6. You and a friend go to the store and purchase 3 candy bars that cost $0.84 each and 2 sodas that cost $1.80 each. You are going to split the cost. You pay for your half with a five dollar bill. How much change will you receive? Please SHOW your work.
A. $3.06
B. $1.60
C. $6.12
D. $1.94

Donte made the mistake of not applying the distributive property correctly for the expression 4(1 + 3i). So, correct option is A.

The distributive property states that when a number is multiplied by a sum of terms, it should be distributed to each term individually. In this case, the number 4 should be multiplied by both 1 and 3i.

However, Donte incorrectly multiplied only the real part, 4, with 1, resulting in 4, and did not multiply the imaginary part, 3i, by 4. This mistake led to an incorrect simplified expression.

The correct application of the distributive property would yield 4 multiplied by both 1 and 3i, resulting in 4 + 12i. Therefore, the correct simplified expression would be:

4(1 + 3i) - (8 - 5i) = 4 + 12i - 8 + 5i = -4 + 17i.

So, the mistake Donte made was not applying the distributive property correctly for 4(1 + 3i). So, correct option is A.

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Complete question is:

Donte simplified the expression below.

4 (1 + 3 i) minus (8 minus 5 i). 4 + 3 i minus 8 + 5 i. Negative 4 + 8 i.

What mistake did Donte make?

He did not apply the distributive property correctly for 4(1 + 3i).

He did not distribute the subtraction sign correctly for 8 – 5i.

He added the real number and coefficient of i in 4(1 + 3i).

He added the two complex numbers instead of subtracted.

Answer:

72 cm³

Step-by-step explanation:

Answer:

Lucas

Step-by-step explanation:

Katie's response would mean that no matter how many ants there are, there will only always be 6 legs, which is incorrect.

Lucas's response would mean that the number of ants would equal the total number of legs divided by 6, which is correct.

Answer:

b2 = 2A/h - b1

Step-by-step explanation:

A = 1/2h(b1+b2)

Multiply both sides by 2

2A = h(b1+b2)

Multiply both sides by 1/h

2A/h = b1+b2

Add -b1 to both sides

2A/h + -b1 = b2

The expression of  b2 in terms of A, h, and b1 is expressed as; b2 = 2A/h - b1

The area of a trapezoid is the half of the product of sum of its parallel sides to the height of that trapezoid (the distance between those parallel sides).

Thus, if we have:

Length of its parallel sides = 'a' and 'b' units respectively

Perpendicular distance between its parallel sides = 'h' units,

Then, we get:

\(A = \dfrac{1}{2}\times(a+b) \times h \: \rm unit^2\)

Given the formula for calculating the area of a trapezoid expressed as;

A = 1/2h(b1 + b2)

Multiply both sides by 2

2A = h(b1 + b2)

Multiply both sides by 1/h;

2A/h = b1 + b2

Add -b1 to both sides;

2A/h + -b1 = b2

Hence the expression of  b2 in terms of A, h, and b1 is expressed as 2A/h + -b1 = b2.

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Answer: yes, 34/6 converted into a mixed number is 5 2/3

Hope this helps..... Stay safe and have a Merry Christmas!!!!!!!!!!!! :D

I just wish i could get at least 25 friends by Christmas because my account got deleted yesterday..

Treatments: warning system frequencies Observational species: woodpeckers

In physics, frequency is the amount of waves that travel through a stationary spot in a unit of time as well as the amount of cycles or oscillations that a substance in periodic motion experiences in a unit of time.

The the wave's frequency is the overall number of pulses generated in one second. Frequency refers to the amount of waves measured each second. Here is an easy illustration: The cadence of the pulses would be 5 hertz (Hz), or 5 cycles each second, if five full waves are generated in one second.

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First, find the slope using the given points.

Slope formula: y2-y1/x2-x1

0-(-2)/4-(-4)

2/8

1/4

Second, find the y-intercept with the slope and one point.

-2 = 1/4/(-4) + b

-2 = -1 + b

-1 = b

Third, put everything we know into the equation.

y = 1/4x - 1

Best of Luck!

Answer:

substitute the values given,

= (2a + b) - (a - 2b)

= (2(x + 2y) + x - 2y) - (x + 2y - 2(x - 2y))

= (2x+4y+x-2y) - (x+2y-2x+4y)

= (3x+2y) - (-x+6y)

= 3x + 2y + x - 6y

= 4x - 4y

then,

(2a+b) - (a-2b) = 4x - 4y

The values of the six trigonometric functions of angle B are:

sin(B) = 0.5

cos(B) = 0.9

tan(B) = 0.6

csc(B) = 2

sec(B) = 1.1

cot(B) = 1.7

To find the values of the six trigonometric functions of angle B, we need to use the coordinates of the point (13, 6).

