Hannah lines up 6 plastic letters on a sign t spell her name. Each letter takes up 5/8 inch of space on the sign.
The total amount of space taken up on the sign by the letters in Hannah's name is between which two whole numbers?

Answer:

Unit rate = 0.6

y = 0.6x

x= 24

Step-by-step explanation:

I cannot see the headings to the table, but on examining the questions, the first column contains the values for variable x and the second column the values for variable y

Unit Rate

Unit rate = increase in y for a unit increase in x
We see that the rate is constant for every unit increase in x and is = 0.6
Unit rate = 0.6

Equation
The equation therefore is y = 0.6x

Value of x when y = 14.4
When y = 14.4, plugging into the equation gives:
14.4 = 0.6x
or
0.6x = 14.4  by switching sides - no effect on equation

Divide both sides by 0.6
0.6x/0.6 = 14.4/0.6
x= 24

In the given equation, the constant 6 represents the initial height of the football when it was thrown. This means that before the football was thrown, it was already at a height of 6 feet above the ground.

A mathematical equation proves the equality of two expressions by using symbols, numbers, and/or variables. Equations can be used to illustrate relationships between several numbers or to locate unknown values in order to solve problems.

An equation typically consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), which are separated by an equal sign (=). The LHS and RHS can contain constants, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

a. The constant 6 in equation f(t) = 6 + 30t - 16t represents the initial height of the football when it was thrown.

b. The term 30t in the equation represents the vertical distance covered by the football per second due to its initial velocity. This term is calculated by multiplying the initial velocity of the football by the time t.

c. The squared term -16t^2 in the equation represents the effect of gravity on the height of the football. This term is calculated by multiplying half the acceleration due to gravity (-16 feet per second squared) with the square of time t. The negative sign indicates that the height of the football is decreasing as time passes due to the influence of gravity.

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Online calculator of variable cost is used to Total Variable Cost = Total Cost-Fixed Costs to calculate the Total Variable Cost.

A variable cost is an expense that changes as a company's production output rises and falls. Variable expenses vary according on the amount of output produced. Basic variable costs include, in large part:

Variable costs are frequently employed in business and are a crucial component of the analysis of the company's break-even point. The revenue or unit that must be sold to cover all costs is examined using the break-even approach.

The following calculation is the break-even point:

Break-even point in units = Fixed costs/(Sales price per unit – Variable cost per unit)

Variable costs are crucial for successful investors because they help them calculate the proportion of the set price and predict how the company will respond to various operational scenarios.

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65  °F is equal to 18.3333 °C.

A temperature unit developed from the SI (International System of Units) is Celsius (symbol: °C).

Prior to the adoption of the metric system, Fahrenheit (symbol: °F) was a commonly used measurement of temperature.

To convert a temperature from Fahrenheit (°F) to Celsius (°C),

We can use the following formula:

°C = (°F - 32) x 5/9

Where °C is the temperature in Celsius

°F is the temperature in Fahrenheit.

Substituting 65 for °F,

We get:

°C = (65 - 32) x 5/9

Simplifying the expression:

°C = 33 x 5/9

°C = 18.3333333333

Therefore, 65 degrees Fahrenheit is equal to nearly 18.3333 degrees Celsius (rounded to four decimal places).

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The numbers between 20 and 30 are: 21,22,23,24,25,26,27,28,29 Even numbers, other than 2 are not prime because by definition of being even they are divisible by 2.

Prime numbers are numbers that can only be divisible by themselves or 1. Examples of prime numbers include 2, 3, 5, 7, 11, and so on. In this tutorial, you will learn how to check if a number is a prime number. We will discuss how to write a prime number program in python – this program prints numbers that are prime numbers within a given range.

There is just one perfect number between 20 and 30. The number 28 is a perfect number. Its factors are 1, 2, 4. 7, 14, and 28. Why is 2 the only prime number? Two is a prime because it is divisible by only two and one. All the other even numbers are not prime because they are all divisible by two. That leaves only the odd numbers.

