Calculate the average rate of change in the graph from time t=0.5 to t=0.75. Include units on your final answer.

the factors of the expression 28r - 16r² are 4r and (-4r + 7).

Factorization is the process of expressing a number or an algebraic expression as a product of its factors, which are numbers or expressions that multiply together to give the original number or expression. In other words, factorization involves breaking down a larger number or expression into smaller factors.

To factor the expression 28r - 16r², we can first rearrange it to put it in descending order of powers of r:

-16r² + 28r

Then we can factor out the greatest common factor, which in this case is 4r:

4r(-4r + 7)

Therefore, the factors of the expression 28r - 16r² are 4r and (-4r + 7).

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Thus, the price of regular brand blueberries is less than the Price of 2 container of Kroger brand blueberries. Hence, Regular Brand is better deal.

A linear equation with two variables is shown by the equation axe + by = r if a, b, and r are all real values and they are not equal to 0. The equation's two variables are represented by the letters x and y. The coefficients are denoted by the numerals a and b.

Given data:

Price of 1 container of Kroger brand blueberries with discount: 3.75 with 15% off.

= 3.75 - 0.15*3.75

= 3.1875

Price of 1 container of Kroger brand blueberries:  $3.1875

Price of 2 container of Kroger brand blueberries:

= 3.1875 * 2

= $6.375

Now,

Price of 2 container of  regular brand blueberries:  $6.25

Thus, the price of regular brand blueberries is less than the Price of 2 container of Kroger brand blueberries. Hence, Regular Brand is better deal.

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No they wouldn't be the same because, the perimeter is adding all sides.

The square has 4 sides so you would add 9, four times.

9 + 9 + 9 + 9 = 36

And a pentagon has 5 sides so you would add 9, five times.

9 + 9 + 9 + 9 + 9 = 45

So, they are not the same.

Answer: To find the unit rate that describes the number of gallons per dollar, we need to divide the number of gallons by the cost in dollars. In this case, we have:

Number of gallons = 5

Cost in dollars = $16.25

Dividing the number of gallons by the cost in dollars, we get:

Gallons per dollar = Number of gallons / Cost in dollars

= 5 / $16.25

= 0.3077...

Rounding to two decimal places, we get:

Gallons per dollar = 0.31

Therefore, the unit rate that describes the number of gallons per dollar is 0.31 gallons per dollar.

Step-by-step explanation:

Answer:

Large Photos: 500

Small Photos: 3000

Step-by-step explanation:

Answer:

2.5

Step-by-step explanation:

The slope of the line represented by the equation y = 2.5x - 7 is 2.5. This means that for every unit increase in x, the value of y increases by 2.5 units.

The slope of the line y = 2.5x - 7 can be identified as the coefficient of the 'x' variable in the equation. Here, the term in front of 'x' is 2.5, so the slope of the line is 2.5. In other words, for every unit increase in x, y will increase by 2.5 units. This is a key concept in linear equations, which are used to represent straight lines in a coordinate system.

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The simplified expressions are, 6. [tex]16^{\frac{1}{2} }[/tex] = 4, 7. [tex]125^{\frac{1}{3} }[/tex] = 5, 8. [tex]36^{\frac{1}{2} }[/tex] = 6, 9. [tex]27^{\frac{1}{3} }[/tex] = 3,10. [tex]49^{\frac{1}{2} }[/tex] = 7.

Algebra is a branch of mathematics that deals with mathematical operations and structures using symbols and letters to represent numbers and quantities. It involves manipulating mathematical expressions and solving equations to find unknown values.

In algebra, the basic operations include addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions can also include variables, which represent unknown quantities, and coefficients, which are the constant values that appear in front of variables.

The study of algebra begins with the basic concepts of arithmetic, such as addition, subtraction, multiplication, and division, and then progresses to more advanced topics, such as equations, inequalities, functions, matrices, and abstract algebra. Algebraic concepts are widely used in other areas of mathematics, including geometry, trigonometry, calculus, and number theory

[tex]16^{\frac{1}{2} }[/tex] = 4

[tex]125^{\frac{1}{3} }[/tex] = 5

[tex]36^{\frac{1}{2} }[/tex] = 6

[tex]27^{\frac{1}{3} }[/tex] = 3

[tex]49^{\frac{1}{2} }[/tex] = 7

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After answering the provided question, we can conclude that As a result,  normal distribution  the new height requirement for women to join this branch of the military is 57.1 inches to 68.6 inches.

