Lara bought 3 yards of fabric and a spool of thread for $28.10. If the spool of thread cost $1.25, how much did the fabric cost per yard? Write and solve an equation to answer.

Step-by-step explanation:

A man by the name of Luigi Fonti wrote this. I hope it can guide you, as it did for me! "The set of rational numbers is closed for all the four operations, so x+y, x-y, x*y and x/y are rational too. And it is easy to demonstrate. A rational number can be expressed as a fraction of two integers. So, x can be expressed as a/b and y as c/d. Hence x+y = a/b + c/d = (ad+bc)/bd, which, as fraction of two integers, is rational."

These are just a few examples, and there are likely more combinations that can result in a total of 20 points. The key is to consider the different point values for catching pop flies, fielding grounders, and making good or bad throws.

There are multiple ways your son could get a total of 20 points in the game of fielding practice. Here are a few possibilities:
1. He catches 1 pop fly and makes a good throw (10 points), and then he fields 2 grounders and makes good throws (7 points each). In this scenario, he would earn a total of 24 points (10 + 7 + 7).
2. He catches 2 pop flies and makes bad throws (8 points each), and then he fields 2 grounders and makes bad throws (5 points each). After that, he makes a good throw after a catching error (1 point). In this case, he would also accumulate a total of 20 points (8 + 8 + 5 + 5 + 1).
3. He catches 2 pop flies and makes a good throw (10 points each), and then he fields 1 grounder and makes a good throw (7 points). Consequently, he would achieve a total of 24 points (10 + 10 + 7).

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Answer: 1 3/4 = 35/20 and 1 4/5 = 36/20

Step-by-step explanation:

1 3/4 = 7/4

Multiply top and bottom by 5 to get 35/20

1 4/5 = 9/5

Multiply top and bottom by 4 to get 36/20

The correct simplification would be \(18x^4 - 36x^3 + 9x^2\) (option a).

To simplify the expression \(9x^2(4x - 2x^2\) - 1), we need to perform the multiplication and combine like terms.

1. Start by distributing the 9x^2 to each term inside the parentheses:

  \(9x^2 * 4x = 36x^3 9x^2 * (-2x^2) = -18x^4 9x^2 * (-1) = -9x^2\)

2. Now we can combine the terms obtained from the distribution:

\(36x^3 - 18x^4 - 9x^2\)

3. Rearranging the terms in descending order of exponents:

\(-18x^4 + 36x^3 - 9x^2\)

4. However, we can simplify this expression further by factoring out a common factor of \(-9x^2\):

\(-9x^2(2x^2 - 4x + 1)\)

5. Thus, the final simplified expression is:

\(18x^4 - 36x^3 + 9x^2\)

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The minimized Boolean function using K-map is F = B'C' + A'C + AC' + BC. To solve this problem, the following steps are used:

Step 1: First, the given Boolean expression is placed on the K-map as shown below:

m0+ m2 + m3 + m5 + m6 + m7 + m8 + m9 + m10 + m12 + m13 + m15

Step 2: Group the minterms in adjacent squares of 1s on the K-map. There are four groups of 1s present in the K-map as follows:

ABC'DC A'C' AC BCBC' B'C'From the above groups of 1s. There are four terms. Each term is made up of variables A, B, and C along with a single complement.

The four terms are B'C', A'C, AC', and BC. Hence, the minimized Boolean function using K-map is F = B'C' + A'C + AC' + BC. Therefore, F = B'C' + A'C + AC' + BC. This is the final minimized Boolean function for the given Boolean expression.

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(a) tangent line to the graph of f(x) = x^3 at the point (4,2).

(b) equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12).

(a) To find the equation of the tangent line to the graph of f(x) = x^3 at the point (4,2), we need to find the slope of the tangent line at that point. We can do this by taking the derivative of f(x) with respect to x and evaluating it at x = 4. The derivative of f(x) = x^3 is f'(x) = 3x^2. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Once we have the slope, we can use the point-slope form of a linear equation to write the equation of the tangent line.

(b) Similarly, to find the equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12), we differentiate f(x) to find the derivative f'(x). The derivative of f(x) = x^2 - x is f'(x) = 2x - 1. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Using the point-slope form, we can write the equation of the tangent line.

In both cases, the equations of the tangent lines will be in the form y = mx + b, where m is the slope and b is the y-intercept.