Hence, The numbers between 20 and 30 are: 21,22,23,24,25,26,27,28,29 Even numbers, other than 2 are not prime because by definition of being even they are divisible by 2.

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Answer:a

Step-by-step explanation:

The antiderivative of sin is -cos(x) + C.

The antiderivative of a function is the inverse operation of differentiation which is is also known as its indefinite integral.

So, the integral of sin

                 ∫sin(x) = -cos(x) + C

where C = constant of integration.

This can be verified by differentiating -cos(x) + C with respect to x, which gives sin(x).

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Option b. 5. The number 125 can be written as 6 times 20 plus 5. Therefore, when x is 125, the expression "x % 6" evaluates to 5.

The adage "x % 6" signifies the rest of x is separated by 6. At the point when x is 125, the rest of 125 is partitioned by 6 can be found by playing out the accompanying whole number division:

125 ÷ 6 = 20 remaining portion 5

This implies that 125 can be composed as multiple times 20 in addition to 5. Consequently, when x is 125, the adage "x % 6" assesses to 5.

So the response is (b) 5.

At the point when we utilize the modulo administrator (%) to track down the rest of x partitioned by 6, the maxim "x % 6" assesses to 5 when x is 125. This is on the grounds that when 125 is separated by 6, the remainder is 20 with a rest of 5. At the end of the day, 125 is equivalent to multiple times 20 in addition to 5. Accordingly, the rest of 125 is partitioned by 6 is 5, and that is the aftereffect of the adage "x % 6" when x is 125.

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The appropriate numerical measures of center and spread to describe a given distribution of a quantitative variable depend on the shape, symmetry, and presence of outliers in the data.

Measures of center include mean, median, and mode. The mean is affected by extreme values, while the median is resistant to outliers. The mode is useful when looking for the most common value or values in a distribution.

Measures of spread include range, interquartile range (IQR), variance, and standard deviation. The range is the difference between the maximum and minimum values, but it is sensitive to outliers. The IQR is the range of the middle 50% of the data and is resistant to outliers. Variance and standard deviation both measure the spread of the data around the mean, with the variance being the average squared deviation from the mean and the standard deviation being the square root of the variance.

In general, if the data is approximately symmetric and without outliers, the mean and standard deviation are appropriate measures of center and spread, respectively.

If the data is skewed or has outliers, the median and IQR are more appropriate. If the distribution has multiple modes, the mode may be useful to describe the distribution, but it should be used with caution as it may not be unique or well-defined for certain distributions.

Ultimately, the choice of measures of center and spread depends on the characteristics of the data and the research question being investigated. It is always a good practice to use multiple measures of center and spread and to visualize the distribution of the data using histograms or boxplots to gain a better understanding of the data.

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Answer:

Step-by-step explanation:

No, the point is not (1,0)

The simplified answer is [tex]-16n^2 - 4n - 4.[/tex]

In mathematics, simplification refers to the process of simplifying an expression or equation without affecting its fundamental meaning or value. Using mathematical tools and rules to simplify an equation makes it simpler to manipulate or solve.

In algebra, simplification might take the form of factoring out common factors, grouping like concepts, or distributing multiplication across addition or subtraction. For instance, merging two like terms will simplify the formula 2x + 4x to 6x. The same strategy can be used to reduce the expression 3(x + 2) - 2(x - 1) to 3x + 4 by spreading out the multiplication and combining related terms.

Other types of mathematical simplification include determining the square root of a number, simplifying trigonometric functions, and reducing fractions to their simplest forms. In order to solve difficulties and comprehend mathematical concepts, simplification is a crucial step that removes superfluous complexity and facilitates understanding of the underlying structure of an equation or problem.

To find the product of 4 and the expression [tex](-4n^2 - n - 1),[/tex] we can distribute the 4 to each term inside the parentheses:

[tex]4(-4n^2 - n - 1) = -16n^2 - 4n - 4[/tex]

Therefore, the simplified answer is [tex]-16n^2 - 4n - 4.[/tex]

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160 children between the ages of 5 and 15 comprise the cases.

