An Algebra II textbook manufacturer determines that its profit, in thousands of dollars, can be modeled by the following function, where x represents the number of Algebra II textbooks sold, in hundreds.



Use a table of values to determine which of the following graphs represents the given situation.

The required, expression -7 + 24i with the form a + bi, we can see that the value of b is 24.

To find the value of b in the expression (3 + 4i)^2, we can simply expand the expression and identify the coefficient of the imaginary part.

(3 + 4i)² = (3 + 4i)(3 + 4i)

Using the FOIL method, we can multiply the terms:

= 3 * 3 + 3 * 4i + 4i * 3 + 4i * 4i

= 9 + 12i + 12i + 16i²

Since i² is defined as -1, we can substitute it:

= 9 + 12i + 12i - 16

= -7 + 24i

Comparing the expression -7 + 24i with the form a + bi, we can see that the value of b is 24.

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Complete question:

(3+4i)²

if the expression above is written in the form a+ bi, where a and b are real numbers, what is the value of b?

To solve the system of equations:

4x - 4y = 24

x - 4y = 3

Multiply the second equation by 4 to get 4x - 16y = 12.

Subtract the first equation from the new equation to eliminate x:

(4x - 16y) - (4x - 4y) = 12 - 24

-12y = -12

Solve for y:

y = 1

Substitute y = 1 into one of the original equations (e.g., x - 4y = 3) to find x:

x - 4(1) = 3

x = 7

Check the solution by substituting x = 7 and y = 1 into both original equations:

4x - 4y = 24 --> 4(7) - 4(1) = 24 (true)

x - 4y = 3 --> 7 - 4(1) = 3 (true)

Therefore, the solution to the system of equations is x = 7 and y = 1.

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Complete question is

solve the system of equations:

4x - 4y = 24

x - 4y = 3

The number of numbers in the sequence is k/2.

The sequence starts with k/2, then k/4, then k/6, and so on. Since k is an odd number, the sequence will stop when we reach 0. Therefore, the number of numbers in the sequence is k/2.

The number of pairs of real numbers in the sequence is k/4.

This is because for every number in the sequence, there is a corresponding number that is its negative. For example, if k = 1, then the sequence is 1/2, -1/2, 1/4, -1/4, and so on. There are k/4 numbers in the sequence, and half of them are positive and half of them are negative.

The sum of the first and last value in the sequence is k/2.

This is because the first value in the sequence is k/2, and the last value in the sequence is -k/2. Since k is an odd number, k/2 is not equal to -k/2. Therefore, the sum of the first and last value in the sequence is k/2.

The summation is equal to 0.

This is because the terms of the summation cancel each other out. For example, if k = 1, then the summation is 1/2 - 1/2 + 1/4 - 1/4 + ... = 0.

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The number of arrangements is 277,695,360

Permutations refer to the number of ways in which a set of distinct objects can be arranged or ordered. In other words, permutations are arrangements of objects where the order matters.

Combinations refer to the number of ways in which a subset of objects can be selected from a larger set of objects. Combinations do not consider the order of the selected objects.

Here we have

Arrangements of length 12 formed by different letters (no repetition) chosen from the 26-letter alphabet are there that contain the five vowels (a,e,i,o,u)

First, choose the positions for the five vowels in \($\binom{12}{5}$\) ways.

Then, we need to fill the remaining 7 positions with the 21 consonants, which we can do in \($21^7$\)

Therefore,

The total number of arrangements that contain the five vowels is:

=> \($\binom{12}{5}$\) ×  \($21^7$\) = 277,695,360

Note that this assumes that the five vowels are the only vowels allowed in the arrangement.

If the arrangement can have additional repetitions of the vowels, we would need to adjust the calculation accordingly.

Therefore,

The number of arrangements is 277,695,360

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To test the claim that there is no preference for raincoat color, we can use a chi-squared goodness-of-fit test.

First, we need to set up the null and alternative hypotheses:

Null hypothesis (H0): There is no preference for raincoat color.

Alternative hypothesis (Ha): There is a preference for raincoat color.

Next, we calculate the expected frequencies under the assumption of no preference. The expected frequency for each color can be calculated as (total number of sales / total number of colors).

Expected frequencies:

Yellow: (64 / 4) = 16

Red: (64 / 4) = 16

Green: (64 / 4) = 16

Blue: (64 / 4) = 16

Now we can calculate the chi-squared test statistic:

χ² = Σ((Observed frequency - Expected frequency)² / Expected frequency)

Using the observed frequencies given, we calculate the test statistic to be:

χ² = [(17-16)²/16] + [(20-16)²/16] + [(15-16)²/16] + [(12-16)²/16] = 1.375

Degrees of freedom (df) = number of categories - 1 = 4 - 1 = 3

Using the chi-squared distribution with df = 3, we find the p-value associated with the test statistic of 1.375.

