Which of the following represents the correct expansion of (x + 2)^5?

A. x5 + 10x4 + 40x3 + 40x2 + 10x +32
B. x5 + 8x4 + 12x3 + 8x2 + x +32
C. x5 + 10x4 + 20x3 + 20x2 + 10x +32
D. x5 + 10x4 + 40x3 + 80x2 + 80x +32

To find the distance between two points (1,5) and (7,9), you can use the distance formula sqrt((x2 - x1)^2 + (y2 - y1)^2). Rounding to the nearest tenth, the distance is approximately 7.2.

To find the distance between two points, we can use the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using the given points (1,5) and (7,9), we substitute the values into the formula:

d = sqrt((7 - 1)^2 + (9 - 5)^2) = sqrt(36 + 16) = sqrt(52)

Rounding to the nearest tenth, the distance between the two points is approximately 7.2.

To find out the number of cups of flour needed for each dozen muffins, you need to divide the total quantity of flour used by the total number of dozens. Therefore, about 2 11/14 cups of flour are required for each dozen muffins.

To find out how many cups of flour are needed for every dozen muffins made, we need to divide the total amount of flour used by the total number of dozens of muffins. The recipe used 312 cups of flour to make 112 dozens of muffins. So, we divide 312 by 112:

312 ÷ 112 = 2.78571428571429

To convert this to a mixed number in simplest form, you can say that approximately 2 11/14 cups of flour are needed for every dozen muffins made.

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For every dozen muffins made, the recipe requires [tex]\(2 \frac{11}{14}\)[/tex] cups of flour. This is determined by simplifying the ratio of 312 cups of flour needed for 112 dozen muffins to its simplest form.

To find the cups of flour needed for every dozen muffins, we can set up a ratio between the cups of flour and the number of dozens of muffins.

[tex]\[ \text{Cups of Flour} : \text{Dozens of Muffins} \][/tex]

Given that 112 dozen muffins require 312 cups of flour, the ratio becomes:

[tex]\[ \frac{312 \text{ cups}}{112 \text{ dozens}} \][/tex]

Now, simplify this ratio by dividing both the numerator and the denominator by the greatest common factor, which is 8.

[tex]\[ \frac{39 \text{ cups}}{14 \text{ dozens}} \][/tex]

Now, express this ratio as a mixed number in simplest form. Since 39 and 14 share no common factors other than 1, the mixed number is [tex]\(2 \frac{11}{14}\).[/tex]

Therefore, the answer is [tex]\(2 \frac{11}{14}\)[/tex] cups of flour for every dozen muffins made.

In the given data set, there are 7 values in the given range.

A data set is a collection of data. In the case of tabular data, a data set corresponds to one or more database tables, where every column of a table represents a particular variable, and each row corresponds to a given record of the data set in question.

Given is a set of data we need to determine how many students are in the range 12 cm to 13.9 cm,

So,

Here we just need to find the number of values between 12cm and 13.9 cm, from the given table, these are:

12.1 cm, 13.5 cm, 12.4 cm, 13.7 cm, 13.8 cm, 12.5 cm, 13.1 cm

So, there are 7 values in the given range, which means that 7 students are in the range of 12cm and 13.9cm.

Then the correct option is 7.

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Answer:

Option 3 - (8,4)

Step-by-step explanation:

Given : Three consecutive vertices of a parallelogram are points (2, 4), (0, 0), and (6, 0).

To find : The fourth vertex is point ?

Solution :

We have given that points are forming a parallelogram.

Let the fourth coordinate is (x,y)

Now, we draw a rough image of the given situation.

Refer the attached figure below.

Draw a parallelogram ABCD with mid point O.

Applying the mid point between two points (2,4) and (6,0).

[tex]O=\frac{2+6}{2}, \frac{4+0}{2}\\\\ O=4,2[/tex]

Now, Applying mid point between points (0,0) and (x,y)

[tex](4,2)=\frac{x+0}{2}, \frac{y+0}{2}[/tex]

[tex]\frac{x+0}{2}=4, \frac{y+0}{2}=2[/tex]

[tex]x=8 ,y=4[/tex]

Therefore, The fourth vertex point is (8,4).

Hence, Option 3 is correct.

There were 30 families that had a parakeet.

By using the concept of Sets :

- Total number of families surveyed (denoted as N) = 240.

- Number of families with dogs (denoted as D) = 91.

- Number of families with cats (denoted as C) = 70.

- Number of families with both dogs and cats (denoted as D ∩ C) = 31.