Age and sex child cheated are the variables and types.

What impact do age, sex, being an only child, and whether or not kids received instructions have on the frequency of cheating in games?

a) What are the cases?

The cases are: the 160 children between the ages of 5 to 15.

b) What are the variables and their types?

The variables and types are: age (discrete numerical), sex (regular categorical), whether they were an only child or not (regular categorical), the result of the coin flip (regular categorical), whether the children were given instructions or not (regular categorical), and whether the child cheated (regular categorical).

c) What is the main research question?

The main research question is: What is the effect of age, sex, only child status, and whether or not children were given instructions on the rate of cheating in a game?

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The integral of sec(x) is ln |sec(x) + tan(x)| + C.

The integral of sec(x) is:

∫sec(x) dx = ln |sec(x) + tan(x)| + C

where C is the constant of integration.

To solve this integral, you can use the method of substitution. Let u = sec(x) + tan(x). Then [tex]du/dx = sec(x)tan(x) + sec^2(x)[/tex], which can be simplified to du/dx = u tan(x). Rearranging, we get du/u = tan(x)dx.

Substituting these expressions into the integral, we have:

∫sec(x) dx = ∫(sec(x) + tan(x))/(sec(x) + tan(x)) dx = ∫(1/u) du

Integrating this expression gives:

∫(1/u) du = ln |u| + C = ln |sec(x) + tan(x)| + C

Therefore, the integral of sec(x) is ln |sec(x) + tan(x)| + C.

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There are 5280 feet in a mile and 6076.12 feet in a nautical mile.

We know that the definition of a mile says that its the distance travelled in 1,760 yards or 1.609344 km. Now we can use this to convert it into feet. Since we know that a Yard is equal to 3 feet or 0.9144 meters , therefore

By using Unitary method :

⇒ 1 yard = 3 feet

⇒ 1760 yards = 3 x 1760 feet

⇒ 1760 yards  =  5280 feet

Therefore, 1 Mile contains 5,280 feet.

Since, it is not mentioned that which Mile we are talking about So, There is another type of mile in Imperial System called 'Nautical Mile' which is slightly larger than a regular mile. Its equal to 6076.12 feet

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We have the following system of equations,

[tex]\left \{ {{y=x^2-1} \atop {y=5-x}} \right.[/tex]

We are asked to solve the system of equations using substitution.

What is substitution?

Substitution is a method of solving a system of equations where you solve for one of the equations (pick either equation) for one of the variables (pick one of the variables), then using this new equation to "substitute" back in to the other.

Given this set of equations, [tex]\left \{ {{y=x^2-1} \atop {y=5-x}} \right.[/tex], notice how both of the equations are already solved for the variable, [tex]y[/tex]. Since both these equations equal [tex]y[/tex], we can set them equal to each other and solve for, [tex]x[/tex].

[tex]\left \{ {{y=x^2-1} \atop {y=5-x}} \right.[/tex]

[tex]\Longrightarrow 5-x=x^2-1[/tex], substituted "[tex]5-x[/tex]" for [tex]y[/tex] into the top equation.

[tex]\Longrightarrow -x^2-x+6=0[/tex]

[tex]-1[\Longrightarrow -x^2-x+6=0][/tex]

[tex]\Longrightarrow x^2+x-6=0[/tex]

[tex]\Longrightarrow (x-2)(x+3)=0[/tex]

[tex]\Longrightarrow x=2 \ and \ x=-3[/tex]

Now take these values of x ([tex]x=2 \ and \ x=-3[/tex]) and plug them into either of the two original equations to solve for [tex]y[/tex].

When x=2:

[tex]y=5-x;x=2[/tex]

[tex]\Longrightarrow y=5-(2)[/tex]

[tex]\Longrightarrow y=3[/tex]

When x=-3:

[tex]y=5-x;x=-3[/tex]

[tex]\Longrightarrow y=5-(-3)[/tex]

[tex]\Longrightarrow y=5+3[/tex]

[tex]\Longrightarrow y=8[/tex]

Thus, we get two solutions to the given system of equations, (-3,8) & (2,3).

