇒ 15/18, 14/18

Thus, Mike made 15/18 of his free throw attempts.

And, Lisa made 14/18 of her free throw attempts.

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The explicit formula for the sequence generated by a₁ = 4, an an-1+5 where n = 2, 3, 4, .... is an = 5n + 4, where n = 1, 2, 3, ....

Explicit formula is a mathematical expression that explicitly states the rule used to calculate the value of a function. It is a formula that provides a direct and unambiguous representation of a given calculation, without relying on any additional information.

The explicit formula for the sequence generated by a₁ = 4, an an-1+5 where n = 2, 3, 4, .... is an = 5n + 4, where n = 1, 2, 3, .... This can be derived by substituting n = 1 into the given recursive formula and solving for a₁. The result is that a₁ = 4, which can be written in the explicit form as a₁ = 5(1) + 4. This can be generalized to an = 5n + 4, where n = 1, 2, 3, ....

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Answer:

554433221100

is in form

and have to divide by 11

554433221100/11

50403020100 is the answer.

Answer: 9 numbers

Step-by-step explanation:

Answer:

To solve the inequality ≤ \frac{3}{8}, we need to find all the values of x that will make the inequality true. We can start by setting the inequality equal to zero and solving for x.

x ≤ \frac{3}{8}

To graph the solution on a number line, we can use an open circle at \frac{3}{8} to indicate that the value is not included in the solution. So the solution set is: (-∞,3/8)

To solve the inequality > -\frac{9}{5}, we need to find all the values of x that will make the inequality true. We can start by setting the inequality equal to zero and solving for x.

x > -\frac{9}{5}

To graph the solution on a number line, we can use an open circle at -\frac{9}{5} to indicate that the value is not included in the solution. So the solution set is: (-9/5, ∞)

Step-by-step explanation:

The required Solutions of the given quadratic equation are 9 or -1.

x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem.

x²−8x−9=0

To solve it by completing the square.

x² − 8x + 16 − 16 −9=0

(x - 4)²  = 25

x - 4 = ± 5

So,

x - 4 = 5     or    x - 4 = -5

x = 9          or     x = -1

Thus required Solution of equation are 9 or -1.

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A set of steps which a student should follow to prove that the diagonals of the square are perpendicular to each other include the following: A) Step 1: Find the slope of diagonal PR and slope of diagonal QS Step 2: Show that m₁ × m₂ = -1.

In order for a quadrilateral to be a square, the two (2) pairs of its sides must be equal (congruent) and perpendicular to each other. Therefore, we would have to calculate the slope of each side by using this mathematical expression:

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Where:

x and y represents the data points or side lengths of a quadrilateral.

For side PQ, the slope is given by:

Slope (m) = (8 - 4)/(6 - 2)

Slope (m) = (4)/(4)

Slope (m) = 1.

In Mathematics, a condition that must be met for two (2) lines or side lengths to be perpendicular is given by:

m₁ × m₂ = -1

1 × m₂ = -1

m₂ = -1

Slope (m₂) = -1

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An algorithm to find the substring from the given string that is the same when read forwards and backwards in python language.

Here's a basic algorithm in Python to find the longest palindromic substring:

def longest_palindromic_substring(input_str):

   n = len(input_str)

   if n == 0:

       return ""

   dp = [[False for _ in range(n)] for _ in range(n)]

   longest_len = 1

   longest_start = 0

   for i in range(n):

       dp[i][i] = True

   for start_idx in range(n - 1, -1, -1):

       for end_idx in range(start_idx + 1, n):

           if input_str[start_idx] == input_str[end_idx]:

               if end_idx - start_idx == 1 or dp[start_idx + 1][end_idx - 1]:

                   dp[start_idx][end_idx] = True

                   if end_idx - start_idx + 1 > longest_len:

                       longest_len = end_idx - start_idx + 1

                       longest_start = start_idx

   return input_str[longest_start : longest_start + longest_len]

The above algorithm uses dynamic programming to solve the problem in O(n^2) time complexity, where n is the length of the input string.

