The given expression is
(4 + 3i) - (2 - i)
We would simplify the terms inside the parentheses. The negative sign(- 1) outside the second parentheses would be used to multiply each term inside. We have
4 + 3i + - 1 * 2 + - 1 * - i
4 + 3i - 2 + i
By collecting like terms, we have
4 - 2 + 3i + i
2 + 4i
Thus, the answer in a + bi form is
2 + 4i
Avery flipped a coin 24 times and recorded the results in the box below. Which of the following best describes the difference between the experimental and theoretical probability of flipping heads?Heads= h Tails= th, t, t, h, t, t, t, h, t, t, h, t, t, t, h, t, t, t, t, h, t, t, t, t.A. According to theoretical probability, Avery would have expected to land on heads ten more times than she did experimentally.B. According the theoretical probability, Avery would have expected to land on heads half as many times as she did experimentally.C. According to theoretical probability, Avery would have expected to land on heads twite as many times as she did experimentally.D. According to theoretical probability, Avery would have expected to land on heads 12 more times than she did experimentally.
In order to determine the best description, first count the number of times for heads h and tails t.
Based on the given information, the number of heads was h = 6 and the number of tails was t = 18.
The theoretical probability in this case results in a 50% of probability for both events, that is, for 24 times at which the coin was flipped, 12 would be tail and 12 would be head.
Then, based on the previous explanation, you can conclude that:
C. According to theoretical probability, Avery would have expected to land on heads twite as many times as she did experimentally.
For each value of y,determine whether it is a solution to y<7
Y < 7 indicates that any value below 7 is included
therefore, 5 is a solution, 12 is NOT a solution, 7 is NOT a solution and 4 is a solution.
8. Su, who is 5 feet tall, is standing at point D in the drawing. The top of her head is at point E. A tree yard is at point B with the top of the tree at point C. Su stands so her shadow meets the end of the t shadow at point A. What is the length of side BC? C С + E 5 ft А 8 ft D 24 ft A) 20 feet B 15 fut B C) 22 feet D) 18 feet
Explanation:
We would be applying similar triangles theorem.
If you check the image, there is a small triangle and a big triangle
For similar triangles, the ratio of the corresponding sides are equal.
Trianglke AEB is similar to triangle ECB
AD corresponds to AB
ED corresponds to CB
AD/AB = ED/CB
AD = 8 ft,
AB = AD + DB = 8+24 = 32
ED = 5 ft
CB = ?
Can you please check 3 and 4 to see if I did them right?
We are given the following linear equation:
[tex]5x+15=45[/tex]The following problem is an example of a situation that can be modeled using the given equation.
Hayle did some chores this week, she got 5 dollars for each chore she did. Her dad forgot to pay her some days and gave her $15 dollars for the missing days. If she has a total of $45 dollars. How many chores did Hayle do?. The number of chores is represented by the variable "x".
Can you help explain how to solve this for me?
SOLUTION:
[tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex][tex]\begin{gathered} d=\sqrt{(-4-8)^2+(5--6)^2} \\ d=\sqrt{-12^2+11^2} \\ d=\sqrt{265}=16.28 \end{gathered}[/tex]b.
[tex]\begin{gathered} m=\frac{x_2+x_1}{2},\frac{y_2+y_1}{2} \\ m=(\frac{-6+5}{2},\frac{-4+8}{2}) \\ m=(-\frac{1}{2},2) \end{gathered}[/tex]Allison stated that 48/90 is a terminating decimal equal to 0.53. Why is she true or why is she wrong.
Answer:
She was Wrong, because it is not a terminating decimal
Explanation:
Given the fraction;
[tex]\frac{48}{90}[/tex]Let us reduce the fraction to its least form, then convert it to decimal.
[tex]\frac{48}{90}=\frac{8}{15}[/tex]converting to decimal we have;
The decimal form of the given fraction is;
[tex]\begin{gathered} 0.533\ldots \\ =0.53\ldots \end{gathered}[/tex]Which is not a terminating decimal, because it has an unending, repeatitive decimal.
Therefore, she was Wrong, because it is not a terminating decimal
1 ptsQuestion 5Jane started jogging 5 miles from home, at a rate of 2 mph. Write the slope-intercept form of an equation for Jane's position relative to home.
Answer
[tex]y=2x+5[/tex]SOLUTION
Problem Statement
The question wants us to model the distance Jane is from her home given her initial starting point (5 miles from home) and her speed (2 mph)
Explanation
To solve the question, we simply need to model her jogging using the equation of a line.
The general equation of a line is given as:
[tex]\begin{gathered} y=mx+c \\ \text{where,} \\ m=\text{slope}=\text{this represents Jane's speed} \\ c=y-\text{intercept}=\text{this represents her initial position from her home} \\ x=\text{time taken for Jane to move} \\ y=\text{Jane's final position after moving for time, x} \end{gathered}[/tex]We have been told that her speed is 2 mph. Thus, m = 2. We have also been given her initial position from her house to be 5 miles.