Answer: 7 x 4 = 28

Step-by-step explanation: 7 + 7 + 7 + 7 = 28

The statement that "a surface generated by a closed plane curve rotated about a line that lies in the same plane as the curve but does not intersect" is true.

The surface generated by a closed plane curve rotated about a line that lies in the same plane as the curve but does not intersect it is called a torus. The torus is a three-dimensional surface that can be thought of as a doughnut shape. The curve that generates the torus is called the generator, and the line about which the curve is rotated is called the axis of rotation. The torus has the interesting property that it has a hole in the center, and the distance from any point on the surface to the center of the torus is constant.

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A table used to find the area under the standard normal distribution to determine the probability of a z-score being less than a given value.

A negative z-score table is a tool used in statistics to find the probability of a z-score being less than a certain value. A z-score is a measure of the number of standard deviations an observation or data point is above or below the mean of a dataset.

The standard normal distribution is a bell curve with a mean of zero and a standard deviation of one. The negative z-score table lists the area under the curve to the left of a negative z-score, which can be used to calculate probabilities. The table is used by finding the corresponding row and column for the desired z-score and reading the probability from the table.

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Answer: The correct digits for the combination lock are 1, 5, and 8, in that order.

Step-by-step explanation:

Based on the given clues, we can deduce the correct digits for the combination lock as follows:

From the clue "128 One digit is right and in its place," we know that one of the digits is 1.

From the clue "157 One digit is right, but in the wrong place," we know that either 5 or 7 is a correct digit, but in the wrong position. Since we already know that one of the digits is 1, the correct digit must be 5. Therefore, the second digit is 5 and it is in the wrong place.

From the clue "841 Two digits are right but both are in the wrong place," we know that the digits 8 and 4 are correct, but they are both in the wrong position. Therefore, the last digit must be 4 or 8. However, we also know from the clue "624 One digit is right, but in the wrong place" that the last digit is not 4. Therefore, the correct third digit is 8.

So, the correct digits for the combination lock are 1, 5, and 8, in that order.

Therefore, the combination for the lock is 158.

Answer:

Step-by-step explanation:

left a book at home. He turned around and walked home at the same speed.

108ft is the length of the of the guy wire

Triangles are known to be similar if the ratio of the similar sides of the triangle are equal.

From the given diagram, we need to determine of the guy wire. Using the similarity theorem of a triangle;

8/2 = l/25+2
8/2 = l/27

2l = 8 * 27

l = 4 * 27

l = 108 ft

Hence the length of the of the guy wire, to the nearest foot is 108ft

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The percent error for patricks estimate for the first day of school is 25%.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

We need to Write the percent as a fraction in simplest form

16.24%

So, we can rewrite it as;

16.24 / 100

16 and 24/100 or 16 6/25

So the percent as a fraction is 16 6/25

We are given that;

Time patrick took= 45min

To find the percent error, we first need to find the difference between Patrick's estimate and the actual time it took him to get ready.

Actual time - Estimated time = Error

45 minutes - 45 minutes = 0 minutes

The error is 0 minutes, which means Patrick's estimate was exactly right and there was no error.

However, if we assume that Patrick made a mistake when he estimated and that his actual time is the correct value, then we can find the percent error as follows:

Error = | Actual time - Estimated time | = | 45 minutes - 60 minutes | = 15 minutes

Percent error = (Error / Estimated time) x 100% = (15 minutes / 60 minutes) x 100% = 25%

Therefore, the percentage error will be 25%.

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The complete ratio table is

Hours       Weeks

168              1

1008             6

840               5

How to complete the table?

The mathematical operation that would be used to determine the missing values are division and multiplication. In order to convert hours to weeks, divide by 168 hours. To convert weeks to hours, multiply by 168.