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The Parallel , Meridian in the geographical coordinate system is defined below and zero Line is where prime meridian is at 0° longitude .

In a Geographic Coordinate system, a Meridian is a line of longitude that runs from the North Pole to the South Pole and is used to indicate the east-west position of a location on the Earth's surface.

A Parallel is a line of latitude that circles the Earth parallel to the equator and is used to indicate the north-south position of a location on the Earth's surface.

The Zero Line  is the line of longitude that is defined as 0° and runs from the North Pole to the South Pole, passing through Greenwich, England. The equator is the line of latitude that is defined as 0° and circles the Earth at an equal distance from the North and South Poles.

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Answer:220.5

Step-by-step explanation:

Do 315 - 30%

You saved $135 off the original price of the guitar. The original price is $450. The sale price is 30% off the original price.

The number of people took more than 25 minutes to finish a crossword is 9.

A stem and leaf plot also called a stem and leaf diagram is a way of organizing data into a form that makes it easy to observe the frequency of different types of values. It is a graph that shows numerical data arranged in order. Each data value is broken into a stem and a leaf.

A stem and leaf plot is represented in form of a special table where each first digit or digit of data value is split into a stem and the last digit of data in a leaf.

From the given stem and leaf plot, we have

10, 11, 14, 24, 25, 26, 27, 28, 34, 34, 40, 42, 45 and 47

So, the number of people took more than 25 minutes is 9.

Therefore, the number of people took more than 25 minutes to finish a crossword is 9.

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The value of  a+ b + c + d + e + f is 2.

It is referred to as being in factored form when a quadratic expression is represented as the sum of two linear factors plus a constant.

We have to factor x² – y² – z² + 2yz.

Using the general rule that p² – 2pq + q² = (p – q)² .

So we want to rearrange the last three terms.

= x² + (–y² – z² + 2yz)

Now, If we were to factor out a –1 from the last three terms, we have

= x² – (y² + z² – 2yz)

Now put y² + z² – 2yz = (y – z)².

= x² – (y – z)²

This expression is actually a differences of squares.

We know p² – q² as (p – q)(p + q).

=x² – (y – z)²

= (x – (y – z))(x  + (y – z))

Now, let's distribute the negative one in the trinomial x – (y – z)

= (x – (y – z))(x  + (y – z))

= (x – y + z)(x + y – z)

Now, comparing (x – y + z)(x + y – z)  and  (ax + by + cz)(dx + ey + fz)

we get a = 1, b = –1, c = 1, d = 1, e = 1, and f = –1.

So, a+ b + c + d + e + f

= 1 - 1 + 1+ 1 +1 - 1

= 2

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The current age of the artifact is 1600 years

Let's call the current age of the artifact "a" and the current age of the book "b".

The artifact is four times as old as the book, so we have:

a = 4b

In 200 years, the artifact will be a + 200 and the book will be b + 200.

From the problem, we know that in 200 years:

a + 200 = 3 (b + 200)

Expanding the right side:

a + 200 = 3b + 600

Substituting a = 4b:

4b + 200 = 3b + 600

Solving for b:

b = 400

So the current age of the book is 400 years old.

Recall that

a = 4b

So, we have

a = 400 * 4 = 1600

And the current age of the artifact is 4 times that, or 1600 years old.

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Answer:B

Step-by-step explanation:If you count the blocks it adds

up to 53

This relationship between AT-1 and A-I be used to determine information about matrix X by option (A) and (C).

(A) Since the two matrices are equal, the nonzero vector x must be a constant multiple of the nonzero vector v and (C) Since the two matrices are inverses, if either (AT-x=0 or (A-AI)v=0 has at least one nontrivial solution, then all of the statements of the Invertible Matrix Theorem are true for both matrices.