- Number of families with neither cats nor dogs nor parakeets (denoted as neither) = 91.

- Number of families with cats, dogs, and parakeets

(denoted as D ∩ C ∩ P) = 7.

We want to find the number of families that had parakeets

(denoted as P).

To find the number of families with parakeets, we can use the principle of inclusion-exclusion. It states that:

N(D ∪ C ∪ P) :

= N(D) + N(C) + N(P) - N(D ∩ C) - N(C ∩ P) - N(D ∩ P) + N(D ∩ C ∩ P).

Substitute the given values:

240 = 91 + 70 + P - 31 - N(C ∩ P) - N(D ∩ P) + 7.

Now, we can calculate the number of families with both cats and parakeets (C ∩ P) and the number of families with both dogs and parakeets (D ∩ P):

C ∩ P + D ∩ P = (C + D + P) - (N(D) + N(C) + N(P)) = 240 - 91 - 70 - P = 79 - P.

From the given information, we also know that the number of families with neither cats nor dogs nor parakeets is 91. Therefore, we can write:

neither + N(D ∩ P) + N(C ∩ P) + N(D ∩ C ∩ P) = 91.

Substitute the values:

91 + N(D ∩ P) + C ∩ P + 7 = 91.

Now, we can solve for C ∩ P:

C ∩ P = 91 - N(D ∩ P) - 7.

Substitute the value of C ∩ P we found earlier:

79 - P = 91 - N(D ∩ P) - 7.

Now, we can find N(D ∩ P):

N(D ∩ P) = 79 - P - 91 + 7 = -P - 5.

However, we know that the number of families cannot be negative. So, we ignore this solution. Instead, we use the previously calculated value of C ∩ P:

C ∩ P = 91 - N(D ∩ P) - 7.

91 - (79 - P) - 7 = 91 - 79 + P - 7 = P - 7.

P - 7 = 30.

Finally, we get the value of P:

P = 30.

Therefore, there were 30 families that had a parakeet.

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Answer:

String form an angle of 18.2° with the ground.

Step-by-step explanation:

Given: Length of the string of a kite = 160 ft.

           Kite stuck on pole at height of = 50 ft.

We need to find: Measure of angle formed by string of kite with ground.

Attached figure showing the given situation.

let α be the required angle.

In ΔABC,

using trigonometric ratio,

[tex]sin\,\aplha=\frac{AB}{AC}[/tex]

[tex]sin\,\aplha=\frac{50}{160}[/tex]

[tex]sin\,\aplha=\frac{5}{16}[/tex]

[tex]sin\,\aplha=0.3125[/tex]

[tex]\aplha=sin^{-1}(0.3125)[/tex]

[tex]\alpha=18.20995686428301[/tex]

[tex]\alpha=18.21[/tex]

Therefore, String form an angle of 18.2° with the ground.

The average polar bear weighs is 800 times more than the average black bear.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We have given that the average polar bear weighs 1,200 pounds.

Average grizzly bear weighs is 800 pounds.

The average black bear weighs is 400 pounds.

To find the average polar bear weighs of x times more than the average black bear.

We need to subtract ;

1,200 - 400 = 800

That is 800

Hence, The average polar bear weighs is 800 times more than the average black bear.

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Answer:

F(1) is not defined

Step-by-step explanation:

Answer:

The Answer is Associative

Step-by-step explanation:

DONT PUT PROPERTY YOU WILL GET IT WRONG...

Answer:

Answer:

Number line with an open circle on 4 and shading to the right.

Explanation:

Call x the number of students that need to sign up so that more than one van is needed to transport them =>

x + 3 > 7

=> x > 7 - 3

=> x > 4

That is the number greater than 4, without including the number 4.

That is the number line is the set of numbers to the right of 4, and the open circle is used to indicate that the number 4 is not included (a closed circle would indicate that the number 4 is included, which is not the case).

Step-by-step explanation:

A relation that passes through the y-axis twice is not considered a function. A function, by definition, can only output one 'y' value for each unique 'x' value. This relation fails the 'vertical line test' which checks that each 'x' value only connects to a single 'y' value.

In mathematical terms, a relation is a set of ordered pairs, where each first element is related to the second element. A function, on the other hand, is a special type of relation where every input (or 'x' value) corresponds to exactly one output (or 'y' value).

Now, if a relation passes through the y-axis twice, it means that there are two 'y' values for a single 'x' value (which in this case, is zero). This violates the definition of a function. Hence, a relation that passes through the y-axis twice is not a function. It is simply a relation because it doesn't pass the 'vertical line test' (a vertical line passing through more than one point on the graph of a relation means that the relation is not a function).

