3. Match each feature of the situation with
a corresponding statement in function
notation.
A maximum height
B. minimum height
C. height staying the same
D. starting height
height (feet)
26200
16
12
8
4
1
2
3 4
5
time (seconds)
1. h(0) = 7
2. h(1.5)
3. h(4)
4. h(t) = 6 for 7 ≤ 1 ≤8
6-7

Answer:

3rd choice down

(x + 9) / (x + 1)

Step-by-step explanation:

(2x + 4 - x + 5) / (x + 1) = (2x - x + 4 + 5) / (x+ 1) = (x + 9) / (x + 1)

The angle measures, considering the linear pair formed by angles 1 and 2, are given as follows:

When a parallel line is cut by a transversal, a linear pair is formed when two adjacent angles add up to 180 degrees. A linear pair of angles is always formed by two adjacent angles that are supplementary, which means that they add up to 180 degrees.

In this case, a linear pair is formed by two adjacent angles that are formed by the intersection of the transversal with each of the parallel lines.

Hence, angles 1 and 2 are supplementary, meaning that the sum of their measures is of 180º, hence the value of x is obtained as follows:

3x + 5 + 2x + 10 = 180

5x + 15 = 180

5x = 165

x = 33.

Then the measures are given as follows:

The diagram that represents the situation is given by the image presented at the end of the answer.

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By answering the above question, we may infer that As a result, the inequality answer is 2 x 1.

A connection between two expressions or values that is not equal is known as an inequality in mathematics. Inequality follows imbalance, therefore. In mathematics, an inequality makes a connection between two values that are not equal. Egality and inequality are different. The not equal symbol is often used to indicate that two values are not equal (). Various inequalities are employed to contrast values of all sizes. By changing the two sides until just the variables are left, one may solve many straightforward inequalities. However a variety of factors support inequality: Negative values are split or added on either side. Switch between the left and right.

We may take 3 off of all sides to find the solution to the inequality 1 x + 3 4:

[tex]1 < x + 3 < 4 \s-3 -3 -3 \s-2 < x < 1[/tex]

As a result, the answer is 2 x 1.

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Emily can buy 9 paperback books and 1 hardcover book without spending more than $45.

Let's start by defining our variables

Let x be the number of paperback books

Let y be the number of hardcover books

We know that a paperback book costs $4.50 and a hardcover book costs $10. If Emily buys x paperback books and y hardcover books, then the total cost of her purchase can be calculated using the following equation:

Total cost = 4.50x + 10y

We also know that Emily cannot spend more than $45. So we can set up the following inequality

4.50x + 10y ≤ 45

Now we can use this inequality to find the maximum number of paperback and hardcover books that Emily can buy.

First, let's rearrange the inequality to solve for y:

10y ≤ 45 - 4.50x

y ≤ (45 - 4.50x) / 10

y ≤ 4.5 - 0.45x

So, Emily can buy up to 4.5 - 0.45x hardcover books for every x paperback books. Let's make a table to see the possibilities

From the table, we can see that the maximum number of paperback books that Emily can buy is 12, and the maximum number of hardcover books she can buy is 0. However, this is not a feasible option since she would be spending $54, which is over her budget of $45.

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Answer: X^4 - (1/3)X^3 + 2\sqrt{X} - 5 = 0

Step-by-step explanation:

The answer is:

X^4 - (1/3)X^3 + 2\sqrt{X} - 5 = 0

This is a quartic equation, meaning it has four terms with the highest degree of X being 4. It cannot be solved in terms of radicals, so an approximate solution must be used. This can be done through numerical methods, such as the Newton-Raphson method, which uses an iterative process to approximate a solution.

The area of this trapezoid is 66 cm².