Therefore, if A is an eigenvalue of A, then λ must be an eigenvalue of AT, and vice versa. This can be seen by comparing the equation (A-λI)x=0 with the equation (AT-λI)v=0. If x is an eigenvector of A with eigenvalue λ, then it follows that v=x is an eigenvector of AT with eigenvalue λ. And if v is an eigenvector of AT with eigenvalue λ, then it follows that x=v is an eigenvector of A with eigenvalue λ.

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Step-by-step explanation: A) The number of miles the earth travels in one complete revolution around the sun can be estimated using the circumference of the circular orbit.

Circumference = 2 * π * radius

Since the average distance from the earth to the sun is 93 million miles, this is the radius of the circular orbit:

Circumference = 2 * π * 93 million miles

Simplifying, we get:

Circumference = 186 million * π miles

So the number of miles the earth travels in one complete revolution is approximately 186 million * π miles.

B) To find the speed of the earth in feet per second, we need to divide the total distance by the time it takes to travel that distance.

The complete revolution takes 1 year, or 365.25 days. So the time it takes to travel the distance is 365.25 days * 24 hours/day * 60 minutes/hour * 60 seconds/minute = 31,536,000 seconds.

Speed = Total distance / Time

Speed = 186 million * π miles / 31,536,000 seconds

We can convert miles to feet:

Speed = 186 million * π * 5280 feet/mile / 31,536,000 seconds

So the speed of the earth in its orbit around the sun is approximately 66,600 feet per second.

Answer:

A) One complete revolution around the sun is equal to the circumference of a circle with radius 93 million miles. The circumference of a circle with radius r is given by 2πr, so the circumference of the earth's orbit is 2π * 93 million = 186 million miles * π.

B) To convert this distance to feet per second, we first need to convert miles to feet (1 mile = 5280 feet). The distance the earth travels in one complete revolution is 186 million miles * 5280 feet/mile = 979,680,000,000 feet. If this distance is travelled in one year, then the speed of the earth in feet per second is 979,680,000,000 feet / (365 days/year * 24 hours/day * 60 minutes/hour * 60 seconds/minute) = 66,620 feet/second.

When taking a measurement using a device with an analog scale, we can determine the last digit in the number you report by Add one estimated value aside from the value given by the analog scale. The estimate will be your best guess on where it falls relative to the object measured.

Analog scales are a type of scale operated manually without using electricity to determine the weight of a weighted object. The definition of scales can be concluded as a tool that has the function of measuring or knowing the mass of an object/substance.

Analog scales existed before the use of electronic/electrical technology on analytical scales. The working principle of analog scales is based on the gravitational swing arm balance.

This is where it is important for you to know the meaning of balances / scales and how to use them.

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The number of possible selections is 13,800.

A permutation is the number of ways an object can be arranged in a particular manner. A permutation is denoted by 'P'.

The combination is the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.

[tex]C_{n,r} = \frac{n!}{(n-r)! r !}[/tex]   ,  [tex]P_{n,r} = \frac{n!}{(n - r) !}[/tex]

where,

n is the number of choices available,

and r is the choices to be made.

According to the question,

The number of possibilities in which the students can be selected and the awards can be given is,

[tex]= \frac{25!}{(25 - 3) !}[/tex]

[tex]= \frac{25 !}{22 !}[/tex]  

= [tex]\frac{25 * 24 * 23 * 22 !}{22!}[/tex] = 1380

Hence, there are 13,800 possible selections.

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The condition "y divide by 7 then add 2" can be represented as expression,    [tex]\frac{y}{7} +2[/tex]

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

A condition,

y divide by 7 then add 2

Here, we have to apply two operation to complete this expression,

1.  Division

2. Addition

First, doing division operation,

y divide by 7

⇒  y/7

Now, second operation which is addition of 2

⇒  [tex]\frac{y}{7} + 2[/tex]

Hence, the expression is   [tex]\frac{y}{7} + 2[/tex]

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