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Parallel lines are two straight lines that never cross. For this to happen, the lines have to have the same slope.

In this case, the equation given is in what's called "slope-intersect" form. The general form of the slope intercept formula is y=mx + b where m is the slope of the line and b is the point on the Y-axis where the line crosses.

The equation given is y=5x+3 and since the 5 is in the place of m from the general equation, 5 is the slope. Since parallel lines have the same slope, 5 is the answer.

Slope-Intercept Form:

When we're given a linear equation we can immediately see if it's in the slope-intercept form if it follows the format  y=mx+b. As long as y does not have a coefficient the slope and y-intercept are the values of m and b.

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Answer:

f(x)=1.25x

Step-by-step explanation:

It goes up at a constant rate of 1.25, meaning it's a linear equation. The formula for a linear equation is:

f(x)=mx+b

M = The average rate of change

B = The initial value

And since the initial value of this data starts at 0 on the x intercept, if you subtract 1.25 from 1.25 you get 0. The average rate of change is 1.25 so you would format the equation as:

f(x)=1.25x

And there is no need to add +0, which means instead of the equation being f(x)=1.25x+0, it is much simpler as f(x)=1.25x.

I hope this was helpful!

The required function to model this data is,

f(x)=1.25x.

A mathematical expression, rule, or law that specifies the relation between an independent variable and a dependent variable (the dependent variable).

The property that every input is related to exactly one output defines a function as a relation between a set of inputs and a set of permissible outputs.

It goes up at a constant rate of 1.25, meaning it's a linear equation. A linear equation is written as:

f(x)=mx+b

M = The average rate of change

B = The initial value

And since the initial value of this data starts at 0 on the x intercept, if you subtract 1.25 from 1.25 you get 0. The average rate of change is 1.25 so you would format the equation as:

f(x)=1.25x

Additionally, there is no need to include 0,

which means instead of the equation being f(x)=1.25x+0,

it is much simpler as f(x)=1.25x.

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Answer:

13a

Step-by-step explanation:

9a + 3a + a = 13a

Answer:

13a

Step-by-step explanation:

Given

9a + 3a + a ← are like terms, they all have the variable a

To simplify add the numeric parts of the terms, that is

= (9 + 3 + 1 )a ← note a has a coefficient of 1

= 13a

Answer: The answer is 1

Step-by-step explanation:

The speed of the current is 3 miles per hour. Answer: The speed of the current is 3 miles per hour.

.Let "t" be the time taken to travel 78 miles downstream and "t" be the time taken to travel 42 miles upstream.

The distance traveled downstream is 78 miles, so we can write:78 = (10 + x)t ... equation (1)

The distance traveled upstream is 42 miles, so we can write:42 = (10 - x)t ... equation (2)

Solving equations (1) and (2) for "t", we get:t = 78 / (10 + x) ... equation (3)

t = 42 / (10 - x) ... equation (4)

We can equate the value of "t" from equations (3) and (4) since the time is the same.

We get:78 / (10 + x) = 42 / (10 - x)

Multiplying both sides by (10 + x)(10 - x), we get:78(10 - x) = 42(10 + x)

Simplifying, we get:780 - 78x = 420 + 42x

Adding 78x and subtracting 420 from both sides, we get:120x = 360x = 3

Therefore, the speed of the current is 3 miles per hour. Answer: The speed of the current is 3 miles per hour.

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Answer: D. $45,320

Step-by-step explanation:

Simply multiply 44,000 by 0.003 and add that to 44,000!

The correct answer is OD. Although the word "then" appears in the statement, it is not used as a logical connective. So the statement is not compound.

The statement "If Laura sells her quota, then Marie will be happy" is a single declarative sentence. It consists of a conditional clause ("If Laura sells her quota") and a consequent clause ("then Marie will be happy"). However, these two clauses are not independent statements that can stand alone. Instead, they are connected in a cause-and-effect relationship. The word "then" in this context is not functioning as a logical connective, but rather as an indicator of the consequent clause.

A compound statement is formed by combining two or more independent statements using logical connectives such as "and," "or," or "if...then." In the given statement, there is no logical connective joining two independent statements.

Therefore, the statement is not compound.