The normal distribution is an example of a constant distribution of probabilities, in which the majority of the points cluster near the range's center and the ones that are left decrease symmetrically towards one of the extremes. The mean of the spread is another term for the range's centre. According to the bell curve, also known as the Distribution function, which is symmetrical well about mean, data that are near the median are more frequent than data that are far from the mean. I'm using heuristics in normality to obtain a child's SAT scores from an innovative exam prep course. The data have a normal distribution with a mean (M) of 1150 and a standard deviation (SD) of 150.

a. To calculate the percentage of women who meet the height requirement, find the area under the normal distribution curve between 58 and 80 inches.

For x = 58 inches: z = (58 - 63.4) / 2.5 = -2.16

For x = 80 inches: z = (80 - 63.4) / 2.5 = 6.64

This means that all women with heights ranging from 58 to 80 inches meet the requirement.

b. For the shortest 1%, we need to find the height that corresponds to z = -2.33:

-2.33 = (x - 63.4) / 2.5

x = 57.1 inches

So the new minimum height requirement is 57.1 inches.

For the tallest 2%, we need to find the height that corresponds to z = 2.05:

2.05 = (x - 63.4) / 2.5

x = 68.6 inches

So the new maximum height requirement is 68.6 inches.

As a result, the new height requirement for women to join this branch of the military is 57.1 inches to 68.6 inches.

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Answer:

y = mx + b

the is the slope intercept formula

The test has average  80 true/false questions, 24 fill in the blank questions, and 28 multiple choice questions, with 7, 9 and 13 points respectively, totaling 1172 points.

The college entrance test consists of 112 questions in total, with different types of questions having different point values. There are 80 true/false questions, each worth 7 points, with a total of 560 points from these questions. There are also 24 fill in the blank questions, each worth 9 points, giving a total of 216 points from these questions. Finally, there are 28 multiple choice questions, each worth 13 points, for a total of 364 points from these questions. All together, the test has 1172 points available. The number of fill in the blank questions is 34 less than the number of true/false questions, meaning that there are more true/false questions than fill in the blank questions. The test is designed to assess a student's knowledge and comprehension of the subject they are taking the test for, and is made up of the three different types of questions to give a comprehensive assessment of their understanding.

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The correct answer is $112.50. She should save $112.50 as the minimum amount every month in order to reach her goal.

To find the minimum amount of money Alejandra needs to save every month to attend her first year of college, we need to first determine the amount she needs to pay herself.

We know that her parents will pay 85% of the tuition cost, which is:

85% of $9,000 = 0.85 x $9,000 = $7,650

Therefore, Alejandra needs to pay the remaining amount:

$9,000 - $7,650 = $1,350

Since Alejandra has one year to save this amount, we need to divide $1,350 by 12 to find the minimum amount she should save every month:

$1,350 ÷ 12 = $112.50

Therefore, Alejandra should save at least $112.50 every month to reach her goal of attending college for her first year.

The correct answer is $112.50.

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Answer:

(i) 4x

2

−5x−3=0

Let us consider, a=4,b=−5,c=−3

So, by using the formula,

x=

2a

−b±

b

2

−4ac

​

​

So let, b

2

−4ac=D

x=

2a

−b±

D

​

​

D

​

=b

2

−4ac

=(−5)

2

−4(4)(−3)

=25+48

=73

​

So

x=[−(−5)±

73

​

]/2(4)

=[5±8.54]/8

=[5+8.54]/8 or [5−8.54]/8

=13.54/8 or −3.54/8

=1.6925 or -0.4425

∴ Value of x=1.69 or -0.44

Hope it helps

The solution to the inequality is: x > 22/5 or x < 6/5

What is inequality?

Inequality is a mathematical concept used to compare two quantities or values, indicating that one value is greater than, less than, or not equal to another value. Inequalities are represented using inequality symbols such as > (greater than), < (less than), ≥ (greater than or equal to), or ≤ (less than or equal to).