Looking up the p-value in the chi-squared distribution table or using a statistical software, we find that the p-value is approximately 0.275.

Therefore, the correct p-value, rounded to 3 significant decimal places, is 0.275.

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Answer:

20%

Step-by-step explanation:

65x=13

x=13/65

x=1/5

x=0.2

x=20%

Answer:

yes but no a statistical question is determined by requiring multiple data

Step-by-step explanation:

Answer:

well A statistical question is one that can be answered by collecting data and where there will be variability in that data. This is different from a question that anticipates a deterministic answer. For example, "How many minutes do 6th grade students typically spend on homework each week?" is a statistical question.

Step-by-step explanation:

mark braniliest pls

The true number sentence is the third option:

6.8*1.3 = 8.84

Here we have number sentences of the form:

A*B = C

This is true only when the value of the product A*B is equal to the value of C.

One key thing to identify the correct one is remembering the rule of signs:

(+)*(-) = (-)

(+)*(+) = (+)

(-)*(+) = (-)

(-)*(-) = (+).

The only option that meets that rule is:

6.8*1.3 = 8.84

Where the product of two positive numbers gives another positive number (and the equality is true) so we conclude that this number sentence is true.

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\(\huge \text{Hello there! :)}\)

Answer:

The algebraic expression is as followed:

Step-by-step explanation:

Given the following question:

If you have any doubts about my answer please let me know.

\(-Nature-\)

\(\huge \text{Thanks for choosing Brainly! :)}\)

The given algebraic expression '4-1/5(6x-3)= 7/3 +3x' is a linear equation in one variable. By solving the linear equation, the value of x is found to be 34/63.

When an algebraic expression has an equality sign, it is known to be an equation. An equation with a single variable is known as an equation in one variable.

The highest power of the variable is the degree of the equation, here the degree is 1, thus it's a linear equation in one variable.

The linear equation contains 2 parts; the left-hand side [LHS] and the right-hand side[RHS]. The linear equation is solved by bringing all the variables to one side and numerals to the other side.

Given,

4-1/5(6x-3)= 7/3 +3x

4-6x/5+3/5=7/3+3x

4+3/5-7/3=6x/5+3x

Taking LCM and solving,

(60+9-35)/15 = (15x+6x)/5

34/15=21x/5

34=3*21x

∴x=34/63

Thus the value of x is found to be 34/63.

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Answer:

7(100-1)

Step-by-step explanation:

That's it right there

The proportion of a normal distribution that is located between two z-scores can be calculated using a standard normal distribution table or a calculator with a normal distribution function.

For the given z-scores:

z = -1.64 and z = +1.64:

The area under the normal distribution curve between these two z-scores is the same as the area between z = 0 and z = +1.64 minus the area between z = 0 and z = -1.64. From a standard normal distribution table, the area between z = 0 and z = +1.64 is 0.4505, and the area between z = 0 and z = -1.64 is also 0.4505. Therefore, the area between z = -1.64 and z = +1.64 is:

0.4505 - 0.4505 = 0

So, there is no area between z = -1.64 and z = +1.64.

z = -1.96 and z = +1.96:

Using the same approach as above, the area under the normal distribution curve between these two z-scores is:

0.4750 - 0.4750 = 0

So, there is no area between z = -1.96 and z = +1.96.

z = -1.00 and z = +1.00:

Again, using the same approach, the area under the normal distribution curve between these two z-scores is:

0.3413 - 0.3413 = 0

So, there is no area between z = -1.00 and z = +1.00.

Therefore, for all three cases, the proportion of a normal distribution that is located between the given z-scores is 0.

To find the output using the numerical method, we perform the convolution operation by multiplying the corresponding samples of the input x[n]  = {1,2,3,2,1) and impulse response h[n]  = {1,2,3,2,1}  , and summing the results.

The numerical method involves directly calculating the convolution algebraically.

a) For x[n] = {1, 2, 3, 2, 1} and h[n] = {1, 2, 3, 2, 1}, we calculate the convolution:

y[n] = x[n] * h[n]

Using the numerical method:

y[0] = 11 + 22 + 33 + 22 + 11 = 17

y[1] = 12 + 23 + 32 + 21 = 14

y[2] = 13 + 22 + 31 = 10

y[3] = 12 + 21 = 4

y[4] = 1*1 = 1

Therefore, y[n] = {17, 14, 10, 4, 1}.

b) For x[n] = {1, 1, 1, 1, 1} and h[n] = {1, -1}, we perform the convolution:

y[n] = x[n] * h[n]

Using the numerical method:

y[0] = 11 = 1

y[1] = 1(-1) + 11 = 0

y[2] = 1(-1) + 11 = 0

y[3] = 1(-1) + 11 = 0

y[4] = 1(-1) + 1*1 = 0

Therefore, y[n] = {1, 0, 0, 0, 0}.

c) For x[n] = {1, 2, 1} and h[n] = {1, 0, 1}, we calculate the convolution:

y[n] = x[n] * h[n]

Using the numerical method:

y[0] = 11 = 1

y[1] = 10 + 21 = 2

y[2] = 11 + 20 + 11 = 2

Therefore, y[n] = {1, 2, 2}.