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Among the given points, only the point (-2.5, 4) lies in the solution set of the equation (x - 2)²/25 + (y - 3)²/4 < 1. (option c)

To determine which point lies in the solution set, we need to substitute the coordinates of each point into the equation and check if the inequality holds true.

a) (4, –0.5):

Substituting the coordinates (4, -0.5) into the equation, we get:

(4 - 2)²/25 + (-0.5 - 3)²/4

= 2²/25 + (-0.5 - 3)²/4

= 4/25 + (-3.5)²/4

= 4/25 + 12.25/4

= 0.16 + 3.0625

= 3.2225

Since 3.2225 is not less than 1, the point (4, -0.5) does not lie in the solution set.

b) (3, –2.5):

Substituting the coordinates (3, -2.5) into the equation, we get:

(3 - 2)²/25 + (-2.5 - 3)²/4

= 1²/25 + (-5.5)²/4

= 1/25 + 30.25/4

= 0.04 + 7.5625

= 7.6025

Again, 7.6025 is not less than 1, so the point (3, -2.5) does not lie in the solution set.

c) (–2.5, 4):

Substituting the coordinates (-2.5, 4) into the equation, we get:

((-2.5) - 2)²/25 + (4 - 3)²/4

= (-4.5)²/25 + 1²/4

= 20.25/25 + 1/4

= 0.81 + 0.25

= 1.06

Since 1.06 is less than 1, the point (-2.5, 4) lies in the solution set.

d) (–4.5, –3):

Substituting the coordinates (-4.5, -3) into the equation, we get:

((-4.5) - 2)²/25 + (-3 - 3)²/4

= (-6.5)²/25 + (-6)²/4

= 42.25/25 + 36/4

= 1.69 + 9

= 10.69

Like the previous points, 10.69 is not less than 1, so the point (-4.5, -3) does not lie in the solution set.

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Complete Question:

Given equation

(x - 2)²/25 + (y - 3)²/4 < 1,

Which point lies in the solution set?

a) (4, –0.5)

b) (3, –2.5)

c) (–2.5, 4)

d) (–4.5, –3)

Answer:

y = 2x + 6

y = -1/4 x - 3

Step-by-step explanation:

We can read from the graph that the equation that slopes up to the right has y-intercept 6 and slope 2. The equation that slopes down to the right has y-intercept -3 and slope -1/4.

The equations are:

y = 2x + 6

y = -1/4 x - 3

The Probability that at least one person did not choose Coke is 7/10.

According to the statement

we have given that the in a consumer survey, 10 people were asked to choose a cola among Coke, Pepsi, and RC.

And we have to find the probability that at least one person did not choose Coke.

So, for this purpose, we have know that the

Probability is the chance that a given event will occur.

In probability, at least mean the minimum value that should occur once a random event happens.

And

the number of person which take part in a survey = 10

Number of items to choose = 3

The probability that the all person choose cola = 3/10

And

we know that the at least probability is:

at least probability = 1 - simple probability

So,

Probability that at least one person did not choose Coke = 1 - Probability that all person did choose Coke

Substitute the values in it then

Probability that at least one person did not choose Coke = 1 - 3/10

Probability that at least one person did not choose Coke = 7/10.

So, The Probability that at least one person did not choose Coke is 7/10.

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Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

Question: Express the following as a linear combination of u =(3, 1,6), v = (1.-1.4) and w=(8,3,8). (14, 9, 14) = ____ u- _____ v+ _____

Current Progress: To express the given vector as a linear combination of u, v, and w, we need to find scalars a, b, and c such that (14, 9, 14) = a*u + b*v + c*w.

Step 1: Write the equation in component form:
(14, 9, 14) = (3a + b + 8c, a - b + 3c, 6a + 4b + 8c)

Step 2: Equate the corresponding components and solve for a, b, and c:
3a + b + 8c = 14
a - b + 3c = 9
6a + 4b + 8c = 14

Step 3: Solve the system of equations using any method (substitution, elimination, etc.). One possible solution is a = 1, b = -1, and c = 3.

Step 4: Plug the values of a, b, and c back into the linear combination equation:
(14, 9, 14) = 1*u + (-1)*v + 3*w

Step 5: Simplify the equation:
(14, 9, 14) = u - v + 3w

Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

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Answer:

B.   3,158

Step-by-step explanation:

h(x) = -49x − 125

Let x = -67

h(-67) = -49(-67) − 125

          =3283-125

          = 3158

Answer:

Answer B

Step-by-step explanation:

To find the value of h(-67) for the function h(x) = -49x - 125,

we substitute -67 for x in the function and evaluate it.

h ( - 67 ) = - 49 ( - 67 ) - 125

Now we can simplify the expression:

h ( -67 ) = 3283 - 125

h ( -67 ) = 3158

5! permutation of the letters abcdefgh contains strings ab, de, and gh.