To find the area of a trapezoid, we use the formula:

Area = (a + b) x h / 2

Where:

a and b are the lengths of the parallel sides of the trapezoid

h is the height

If we assume that the 22 cm and 11 cm sides are parallel sides, that is

a = 22

b = 11

and h = 4 cm

Now we can use the formula to find the area:

Area = (22 cm + 11 cm) x 4 / 2

Area = 66 cm²

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The Johnston index of each voter is 3.317 and the Deegan-Packel index of each voter is  0.154

The Johnston index and the Deegan-Packel index are two measures of voting power that take into account the number of votes each voter has and the number of votes required for passage.

a) The Johnston index is calculated by taking the square root of the product of the number of votes a voter has and the number of votes they need for passage. In this case, the Johnston index for each voter is:
MA: √(4*(12-4)) = √32 = 5.657
ME: √(3*(12-3)) = √27 = 5.196
NH: √(2*(12-2)) = √20 = 4.472
CT: √(4*(12-4)) = √32 = 5.657
RI: √(3*(12-3)) = √27 = 5.196
VT: √(1*(12-1)) = √11 = 3.317

b) The Deegan-Packel index is calculated by taking the number of winning coalitions that a voter is a part of and dividing it by the total number of winning coalitions. In this case, the Deegan-Packel index for each voter is:
MA: 20/26 = 0.769
ME: 14/26 = 0.538
NH: 8/26 = 0.308
CT: 20/26 = 0.769
RI: 14/26 = 0.538
VT: 4/26 = 0.154

Overall, the Johnston index and the Deegan-Packel index provide different perspectives on the voting power of each voter. The Johnston index takes into account the number of votes each voter has and the number of votes required for passage, while the Deegan-Packel index takes into account the number of winning coalitions each voter is a part of.

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Answer:

Step-by-step explanation:

Since he's applying stain (painting) he must be doing only the surface.

Finding the surface area:

33x18=594

33x15=495

18x15=270

594+495+270=

1359 square inches

We will then x2 1359 since we found the area for 1/2 of the box.

It is: 2718

Let the cost of 1 pound of zucchini be 'z' and the cost of 1 pound of tomatoes be 't'. We can set up two equations using the given information:

9z + 6t = 21.15 (equation 1)

4z + 3t = 9.83 (equation 2)

We can solve for 'z' and 't' using the method of substitution:

From equation 2, we can express 4z as 9.83 - 3t:

4z = 9.83 - 3t

Substituting this expression for 4z in equation 1, we get:

9(9.83 - 3t)/4 + 6t = 21.15

Multiplying both sides by 4 to eliminate the fraction, we get:

9(9.83 - 3t) + 24t = 84.6

Expanding the left side, we get:

88.47 - 27t + 24t = 84.6

Combining like terms, we get:

-3t = -3.87

Dividing both sides by -3, we get:

t = 1.29

Substituting this value of 't' in equation 2, we get:

4z + 3(1.29) = 9.83

Simplifying, we get:

4z = 5.56

Dividing both sides by 4, we get:

z = 1.39

Therefore, 1 pound of zucchini costs $1.39 and 1 pound of tomatoes costs $1.29 at the farm stand.

Answer:

z = 1.39

Step-by-step explanation:

If Angela used 1/5 of her beads and gave 78 to Santiago, she would have 130 beads left.

To find out how many beads Angela had left, we need to first find out how many beads she started with. We can do this by using the information given in the question and setting up an equation. Let's let x represent the number of beads Angela started with.

According to the question, Angela used (1)/(5) of her beads to make bracelets, so she had (4)/(5) of her beads left. She then gave 78 beads to Santiago, which left her with (1)/(2) of her original number of beads. We can write this as an equation:

(4)/(5)x - 78 = (1)/(2)x

To solve for x, we can first multiply both sides of the equation by 10 to get rid of the fractions:

8x - 780 = 5x

Next, we can subtract 5x from both sides of the equation to isolate the variable:

3x = 780

Finally, we can divide both sides of the equation by 3 to find the value of x:

x = 260

So Angela started with 260 beads. We proceed to find out how many you have left:

P = (1/2)(260)

P = 130

So Angela had 130 beads left after giving 78 beads to Santiago.

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Answer:

1/2

Step-by-step explanation:

because 5 times 1/2 and you get 2 1/2

The mean of the given probability distribution is 2.8.