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Answer:

The 27 foot tall garage makes a 4.5 foot shadow.

The shadow is (4.5/27) = one sixth the garage height

So the building's shadow should be one sixth times 72 feet or

72 * (1/6) or 12 feet

Step-by-step explanation:

Given statement solution is :- The correlation coefficient between weight and spending is approximately 0.5.

To calculate the correlation coefficient (also known as the Pearson correlation coefficient), you need to follow these steps:

Calculate the mean (average) of both the weight and spending data.

Calculate the difference between each weight measurement and the mean weight.

Calculate the difference between each spending measurement and the mean spending.

Multiply each weight difference by the corresponding spending difference.

Calculate the square of each weight difference and spending difference.

Sum up all the products from step 4 and divide it by the square root of the product of the sum of squares from step 5 for both weight and spending.

Round the correlation coefficient to an appropriate number of decimal places.

Here's an example using sample data:

Weight (in pounds): 150, 160, 170, 180, 190

Spending (in dollars): 50, 60, 70, 80, 90

Step 1: Calculate the mean

Mean weight = (150 + 160 + 170 + 180 + 190) / 5 = 170

Mean spending = (50 + 60 + 70 + 80 + 90) / 5 = 70

Step 2: Calculate the difference from the mean

Weight differences: -20, -10, 0, 10, 20

Spending differences: -20, -10, 0, 10, 20

Step 3: Multiply the weight differences by the spending differences

Products: (-20)(-20), (-10)(-10), (0)(0), (10)(10), (20)(20) = 400, 100, 0, 100, 400

Step 4: Calculate the sum of the products

Sum of products = 400 + 100 + 0 + 100 + 400 = 1000

Step 5: Calculate the sum of squares for both weight and spending differences

Weight sum of squares: (\(-20)^2 + (-10)^2 + 0^2 + 10^2 + 20^2\)= 2000

Spending sum of squares: \((-20)^2 + (-10)^2 + 0^2 + 10^2 + 20^2\) = 2000

Step 6: Calculate the correlation coefficient

Correlation coefficient = Sum of products / (sqrt(weight sum of squares) * sqrt(spending sum of squares))

Correlation coefficient = 1000 / (sqrt(2000) * sqrt(2000)) = 1000 / (44.721 * 44.721) ≈ 1000 / 2000 = 0.5

Therefore, the correlation coefficient between weight and spending in this example is approximately 0.5.

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Since none of the 13 classmates had been given math homework between the original survey and Kelly's second survey, the sum of the values in the second data set is the same as the sum of the values in the original data set. Therefore, the change in the means can be determined without calculating the mean of either data set by considering the number of data points in each set.

Since both data sets have the same number of data points, the change in the means will be zero. This is because the mean is calculated by dividing the sum of the values by the number of data points, and since the sum of the values is the same in both data sets, the means will also be the same.

In other words, if the mean of the first data set is x, then the sum of the values in the first data set is 13x (since there are 13 classmates), and the sum of the values in the second data set is also 13x (since none of the values have changed). Therefore, the mean of the second data set will also be x, and the change in the means will be zero.

Answer:

  2123

Step-by-step explanation:

You want to know the amount paid to principal in the last payment of a loan for $9000 at an interest rate of 9%, paid annually over 5 years.

The amount of the payment due is found using the formula ...

  A = P(r/n)/(1 -(1 +r/n)^(-nt))

where P is the principal amount of the loan at annual rate r for t years with n payments per year.

The payments on this loan are ...

  A = 9000(0.09)/(1 -1.09^-5) ≈ 2313.83

After 4 payments the remaining principal balance is ...

  A = 9000·1.09^4 -2313.83(1.09^4 -1)/0.09 ≈ 2122.79

This remaining balance on the loan is the amount of principal in the last payment: $2123.