The number of permutations of 'n' objects taken 'r' at a time is determined by the following formula:

P(n,r)=n! / (n−r)!

We can also find permutation using the Selection and Formation Method:

For example:

1. Number of ways to arrange the letter SANOJ:

here number of alphabets are 5, and we have to arrange all the letter so using permutation formula:

P(5, 5 ) = 5! / (5-5)!

P(5, 5 ) = 5!                : 0! = 1

without using the formula we can simply write 5! as the answer.

Here, we have given the word, " abcdefgh "

and we have to make those arrangements in which ab, de, and gh come together:

so now, we will count ab, de, and gh as a single word.

now, we will have 5 different words/alphabet:

1 → ab

2 → c

3 → de

4 → f

5 → gh

Number of ways to arrange all the 5 words/alphabet: 5!

Hence,

5! permutation of the letters abcdefgh contains strings ab, de, and gh.

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The simplified polynomial expression in standard form to represent the area of the rectangle is 2x^2 - 4x - 20.

To find the area of a rectangle, we multiply its length by its width. The length of the rectangle is given as 2x - 4, and the width is x + 5. Multiplying these expressions, we get 2x^2 - 4x - 20, which is the simplified polynomial expression in standard form representing the area of the rectangle.

To explain further, let's break down the problem step by step.

First, we are given the length of the rectangle as "2x - 4" and the width as "x + 5." To find the area, we need to multiply these two expressions.

Using the distributive property, we multiply each term of the length expression by each term of the width expression:

\((2x) * (x) + (2x) * (5) + (-4) * (x) + (-4) * (5)\)

This simplifies to:

\(2x^2 + 10x - 4x - 20\)

Combining like terms, we get:

\(2x^2 + 6x - 20\)

So, the simplified polynomial expression in standard form to represent the area of the rectangle is 2x^2 - 4x - 20.

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Answer:

X=16

Step-by-step explanation:

you multiply 8 and 24 then get 192 and then you divide by 12 which gives you 16

The equation T = 2π√(L/g) satisfies dimensional consistency, indicating that it is a valid relationship for the periodic time T of a simple pendulum.

To test the validity of the equation x = x₀ + v₀t + (1/2)at², we can check if the dimensions on both sides of the equation are consistent.

Breaking down the dimensions of each term:

x: Displacement has dimensions of length (L).

x₀: Initial displacement has dimensions of length (L).

v₀t: Velocity times time has dimensions of (L/T) * T = L.

(1/2)at²: Acceleration times time squared has dimensions of (L/T²) * T² = L.

Since the dimensions on both sides of the equation are consistent (L = L), the equation x = x₀ + v₀t + (1/2)at² is valid.

Now, let's use dimensional analysis to find the relationship of the periodic time T of a simple pendulum using the factors affecting it: mass of the bob (m), length (L) of the pendulum, and acceleration due to gravity (g).

The factors affecting the periodic time T of a simple pendulum are:

Mass (m): Denoted by [M].

Length (L): Denoted by [L].

Acceleration due to gravity (g): Denoted by [LT⁻²].

The periodic time T of a simple pendulum is expected to depend on these factors in some way.

By applying dimensional analysis, we can determine the relationship between these factors. The equation is given as T = 2π √(L/g), where T is the periodic time, π is a constant, L is the length, and g is the acceleration due to gravity.

Breaking down the dimensions of each term:

T: Periodic time has dimensions of time (T).

2π: A constant, so it is dimensionless.

√(L/g): The square root of the ratio of length to acceleration due to gravity has dimensions of √([L]/[LT⁻²]) = √(T²) = T.

Therefore, the equation T = 2π√(L/g) satisfies dimensional consistency, indicating that it is a valid relationship for the periodic time T of a simple pendulum.