To solve the inequality |14 - 5x| > 8, we can break it down into two cases:

Case 1: 14 - 5x > 8

In this case, we solve for x:

14 - 5x > 8

-5x > 8 - 14

-5x > -6

x < 6/5

However, we need to check if this solution satisfies the original inequality:

|14 - 5x| = |14 - 5(6/5)| = |14 - 6| = 8

Since the absolute value of the expression is exactly 8, the solution x < 6/5 does not satisfy the inequality |14 - 5x| > 8.

Case 2: 14 - 5x < -8

In this case, we solve for x:

14 - 5x < -8

-5x < -8 - 14

-5x < -22

x > 22/5

Again, we need to check if this solution satisfies the original inequality:

|14 - 5x| = |14 - 5(22/5)| = |14 - 22| = 8

Since the absolute value of the expression is exactly 8, the solution x > 22/5 satisfies the inequality |14 - 5x| > 8.

Therefore, the solution to the inequality is:

x > 22/5 or x < 6/5

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The slope of the line is -1, and the y-intercept is 4.

What is linear function ?

A linear function is a type of mathematical function where the graph of the function is a straight line. It is a function that has a constant rate of change (or slope) between any two points on the line.

In the form of the equation y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis). This equation represents a linear function since the graph of the function is a straight line.

Linear functions are used in many areas of mathematics and science, as well as in real-world applications such as engineering, economics, and physics. They are useful in modeling and predicting relationships between variables that have a constant rate of change over time.

To find the equation of the linear function in the form y = mx + b, we need to determine the slope (m) and y-intercept (b) of the line.

From the graph, we can see that the y-intercept is 4, since the line intersects the y-axis at the point (0, 4).

To find the slope, we can choose two points on the line and use the slope formula:

slope (m) = (y2 - y1) / (x2 - x1)

Let's choose the points (2, 6) and (6, 2):

slope (m) = (2 - 6) / (6 - 2) = -4 / 4 = -1

Therefore, the equation of the linear function is:

y = -x + 4

So, the slope of the line is -1, and the y-intercept is 4.

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The measure of the diagonal of the square table is 15 * [tex]\sqrt{2}[/tex] feet (approximately 21.21 feet).

The diagonal of a square is the line segment that links two opposed corners of the square. The Pythagorean theorem asserts that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the diagonal of the square is the hypotenuse of a right triangle with two legs of length 15ft each (since the sides of a square are equal in length). So, we can use the Pythagorean theorem as follows:

[tex]diagonal^2[/tex] = [tex]15^2 + 15^2[/tex]

[tex]diagonal^2[/tex] = 450

diagonal = [tex]\sqrt{450}[/tex]

Using a calculator or simplifying by factoring out perfect squares, we get:

diagonal = [tex]\sqrt{(225 * 2)}[/tex] = 15 * [tex]\sqrt{2}[/tex]

Therefore, the measure of the diagonal of the square table is 15 * [tex]\sqrt{2}[/tex] feet (approximately 21.21 feet).

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the simplified difference is -1 - 4x + 524. To simplify the difference (1 + 2x) - (6x+2-524), we need to first distribute the negative sign to the second expression inside the parentheses:

(1 + 2x) - (6x+2-524) = 1 + 2x - 6x - 2 + 524  

Now we can simplify by combining like terms:

1 + 2x - 6x - 2 + 524 = (1 - 2) + (2x - 6x) + 524

Simplifying further:

-1 - 4x + 524

Therefore, the simplified difference is -1 - 4x + 524.

It's worth noting that this expression could be simplified further by combining like terms, but it depends on the context and purpose of the expression. For example, if we were trying to solve an equation involving this difference, we might want to simplify it further to make it easier to solve. However, if we were simply asked to simplify the expression, then the answer we have above is sufficient.

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Finding a quotient of  [tex]2,125/4[/tex] is [tex]531.25[/tex] with the use of partial quotients is possible.