Given that the terminal side of angle B passes through the point (13, 6), we can calculate the values of the trigonometric functions as follows:

sin(B) = y / r

= 6 / √(13^2 + 6^2)

= 0.5

cos(B) = x / r

= 13 / √(13^2 + 6^2)

= 0.9

tan(B) = y / x

= 6 / 13

= 0.6

csc(B) = 1 / sin(B)

= 1 / 0.5

= 2

sec(B) = 1 / cos(B)

= 1 / 0.9

= 1.1

cot(B) = 1 / tan(B)

= 1 / 0.6

= 1.7

Therefore, the values of the six trigonometric functions of angle B are:

sin(B) = 0.5

cos(B) = 0.9

tan(B) = 0.6

csc(B) = 2

sec(B) = 1.1

cot(B) = 1.7

The values of the six trigonometric functions of angle B, where the terminal side passes through the point (13, 6), are given as above

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Answer:

Step-by-step explanation:

Angle measures should be ordered in same way as the opposite sides.

Sides in the ascending order:

Their opposite angles in same order:

Correct choice is B

Answers:

-3.5 < 5

|-3.5| < |5|

============================================

Explanation:

Any negative number is always smaller than any positive number. So that's why -3.5 is smaller than 5 and where -3.5 < 5 comes from. It might help to set up a vertical number line. Stuff on top is larger than stuff down below.

---------

The vertical bars represent absolute value. The result of |-3.5| is 3.5 because this is the distance from -3.5 to 0 on the number line. Likewise, |5| = 5.

So that's how we get to |-3.5| < |5| which is effectively saying -3.5 is closer to zero than 5 is to zero.

In a group of 150 students, 20 are freshmen 30 are sophomores 49 are juniors and 51 are seniors if a student is randomly selected the probability that we select a sophomore before freshmen is 2.69%.

So the given data we get from the question is as follows,

  Total number of students, N = 150

  A number of freshmen students, F = 20

  The number of sophomore students, S = 30

  Number of junior students, J = 49

  Number of senior students, R = 51

              We need to find the probability of selecting a sophomore student before a freshman student. The probability that a sophomore student is selected first,

             P(S) = Number of sophomore students/Total number of students

                    = S/N

   Probability that a freshman student is selected after a sophomore student,

          P(F|S) = Number of freshman students left/Total number of students left

                    = F/N-1

    Where N-1 is used because one student has already been selected.

     The probability that a sophomore student is selected first and then a freshman student is selected,

       P(S∩F) = P(S) × P(F|S)

                   = S/N × F/N-1

      Therefore, the probability of selecting a sophomore student before a freshman student is:

       P(S∩F) = S/N × F/N-1P(S∩F)

                   = 30/150 × 20/149P(S∩

                   = 0.0269 or 2.69%

      Therefore, the probability of selecting a sophomore student before a freshman student is 0.0269 or 2.69%.

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Answer:

44

Step-by-step explanation:

11*4=44

Answer:

44

Step-by-step explanation:

4 times 11 is 44 anything times 1 equal that number for example 4 time 1 equals 4 so 11 is just two ones therefore its like 4 times 1 twice so 44

Answer:

I may be wrong, but I believe the answer is $200.

The change in consumer price index from the year 2000 to 2007 in percentage is 0.333%

Given, In the year 2000  the consumer price index of dairy products was 160.7

and In the year 2007 it was 194,0

we are asked to determine the change in consumer price index from the year 2000 to 2007.

Calculate the difference in the product prices.

consumer product price in 2000 = 160.7

consumer product price in 2007 = 194.0

difference in the consumer product prices = 194.0 - 160.7

= 33.3

convert it into percentage.

= 33.3/100

= 0.333%

Hence the change in consumer price index is 0.333%.

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Answer:

x = 14

Step-by-step explanation:

10x-30+5x = 180

Combine like terms

* 15x-30 = 180

Add 30 from both sides

* 15x 30+-30 = 180+30

Divide 15 both sides

* 15x/15x = 210/15x

x = 14

Hope this helps :)

Answer:

2x + 3

Step-by-step explanation:

you add the like terms

hope this helps

Answer:

Step-by-step explanation:

Parallel lines have the same slope.

The slope-intercept form of an equation of a line:

y = mx + b

m - slope

b - y-intercept

The point-slope form of an equation of a line:

y - y₁ = m(x - x₁)

(x₁, y₁) - point on a line

m - slope

We have the line y - 9 = 7(x + 5). The slope m = 7.

A) y - 9 = 3x + 4 → m = 3

B) y = -9x - 5 → m = -9

C) y + 5 = 7(x - 9) → m = 7

D) y - 9 = 5(x + 4) → m = 5

The line C) y + 5 = 7(x - 9) has the same slope.

Mei will have written a total of 430 pages at the end of the 30 days.

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Step-by-step explanation:

handshakes are there

⁷C2

Answer:

1 group of 7

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

You would add 14 and 8.    