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Answer: the answer is C

Step-by-step explanation:

The recursive sequence is given by the relation a₁ = 1 and aₙ = -2aₙ₋₁ + 2

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁

Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Given data ,

Let the sequence be represented as A

Now , the value of A is

A = { 1 , 0 , 2 ... }

And , let the first term be a₁ = 1

Let the second term be a₂ = 0

So , the sequence is given by the relation

aₙ = -2aₙ₋₁ + 2

where the the next term is multiplying the previous term by -2 and then adding 2

Hence , the recursive relation is aₙ = -2aₙ₋₁ + 2

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Answer:

Stefan originally spent $120 because we can say 180 dollars(164+16), than they want 150 percent. so 180 x 1.5 =120, but he sold it for 180 dollars so he made an additonal 60 dollars. Hoped that helped.

Answer:

8

Step-by-step explanation:

Use the pythagorean theorem.

Answer:

C. 24

Step-by-step explanation:

The integer which represents the rise in temperature of 19° is -|19|

Positive, negative, and zero numbers all fall under the category of integers. The word "integer" is a Latin word that signifies "whole" or "intact." Therefore, fractions and decimals are not considered to be integers.

A number without a decimal or fractional element is known as an integer, which encompasses both positive and negative numbers, including zero. The following are some examples of integers: -5, 0, 1, 5, 8, 97, and 3,043. Z denotes a collection of integers,

hence the correct form is answered.

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The percent error of the measurement, to the nearest tenth of a percent, is 5.6.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

John measured a line to be 1.7 inches long.

The actual length of the line is 1.8 inches.

The amount of error = 1.8 - 1.7

The amount of error = 0.1

Let 1 - n be the required percentage of error.

Then applying the percentage formula,

1.8 x n /100 = 1.7

Applying cross multiplication,

we get,

1.8n = 170

n = 170/1.8

n = 94.4

So, 1 - n = 100 - 94.4 = 5.6

Therefore, the percentage is 5.6.

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The B option is correct.

Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.

Given

A number is -906,060.

The equivalent number of the given number.

We know the number is -906,060.

It can be represented as \(\rm -906,060 = -9.0606 \ times\ 10^5\).

Thus, the B option is correct.

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Given:

The inequality is 2x < 9

Required:

Find solution for inequality.

Explanation:

We will solve as

Answer:

Hence, answer is x < 4.5

Answer:

6

Step-by-step explanation:

Replace x with 1 and solve

Replace x with 2 and solve

Subtract the 2 solutions:

3^1 - 2 = 3-2 = 1

3 ^2 -2 = 9-2 = 7

7-1 = 6

Answer: 6

Answer:

42.57 inch

Step-by-step explanation:

Calculate area of square and area of 4 triangles and sum them up to get.

The linearized equation around its equilibrium position is given as;f(x) = -4.8(x - 1.39)

The given equation is x² + 2x* + 2x² - 12x + 10 = 0.

It needs to be linearized around its equilibrium position.

Linearizing the given equation around its equilibrium position x0, we have;

f(x) = f(x0) + f'(x0)(x - x0)

Where f(x) = x² + 2x* + 2x² - 12x + 10

The equilibrium position is the point where f(x) = 0.

Hence, f(x0) = 0.

Thus, x² + 2x* + 2x² - 12x + 10 = 0⇒ 3x² - 6x = -10⇒ x² - 2x + (2.33) = 0(x-1)² = 0.77x - 0.77 or

x = 1 + (0.77)/(2) or x = 1.39

Hence, the equilibrium position x0 = 1.39.

Substitute x0 = 1.39 in the equation and simplify to get f'(x0):

f(x) = x² + 2x* + 2x² - 12x + 10

f(x) = 3.84 - 8.34 + 10

f'(x0) = f'(1.39) = -4.8

Therefore, the linearized equation around its equilibrium position is given as;f(x) = -4.8(x - 1.39)

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Answer:

Choice C: Lauren is faster than Kevin, slower than Jeremy.

Step-by-step explanation:

Ok, so it directly says that Jeremy is going at y=12x, or 12 miles per hour. To find how fast Kevin is riding, take two points of the table and use the slope formula to get the speed(.

Slope Formula: (y2-y1) / (x2-x1)

So lets take the table plots (2, 22) and (4, 33) to do this.

(y2-y1) / (x2-x1)

(33-22) / (4-2)

(11) / (2)

The speed of Kevin is 5.5 miles by hour.

Then, it asks for how fast Lauren is going, saying she is twice as fast as Kevin. Therefore, simply do:

5.5 * 2 = 11 miles per hour

To get the third biker's speed.

Now, with all of the speeds of the bikers, we can now compare them. Here's a listing of their speeds to make things easier to compare:

Jeremy: 12 mph

Kevin: 5.5 mph

Lauren: 11 mph

From this, we can see that Lauren is the second fastest. She is slower than Jeremy but faster than Kevin. Therefore, the correct answer choice is C.