A fraction's quotient is the whole integer that results from simplifying the fraction. The division is the fraction's decimal form if the simplified fraction yields a non-whole number. The answer to a division issue involving two fractions can also be found in the quotient.

Latin's "how many times" is the meaning of the word "quotient." It makes perfect sense: by dividing two numbers, you can determine "how many time" the second number enters the first. The number being divided is referred to as the payout, and the number being divided by it is referred to as the divisor.

40)2125(531.25

     20

    -------

        12

       -12

       ------

          5

         -4

        --------

           10

            -8

           --------

              20

             -20

             ----------

                00

              ----------

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Yes,the statement "phillies fans prefer redcars more than the general population" is convincing evidence

The sample provides convincing evidence that Phillies fans are more likely to drive red cars than the general population.

This can be supported through a test of significance.

A statistical test is referred to as a significance test or a hypothesis test. The test is used to determine if there is enough evidence to reject a null hypothesis that a specific condition is true.

A hypothesis test is typically used to determine if there is enough evidence to support or reject a claim about a population parameter based on a sample statistic.

In this scenario, the proportion of red cars in the population is 0.12. The sample size is 210 cars parked at Citizens Bank Park, with 35 of them being red.

To test whether Phillies fans prefer red cars more than the general population, the following null and alternative hypotheses can be used:

Null hypothesis:

The proportion of red cars driven by Phillies fans is equal to the proportion of red cars in the general population.

Alternative hypothesis:

The proportion of red cars driven by Phillies fans is greater than the proportion of red cars in the general population.

Using a one-tailed test and a significance level of 0.05, we can compute the test statistic as follows:

Z = (0.17 - 0.12) / √(0.12 * 0.88 / 210) = 1.77

The critical value for a one-tailed test with a 0.05 significance level and 209 degrees of freedom is 1.65. Since the test statistic (1.77) is greater than the critical value (1.65),

We reject the null hypothesis and conclude that there is sufficient evidence to support the claim that Phillies fans are more likely to drive red cars than the general population.

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See pics for answers

The vertices after the dilation arE:

C A'(4, 4), B'(8, 4), C'(8, 6)

The original vertices are  A(2, 2), B(4, 2), and C(4, 3). And we apply a dilation of scale factor 2, then to get the new coordinates ust multiply all the coordinates by 2, we will get.

A' = (2*2, 2*2) = (4, 4)

B' = (4*2, 2*2) = (8, 4)

C' = (4*2, 3*2) = (8,6)

Then the correct option in this case is:

C A'(4, 4), B'(8, 4), C'(8, 6)

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The minimum number of individuals (MNI) of bison bones is 7.

Explanation:

The minimum number of individuals (MNI) of the bison bones discovered by archaeologists working at Head-Smashed-In-Buffalo-Jump is 5.

Head-Smashed-In Buffalo Jump is an archaeological site in Alberta, Canada. It is a cliff site used by First Nations people for bison hunting. Head-Smashed-In Buffalo Jump is a UNESCO World Heritage Site and is one of the world's oldest, largest, and best-preserved buffalo jump sites

              The minimum number of individuals (MNI) of bison bones is the smallest possible number of bison from which the bones could have come. The minimum number of individuals (MNI) is calculated using the least number of right or left paired bones, such as femurs or humeri. The right femurs are the fewest paired bones with only seven out of the fifteen femurs found at the Head-Smashed-In Buffalo Jump site.

Therefore, the minimum number of individuals (MNI) of bison bones is 7.

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As per the combination method, there are 1260 ways in which a team of 10 students with 6 boys and 4 girls can be formed from a middle school classroom containing 15 students with 9 boys.

To solve this problem, we need to use the concept of combinations. A combination is a way of selecting items from a larger group where the order of selection does not matter. In this problem, we are selecting a team of 10 students, and the order in which we select the students does not matter.

Using this formula, we can find the number of ways to select 6 boys from a group of 9 as:

⁹C₆ = 9! / (6! x (9-6)!) = 84

Similarly, the number of ways to select 4 girls from a group of 6 is:

⁶C₄ = 6! / (4! x (6-4)!) = 15

To find the total number of ways to form a team of 10 students with 6 boys and 4 girls, we need to multiply the number of ways to select 6 boys and 4 girls. This is because the selection of boys and girls is independent of each other, and we can choose them in any order.