1008 hours to weeks = 1008 / 168 = 6 weeks

5 weeks to hours = 5 x 168 = 840 hours

Hence , The complete ratio table is

Hours       Weeks

168              1

1008             6

840               5

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Answer:

Penny had 13/20 of the pizza left.

Step-by-step explanation:

Let's start with the whole pizza, which we can represent as 1.

Pania ate a quarter of the pizza, leaving 3/4 (since 1/4 + 3/4 = 1) for Pita and Paula.

Pita then ate one sixth of what remained, which is one sixth of 3/4 or 3/24, leaving 21/24 (or simplifying to 7/8) for Paula.

Paula then ate two fifths of what remained after Pita had eaten, which is two fifths of 7/8 or 14/40, leaving 26/40 (or simplifying to 13/20) for Penny.

Therefore, Penny had 13/20 of the pizza left.

I hope this helps! And if you could label my answer brainliest that would be awesome.

- Dante

Answer:

3/8 of the pizza was left for Penny.

Step-by-step explanation:

Pania ate 1/4 and left 3/4.

Pita ate 1/6 (of the 3/4) and left 5/6.

Paula ate 2/5 (of the 5/6) and left 3/5.

What was left?

3/5 of 5/6 of 3/4

"of" means times

3/5•5/6•3/4

(cancel the 5s and a 3 with the 6, leaving a 2)

= 3/8

But see the illustrated story, it makes way more sense! See image

He also added lettuce, tomatoes, and cheese. Kenneth also made sure to put plenty of condiments like mayonnaise and mustard on each sandwich.

Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.


Kenneth's family was excited to get to the beach. When they arrived, they set up their umbrellas and beach chairs and found a spot to settle down. After they were all settled, Kenneth passed out the sandwiches he had made. Everyone was satisfied with the delicious sandwiches Kenneth had created.

Kenneth's family enjoyed their day at the beach. They swam in the ocean, built sandcastles, and played volleyball. They even laid out and got a nice tan. As the day got hotter, Kenneth's family got hungrier. Fortunately, they still had the sandwiches Kenneth had made. Everyone was thankful for the delicious sandwiches that Kenneth had prepared for them.

After a fun day at the beach, Kenneth's family packed up their things and headed home. Kenneth was happy that he could provide for his family and make their day even better. He was grateful for the opportunity to make the sandwiches for his family and make their day at the beach even more enjoyable.

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The correct answer is option B and it is equal to 30% of 81 because it shows 0.30 x 81.

We have to find that how much is equal to the 30% of 81.

We can use the percentage formula here and that is,

%age = Obtained value/total value x 100

Here in this case, we have to find the obtained value and the total value is 81 and the percentage that we are going to get  is equal to 30.

So, putting all the values, we get,

obtained value = 30 x 81/100

obtained value = 0.30 x 81

Hence, the value 0.30 x 81 is equal to 30 % of 81. hence option B is the correct answer.

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Complete question - Which of the following options have the same value as 30% of 81?

A. 0.03 x 81

B. 0.3 x 81

C. 0.03 x 81

D. 3 x 81

Answer:

21x + 7

Step-by-step explanation:

See picture below :)

Answer:

67.872

Step-by-step explanation:

The features of the sine function are given as follows:

The equation is given as follows:

y = 3sin(0.25πx) + 1.

The standard definition of a sine function is given as follows:

y = Asin(Bx) + C.

The parameters are given as follows:

The minimum value is of -2, while the maximum value is of 4, hence the midline is given as follows:

y = (-2 + 4)/2

y = 1.

The difference between the minimum and the maximum value is of 6 units, hence the amplitude is obtained as follows:

2A = 6

A = 3.

The function with no vertical shift would oscillate between -A = -3 and A = 3, while this function oscillates between -2 and 4, hence the vertical shift is given as follows:

C = 1.

The shortest distance between repetitions of the function is of 8 units, hence the period is of 8, the frequency is of 1/8, and the coefficient B is given as follows:

2π/B = 8

8B = 2π

B = π/4.

B = 0.25π.

Hence the function is defined as follows:

y = 3sin(0.25πx) + 1.

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