22-8=14

Check it on your calculator

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Answer:

x = 22

Step-by-step explanation:

Solving for x means having x alone on the left side as in

x = some number

Since 8 is being subtracted from x on the left side, you need to do the opposite operation of subtracting 8. The opposite operation of subtraction is addition. That means you need to add 8 to the left side to get rid of the subtraction of 8. The rule with equations is that you must do the same operation to both sides of the equation. Therefore, you need to add 8 to both sides of the equation.

x - 8 = 14

Add 8 to both sides.

x - 8 + 8 = 14 + 8

On the left side, -8 + 8 = 0, so you end up with just x.

On the right side, 14 + 8 = 22, so you end up with 22.

x = 22

Answer: x = 22

Answer:

4 + b² = 104

Hope this helps. :)

Answer:

b^{2}  + 4 = 104.

Step-by-step explanation:

The sum of 4 and the second power of b basically means 4 + b^2.

b^2 + 4 = 104

\(b^{2} + 4 = 104\)

b^2 = 100

b = plus or minus 10.

Hope this helps!

Since Tony is self-employed, he will have to pay all of the tax himself.

Take his adjusted earnings times the tax rate

58238.74 * 2.9%

58238.74 * .029

1688.92346

Rounding to the nearest cent

1688.92

The researchers are investigating the perception of three-dimensional shapes on computer screens and specifically examining the components of a square figure or cube necessary for viewers to perceive details of the shape. They vary the stimuli to include fully rendered cubes, cubes with incomplete sides, and cubes with missing corner information. Four participants are recruited for an intense study, and their accuracy rates are measured across the three figure conditions. The trials are presented in different orders for each participant using a random-numbers table to determine unique sequences.

In this study, the researchers are interested in understanding how viewers perceive details of three-dimensional shapes on computer screens. They manipulate the stimuli by presenting fully rendered cubes, cubes with incomplete sides, and cubes with missing corner information. By varying these components, the researchers aim to identify which elements are necessary for viewers to accurately perceive the shape.

Four participants are recruited for an intense study, indicating a small sample size. While a larger sample size would generally be preferred for generalizability, intense studies often involve fewer participants due to the time and resource constraints associated with conducting a large number of trials. This approach allows for in-depth analysis of individual participant performance.

The participants are trained on how to detect subtle deformations in the shapes, which suggests that the study aims to assess their ability to perceive and discriminate fine details. After the training, the participants' accuracy rates are measured across the three different figure conditions, likely reported as a percentage of correctly identified shape details.

To minimize potential biases, the trials are presented in different orders for each participant, using a random-numbers table to determine unique sequences. This randomization helps control for order effects, where the order of presenting stimuli can influence participants' responses.

The researchers in this study are investigating the perception of three-dimensional shapes on computer screens. By manipulating the components of square figures or cubes, they aim to determine which elements are necessary for viewers to perceive shape details accurately. The study involves four participants, an intense study design, and measures accuracy rates across different figure conditions. The use of randomization in trial presentation helps mitigate potential order effects.

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Answer:

What least number should be added to 15871 to make it a perfect Square

The range of graph is {y | -2 < y < 2}.

The y-axis on a graph represents the possible output values, or range. Remember that the domain and range of the graph may be larger than the values seen if the graph extends beyond the area that is visible.

Given:

y = ∛(x - 1)

and, reflection and translation  y = ∛x

Then, Reflection across the x-axis is accomplished by negating the output of the function. That is, ∛x has been transformed to -∛(x-1).

So, y∈ [-2, 2)

Hence, the range is {y | -2 < y < 2}

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Answer:

Hey there!

That would result in 0.00735.

Let me know if this helps :)

Hence, the significant figures are \(0.00735.\)

What is the approximation?

An approximation is anything that is similar, but not exactly equal, to something else. A number can be approximated by rounding. A calculation can be approximated by rounding the values within it before performing the operations.

Here given that,

Approximate \(0.007349\) to  significant figures​

So, the significant figures are \(0.00735.\)

Hence, the significant figures are \(0.00735.\)

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The total number of visitors to the zoo that day=3980.

Given:

cost of each ticket for an adult=$25

cost of each ticket for an adult=$10

Total ticket sales one day=$47,750.

⇒$25+$10=47,750

⇒25+10=47,750-----(1)

Also,

c=6a+270

6a-c=-270------(2)

multiplying eq(2) with 10 we get:

60a-10c=-2700----(3)

Adding eq(1) and eq(3) we get

25a+10c=47,750

60a-10c=-2700

--------------------------

85a=45050

--------------------

To calculate a value just divide 45050 by 85 we get

a=45050/85

a=530

Now to get the value of c substitutes a value.

c=60(530)+270

c=3450

Number of Adult visitors=530

Number of children visitors=3450

Total Number of visitors=3980.

Therefore, the total number of visitors to the zoo that day=3980.

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Answer:

No real solutions

Step-by-step explanation:

Distribute the -3

-3x - 9 = -3x -3 -5

-3x - 9 = -3x - 8

add 3x to both sides

-9 = -8

makes it no real solution

Answer:

A. \(\frac{17}{10}\)

Step-by-step explanation:

The square root of three is 1.73205080757. A is the closest because \(\frac{17}{10}=1.7\).