Therefore, the total number of ways to form a team of 10 students with 6 boys and 4 girls is:

84 x 15 = 1260

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The fractions less than [tex]\frac{1}{2}[/tex] are:

a. [tex]\frac{2}{5}[/tex]

d. [tex]\frac{1}{6}[/tex]

e. [tex]\frac{3}{8}[/tex]

To see why, we can compare each fraction to [tex]\frac{1}{2}[/tex], which is equivalent to [tex]\frac{4}{8}[/tex]:

The complete question is:-

Which fractions are less than 1/2 ? choose all the correct answers

a. 2/5 b. 6/8 c. 4/5 d. 1/6 e. 3/8 f. 5/6

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Answer: 4 hours

Step-by-step explanation:

3/1=12/x

3x=12

x=4

Answer:

x=7

Step-by-step explanation:

The equation can be represented as following:

[tex](\frac{x}{14} +3\frac{1}{2})=2(\frac{x}{21} +1\frac{2}{3})[/tex]. If we open the parenthesis, we can get as following:

[tex]\frac{1}{14}x +3\frac{1}{2}=\frac{2}{21}x +3\frac{1}{3} \\[/tex], which then subtract [tex]2\frac{2}{21} x[/tex] from both sides to get the following:
[tex]\frac{7}{2}-\frac{1}{42} x=\frac{10}{3}[/tex];

subtract [tex]\frac{7}{2}[/tex] from both sides to get [tex]\frac{-1}{42} x=\frac{-1}{6}[/tex], and multiply both sides by -42 to get our final answer of x=7

The difference between the shortest and longest species of frog is [tex]3^{3\\}[/tex].

A line plot is a graph that shows data as checkmarks or points over a number line, indicating the frequency of each value.

When displaying information that changes over time, a line graph, also referred to as a line chart or a line plot, is frequently used. It can be visualized using a series of points connected by straight lines. The "x-axis" and the "y-axis" are two of its axes.

is a graph where the lines connecting the various data points are used. A line graph shows numerical values over a predetermined period of time. The shortest and longest frog species differ in terms of [tex]3^{3}[/tex].

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Therefore, the football team scored 4 touchdowns, 2 field goals, and 1 safety in the game.

An equation is a mathematical statement that asserts that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and so on. An equation is often written with an equal sign (=) between the two expressions. The goal of solving an equation is to find the values of the variables that make the equation true. Equations are used extensively in mathematics, physics, engineering, and many other fields to describe relationships between different quantities.

by the question.

Let's denote the number of touchdowns scored by "T", the number of field goals scored by "F", and the number of safeties scored by "S".

From the problem, we know:

[tex]T + F + S = 8 (they scored points 8 times)\\7T + 3F + 2S = 38 (the total score was 38 points)\\T = F + S[/tex] (they scored as many touchdowns as they did field goals and safeties combined)

Substituting the third equation into the first, we get:

[tex]F + S + F + S = 8\\2F + 2S = 8\\F + S = 4[/tex]

We now have a system of three equations:

[tex]T + F + S = 8\\7T + 3F + 2S = 38\\T = F + S[/tex]

Substituting the third equation into the first two, we get:

[tex]7(F + S) + 3F + 2S = 38\\8(F + S) = 21[/tex]

Solving for F + S, we get:

[tex]F + S = 21/8[/tex]

However, we also know that F + S = 4, so there must be a mistake somewhere. Looking back at the problem, we see that the statement "they scored as many touchdowns as they did field goals and safeties combined" implies that T = F + S + 1 (since a touchdown is worth 7 points and a field goal and safety combined are worth 4 points). Substituting this into the first two equations, we get:

[tex](F + S + 1) + F + S = 8\\7(F + S + 1) + 3F + 2S = 38[/tex]

Simplifying, we get:

[tex]2F + 2S = 6\\10F + 9S = 31[/tex]

Solving for F and S, we get:

[tex]F = 2\\S = 1[/tex]

Substituting these values back into the equation T = F + S + 1, we get:

[tex]T = 4[/tex]

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