To find the mean, we multiply each possible value of X (the number of adults with a college degree) by its corresponding probability, and then add up the products.

So, the mean is:

(0)(0.0081) + (1)(0.0756) + (2)(0.2646) + (3)(0.4164) + (4)(0.2401) = 2.8

This means that on average, out of 4 randomly selected adults in the town, 2.8 of them will have a college degree. This is a useful measure of the central tendency of the probability distribution, as it gives us an idea of what to expect if we were to repeat this process of randomly selecting 4 adults many times.

It's important to note that the mean is not necessarily a value that is actually observed in the data, but rather a summary statistic that tells us about the distribution as a whole. In this case, it tells us that the distribution is slightly skewed towards higher values, since the mean is greater than the median (which would be the value of X with cumulative probability of 0.5, or 2 in this case).

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I think that the answer for your problem would be

.

.

.

a.a=(p÷4)×(p÷4)

Answer: We know that the perimeter of a square is given by the formula:

P = 4s

where s is the side length of the square.

We can rearrange this equation to get:

s = P/4

The area of a square is given by the formula:

A = s^2

Substituting s = P/4, we get:

A = (P/4)^2

Simplifying this equation:

A = P^2/16

Therefore, the equation that can be used to find the area of a square that has a perimeter of P units is:

A = P^2/16

So, the correct answer is:

A. A = (P ÷ 4) x (P ÷ 4)

Step-by-step explanation:

Answer: split it into smaller solids and calculate their separate volumes.

Step-by-step explanation:

The value of m² - 1 + 1/m² is 5, given that m + 1/m = 3.

In mathematics, a quadratic equation is one with degree 2, which means that its maximum exponent is 2. A quadratic has the standard form y = ax2 + bx + c, where a, b, and c are all numbers and a cannot be zero. All of these are examples of quadratic equations: y = x2 + 3x + 1.

The equation m + 1/m = 3 must first be changed in order to solve for m2 - 1 + 1/m2.

When we multiply both sides by m, we obtain:

m² + 1 = 3m

Rearranging gives us:

m² - 3m + 1 = 0

We can find m using the quadratic formula:

m = (3 ± sqrt(5))/2

When we enter these values into m2 - 1 + 1/m2, we obtain:

((3 + sqrt(5))/2) = m2 - 1 + 1/m2² - 1 + (2/(3 + sqrt(5)))²

If we condense this phrase, we get:

m² - 1 + 1/m² = 5

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Answer: 7.5

Step-by-step explanation:

     A percent divided by 100 becomes a decimal.

           10% / 100 = 0.1

     Next, since we are finding 10% of 75, we will multiply.

     This will give us 10% of 75.

           0.1 * 75 = 7.5

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To determine the sample size needed to estimate the proportion of supporters with a margin of error of 2.3% and a 90% confidence level,

we can use the formula:
n = (Z^2 * p * (1-p)) / E^2
Where:
- n is the sample size
- Z is the Z-score for the desired confidence level (for 90% confidence, Z = 1.645)
- p is the estimated proportion of supporters (if we have no prior knowledge, we can use 0.5 as a conservative estimate)
- E is the desired margin of error (2.3% or 0.023)

Plugging in the values, we get:
n = (1.645^2 * 0.5 * (1-0.5)) / 0.023^2
n = 752.3
Since we cannot have a fraction of a person, we round up to the nearest whole number to get a sample size of 753.

Therefore, a sample size of 753 is needed to estimate the proportion of supporters with a margin of error of 2.3% and a 90% confidence level.

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The formula for testing the significant difference between two population variances is the F-test. The F-test is used to compare the variances of two populations and is calculated by dividing the larger variance by the smaller variance. The formula for the F-test is:

F = s1^2 / s2^2

Where s1^2 is the variance of the first population and s2^2 is the variance of the second population.

If the calculated F value is greater than the critical F value from the F distribution table, then there is a significant difference between the two population variances. If the calculated F value is less than or equal to the critical F value, then there is not a significant difference between the two population variances.