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Step-by-step explanation:

Blank 1 = 82

Blank 2 = 82

Blank 3 = 98

Answer:

All the sides of the square are equalso the squares are congruent.. Are congruent shapes? Two shapes that are the same size and the same shape are congruent.

hope this helps

mark me brainliest

Step-by-step explanation:

The margin of error of the random selection is 0.20

The given parameters are:

\(n = 420\) --- the sample size

\(\sigma = 1.6\) --- the standard deviation

\(\bar x = 10\) --- the mean

\(\alpha = 99\%\) --- the confidence level.

The margin of error (E) is calculated as follows:

\(E = z \times \sqrt{\frac{\sigma^2}{n}}\)

So, we have:

\(E = z \times \sqrt{\frac{1.6^2}{420}}\)

\(E = z \times \sqrt{\frac{2.56}{420}}\)

The z-value for 99% confidence level is 2.576.

Substitute 2.576 for z

\(E = 2.576 \times \sqrt{\frac{2.56}{420}}\)

\(E = 2.576 \times \sqrt{0.006095}\)

Take square roots

\(E = 2.576 \times 0.0781\)

Multiply

\(E = 0.2012\)

Approximate

\(E = 0.20\)

Hence, the margin of error is 0.20

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a) The dipole moment of this arrangement is zero.

b) The value 'd' required for the dipole moment to be the same as the hemisphere arrangement is zero.

c) V(r,θ) very far away from the hemisphere arrangement is zero.

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If Mr. Vara's square pyramid post caps have a volume of 94.5 cubic centimeters, and he assumes that the height and side length are equal, then the side length of each cap should be approximately 6.04 centimeters.

Mr. Vara is designing post caps in the shape of a square pyramid for his fence. The caps are solid wood and have a volume of 94.5 cubic centimeters. To calculate the dimensions of the pyramid, we need to use the formula for the volume of a square pyramid, which is V = (1/3)bh, where b is the area of the base and h is the height of the pyramid.

Since the caps are square pyramids, the base is a square. Let's call the side length of the base s. Then the area of the base is s². We can rearrange the formula for volume to get h = (3V)/b. Plugging in the given volume of 94.5 cubic centimeters, we get:

h = (3 x 94.5) / s²
h = 283.5 / s²

We still need to find the side length s. We can use the fact that the volume of the pyramid is also equal to \((1/3)s^{2h\). Plugging in the volume and height from above, we get:

94.5 = (1/3)s²(283.5 / s²)
94.5 = 94.5

This equation simplifies to 1 = 1, which doesn't give us any information about s. However, we can make an assumption about the dimensions of the pyramid. Let's say that the height h is equal to the side length s. Then we can solve for s using the volume formula:

\(94.5 = (1/3)s^{2s\)
94.5 = (1/3)s³
283.5 = s³
s = 6.04

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As stated in the assertion The ladder will be able to climb up the building around 34.64 feet.

We can use the Pythagorean theorem to address this issue by referring to "height" and taking into account the 40-foot ladder that is situated 20 feet from the building's base. According to the theorem, the square root of the length of the hypotenuse, or side opposite the side with the right angle, in a right-angled triangle, is equal to the sum of each square of the lengths of each of the other two sides.

In this instance, the height of the ladder on the building serves as the hypotenuse, with the distance to the building's base serving as one of its sides. These sides should be labelled as follows:

The Ladder's hypotenuse measures 40 feet

- Side 1 is 20 feet away from the base.

Side 2 (height attained) equals h

The Pythagorean theorem yields the following result: 402 = 202 + h2.

1600 = 400 + h2 h2 = 1200 h 34.64 feet when h is solved for.

The ladder may therefore climb the building to a height of about 34.64 feet.

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The date on which the loan amount is to be fully paid is called the maturity date.

The maturity date is an essential component of a loan agreement, particularly for loans with a fixed repayment schedule. It represents the deadline by which the borrower is required to repay the entire loan amount, including any interest and fees.

When a loan is taken out, the lender and borrower agree upon the terms and conditions, including the repayment schedule. The maturity date is determined based on these terms, specifying the duration over which the borrower is expected to make regular payments.

For example, in a mortgage loan, the maturity date could be set for 30 years from the loan origination date. This means that the borrower has 30 years to repay the loan in full, either through monthly installments or other agreed-upon payment arrangements.

The maturity date is important for both the lender and the borrower as it establishes a clear timeline for the loan repayment. It helps ensure that the borrower understands the duration of the financial obligation and allows the lender to plan their cash flows and monitor the progress of the loan repayment.

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