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40 miles x 5280 = 211200 feet per hour

1 hour = 3600 seconds

211200 / 3600 = 58.67 feet per second

Answer:

The answer is 59 feet per second (B)

Step-by-step explanation:

edge hope ya do well

Firstly, define a variable `usernum` and let's use 10 as an example. Then, define another variable `summedvalue` and set it as 0 initially. This variable will hold the sum of all odd numbers up to `usernum`.

Next, we start a for loop. This loop will go through each number in the range from 1 to `usernum` inclusive. That's why in the range function we provide `usernum + 1` as the second parameter.

Now, for every number `i` in this range, we check whether it is odd. A number is odd if it gives a remainder of 1 when divided by 2. In other words, we're checking if `i % 2` is not equal to 0 (`i % 2 != 0`).

If the current number `i` is indeed odd, we add it to `summedvalue` (`summedvalue += i`). Then, the loop goes to the next number and the process repeats itself until we've considered all numbers from 1 to `usernum`.

Finally, when the loop ends, the value of `summedvalue` is the sum of all odd numbers from 1 up to (and including) `usernum`. Return this `summedvalue`.

In the case of `usernum = 10`, the odd numbers between 1 to `usernum` are 1, 3, 5, 7, and 9. When you add them together, you get 25. That's why in this case, the result will be 25.

The number of the fraction 3/8 that we can get in 6, is: 16.

We are asked to find how many of the fraction, 3/8, we will have in 6.

This implies that, what number would we need to multiply with 3/8 to get 6?

To determine this, all we need to do is to divide 6 by the fraction, 3/8.

[tex]6 \div \frac{3}{8}[/tex]

[tex]6 \times \frac{8}{3} \\\\= \frac{6 \times 8}{3} \\\\= \frac{48}{3} \\\\\mathbf{= 16}[/tex]

Therefore, the number of the fraction 3/8 that we can get in 6 is: 16.

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A Z-score helps us to understand how far is the data from the mean. The percentage of children who spend over 10 hours per day unsupervised is 0.005%.

A Z-score helps us to understand how far is the data from the mean. It is a measure of how many times the data is above or below the mean. It is given by the formula,

[tex]Z = \dfrac{X- \mu}{\sigma}[/tex]

Where Z is the Z-score,

X is the data point,

μ is the mean and σ is the standard variable.

Given that the average time that is unsupervised is 3 hours and the standard deviation is 1.8 hours. The percentage of children who spend over 10 hours per day unsupervised is,

P(X>10) = 1 - P(X<10)

            [tex]= 1 - P(Z < \dfrac{10-3}{1.8})[/tex]

            = 1 - P(Z< 3.889)

            = 1 - 0.99995

            = 0.00005

Hence, The percentage of children who spend over 10 hours per day unsupervised is 0.005%.

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Less than 0.01% of rural 4-year-olds spend over 10 hours unsupervised per day based on mean, standard deviation, and normal distribution.

To find the percentage of children spending over 10 hours per day unsupervised, we can use the z-score formula to standardize the value and then find the area under the normal distribution curve.

The formula for the z-score is:

[tex]\[ z = \frac{x - \mu}{\sigma} \][/tex]

Where:

[tex]- \( x \) is the value we're interested in (10 hours per day)\\- \( \mu \) is the mean (3 hours per day)\\- \( \sigma \) is the standard deviation (1.8 hours)[/tex]

Let's calculate the z-score:

[tex]\[ z = \frac{10 - 3}{1.8} = \frac{7}{1.8} \approx 3.89 \][/tex]

Now, we'll find the area to the right of this z-score in the standard normal distribution table (or using a calculator). This represents the percentage of children spending over 10 hours per day unsupervised.

From the standard normal distribution table or calculator, a z-score of 3.89 corresponds to approximately 0.9999.

This means that approximately 99.99% of the children spend less than 10 hours per day unsupervised.

However, if you're looking for the percentage of children spending over 10 hours per day unsupervised, you'd subtract this from 100%:

100% - 99.99% =approx 0.01%

So, only about 0.01% of the children spend over 10 hours per day unsupervised.

calculate the slopes

3-0 / -2 - 2 = 3/-4 = -3/4

3 - -4 / -2 - -1 = 7/-1 = -7/1

0 - -4 / 2 - -1 = 4/3

-3/4 and 4/3 are negative reciprocals so this is a right triangle

Answer is A