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Answer:

y - 17 = - 5(x + 7)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = - 5 and (a, b ) = (- 7, 17 ) , then

y - 17 = - 5(x - (- 7) ) , that is

y - 17 = - 5(x + 7)

Answer:

y = -5x - 18.

Step-by-step explanation:

The point-slope form of the equation of a line is given by:

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is a point on the line.

We are given that the line passes through the point (-7, 17) and has a slope of -5. Thus, we can substitute these values into the point-slope form equation to get:

y - 17 = -5(x - (-7))

Simplifying the right-hand side of the equation:

y - 17 = -5(x + 7)

y - 17 = -5x - 35

Finally, adding 17 to both sides of the equation, we get the slope-intercept form of the equation:

y = -5x - 18

Therefore, the equation of the line that passes through the point (-7,17) with slope -5 is y = -5x - 18.

Yes, we can determine the sampling distribution of the sample mean.

The name of the distribution is the Student's t-distribution. The mean of the sampling distribution is the same as the mean of the population, which is $51000. The standard error of the sampling distribution is calculated by dividing the standard deviation of the population by the square root of the sample size. So, the standard error is $5500 / sqrt(18) = $1296.56.

Here is the answer formatted in HTML:
Yes, we can determine the sampling distribution of the sample mean. The name of the distribution is the Student's t-distribution.

The mean of the sampling distribution is the same as the mean of the population, which is $51000. The standard error of the sampling distribution is calculated by dividing the standard deviation of the population by the square root of the sample size. So, the standard error is $5500 / sqrt(18) = $1296.56.

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Dina's older brother has a hot chocolate that is more chocolaty, as his recipe has a percentage of cocoa of 40%, which is higher than the percentage of 37.5% for Dina's recipe.

The more chocolaty recipe is defined obtain the proportion of cocoa for each recipe, and then whoever's recipe has the higher proportion has the more chocolaty recipe.

The proportion of cocoa for each recipe is obtained with the division of the amount of cocoa used by the sum of the amounts of cocoa and milk used for the recipe.

Hence the proportion for Dina's older brother is obtained as follows:

2/(2 + 3) = 2/5 = 0.4 = 40% cocoa.

The proportion for Dina's is obtained as follows:

3/(3 + 5) = 3/8 = 0.375 = 37.5% cocoa.

40 > 37.5, hence Dina's older brother has a hot chocolate that is more chocolaty, as his recipe has a higher proportion of cocoa.

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Therefore, the lengths of the sides of quadrilateral HIJK are √(65),  13, √(65), and √(52).

A quadrilateral is a polygon with four sides and four vertices. The sum of the interior angles of a quadrilateral is always equal to 360 degrees. There are many different types of quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombuses, and kites. Each type of quadrilateral has its own unique properties, such as having four equal sides (square), having opposite sides parallel (parallelogram), or having two pairs of equal adjacent sides (kite). Quadrilaterals can be classified based on their sides, angles, or both.

Here,

The point H has coordinates (-5, 6), which means it is located 5 units to the left of the y-axis and 6 units above the x-axis. The point I has coordinates (3, 4), which means it is located 3 units to the right of the y-axis and 4 units above the x-axis. The point J has coordinates (0, -8), which means it is located at the intersection of the x-axis and the y-axis, but 8 units below the x-axis. Finally, the point K has coordinates (-7, -2), which means it is located 7 units to the left of the y-axis and 2 units below the x-axis.

We can see that HIJK is a general quadrilateral, meaning that it does not have any special properties like being a rectangle or a parallelogram. We can find the lengths of its sides and the measures of its angles by using the distance formula and the slope formula, respectively. The distance formula gives us the distance between any two points (x1, y1) and (x2, y2):

distance = √((x2 - x1)² + (y2 - y1)²)

The slope formula gives us the slope of a line passing through two points (x1, y1) and (x2, y2):

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

Using these formulas, we can find that the lengths of the sides of HIJK are:

HI = √((3 - (-5))² + (4 - 6)²) = √(65)

IJ = √((0 - 3)² + (-8 - 4)²) = √(169) = 13

JK = √((-7 - 0)² + (-2 - (-8))²) = √(65)

KH = √((-7 - (-5))² + (-2 - 6)²) = √(52)

We can also find the slopes of the lines passing through each pair of adjacent vertices:

The slope of line segment HI passing through points H and I is:

(4 - 6) / (3 - (-5)) = -1/2.

The slope of line segment IJ passing through points I and J is:

(-8 - 4) / (0 - 3) = 4/3.

The slope of line segment JK passing through points J and K is:

(-2 - (-8)) / (-7 - 0) = 6/7.

The slope of line segment KH passing through points K and H is:

(6 - (-2)) / (-5 - (-7)) = 4/3.

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Complete question:

Quadrilateral HIJK has vertices at H(-5,6), I(3,4), J(0,-8), and K(-7,-2). find the length of sides as well as the slopes.

Answer:

B is correct

Step-by-step explanation:

The points all go downhill as you move from left to right. We can draw a straight line that is fairly close to all of them. This is known as the regression line. The regression line having a negative slope tells us the linear association is negative. This means the correlation coefficient r is negative, so,  (r = -1 is not possible as not all points fall on the same straight line)

The probability of getting two heads and three tails in a single throw of five unbiased coins is 0.3125.

The probability of getting two heads and three tails in a single throw of five unbiased coins can be calculated using the formula:

P = (5! / (2! * 3!)) * (0.5)^2 * (0.5)^3

Where 5! is the factorial of 5, 2! is the factorial of 2, and 3! is the factorial of 3.

First, calculate the factorial of 5, 2, and 3:

5! = 5 * 4 * 3 * 2 * 1 = 120
2! = 2 * 1 = 2
3! = 3 * 2 * 1 = 6

Next, plug these values into the formula:

P = (120 / (2 * 6)) * (0.5)^2 * (0.5)^3

Simplify:

P = (120 / 12) * (0.25) * (0.125)

P = 10 * 0.25 * 0.125

P = 0.3125

Therefore, the probability of getting two heads and three tails in a single throw of five unbiased coins is 0.3125.

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Answer: end balance: $8,496.95

total interest: $1,496.95

Step-by-step explanation: total interest = $7000 × 8.554% × 30 ÷ 12 = $1,496.95

end balance = $7000 + $1,496.95 = $8,496.95

Answer: 25 minutes

Step-by-step explanation:

40km an hour = 35 min

45km an hour = 30 min

50km an hour = 25 min

It takes 25 minutes to drive the distance between 2 villages.

We want to graph a number line and graph some locations on it, the graph can be seen at the end of the answer.

A number line is just a line with equidistant marks on it, that can be used to find the distance between numbers, so to graph the number line we just graph a line and do marks on it.

The north will be referred to as the right side of a number line that is positive, and the south will be the opposite.

Now let's complete the graph:

a) We want to graph the truck stop; we can do this at the zero of the number line.

b) 5 miles up north of the truck stop.

Here, if each mark represents a mile, we just mark a point that is 5 marks at the right of the truck stop.

c) 3.5 miles south of a truck stop, at this location.

Here we mark a point that is at 3 and a half marks at the left of the truck stop.

The graph can be seen below.

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'x' is an unknown variable, so a value that is not known

The set G = Zp × is a group under modular multiplication. This is because the set contains all the non-zero elements of Zp, and modular multiplication satisfies the four group properties:

Using Lagrange's Theorem, we can prove Fermat's Little Theorem: that for any integer a not divisible by p, ap-1 ≡ 1 (mod p). Let n be the smallest positive integer such that an ≡ 1 (mod p).

Since a is not divisible by p, the order of a (the smallest value of n) must divide p - 1, or in other words, n | (p - 1). By Lagrange's Theorem, this implies n = p - 1, which in turn implies that ap - 1 ≡ 1 (mod p). This proves Fermat's Little Theorem.

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