Jane starts jogging 5 miles from her home, thus, her position relative to her home will continue to increase as she jogs on at 2 mph. Thus, c = 5 and NOT -5.
This means we can write the equation for her position is:
[tex]\begin{gathered} m=2,c=5 \\ \therefore y=2x+5 \end{gathered}[/tex]Final Answer
[tex]y=2x+5[/tex]In the figure, ABCD and EFGF are rectangle. ABCD and EFGH are similar.(a) If the length of AB is a cm, try to use a to Indicate the length of EF(b) Find the ratio of the areas of ABCD and EFGH.(English isn't my native language. Please correct me if I have any grammatical mistakes.)
Given:
BC = 3 cm, FG = 4 cm
Required: bLength of EF and ratio of areas
Explanation:
(a) Since the rectangles ABCD and EFGH are similar, the correponding angles are proportional. Hence
[tex]\frac{AB}{EF}=\frac{BC}{FG}[/tex]Plug the given values.
[tex]\frac{AB}{EF}=\frac{3}{4}[/tex]If AB = a cm, then
[tex]\begin{gathered} \frac{a}{EF}=\frac{3}{4} \\ EF=\frac{4a}{3} \end{gathered}[/tex](b) Ara of ABCD
[tex]\begin{gathered} =\text{ Length}\times\text{ Width} \\ =3a\text{ cm}^2 \end{gathered}[/tex]Area of EFGH
[tex]\begin{gathered} =\text{ Length}\times\text{ Width} \\ =4\times\frac{4a}{3} \\ =\frac{16a}{3}\text{ cm}^2 \end{gathered}[/tex]Ratio of areas
[tex]\begin{gathered} =3a:\frac{16a}{3} \\ =9:16 \end{gathered}[/tex]Final Answer: The ratio of areas of ABCD to EFGH is 916.
Help with this plsss !!!
The average rate of change of function f(x) over the interval 12 ≤ x ≤ 21 is 2/3
We use the formula of average rate of change of function over the interval [x1, x2],
r = [f(x2 - f(x1)]/ (x2 - x1)
We need to find the average rate of change of function f(x) over the interval 12 ≤ x ≤ 21
r = [f(21) - f(12)] / (21 - 12)
r = (31 - 25) / 9
r = 6/9
r = 2/3
Therefore, the average rate of change of function f(x) over the interval 12 ≤ x ≤ 21 is 2/3
Learn more about the average rate of change of function here:
https://brainly.com/question/23715190
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Solve for v.37+1=-2v-8v-4
It cost Kaylee $7.26 to send 66 text messages. How much does each text cost to send? On the double number line below, fill in the given values, then use multiplication or division to find the missing value. dollars o text messages Answer: $ Submit Answer
This situation is represented by the equation
[tex]7.26=66x[/tex]Where x is the cost for each text sent, to find it, clear x from the equation
[tex]\begin{gathered} 7.26=66x \\ \frac{7.26}{66}=x \\ 0.11=x \\ x=0.11 \end{gathered}[/tex]It costs $0.11 to send a text
can you please help me
AB = 3x + 4
BC = 7x + 9
AB + BC = AC
AC = 143
Let us add AB and BC then equate their sum by 143
[tex]AC=AB+BC=3x+4+7x+9=(3x+7x)+(4+9)[/tex]First, step add the like terms
[tex]AC=10x+13[/tex]Equate AC by its length 143
[tex]10x+13=143[/tex]Now we have an equation to solve it
To solve the equation let us move 13 from the left side to the right side by subtracting 13 from both sides
[tex]\begin{gathered} 10x+13-13=143-13 \\ 10x=130 \end{gathered}[/tex]To find x divide both sides by 10 to move 10 from the left side to the right side
[tex]\begin{gathered} \frac{10x}{10}=\frac{130}{10} \\ x=13 \end{gathered}[/tex]Now let us find AB and BC
Substitute x by 13 in each expression
AB = 3(13) + 4 = 39 + 4 = 43
BC = 7(13) + 9 = 91 + 9 = 100
The length of AB is 43 units
The length of BC is 100 units
Which is the graph of y = = where k is a constant?TO A.R०B.कOD. REE.
Step 1
Given;
[tex]\begin{gathered} y=\frac{k}{x} \\ where\text{ k is a constant.} \end{gathered}[/tex]Required; To find the graph of the function.
Step 2
Since the graph is that of a fraction it will be a graph that may have a discontinuity and the answer will be;
The graph below shows a company’s profit f(x) in dollars, depending on the price of goods x, in dollar’s, being sold by the company: Part A: What do the x-intercepts and maximum value of the graph represent in context of the disrobed situation?Part B: What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit for the company in the situation described?Part C: What is an approximate average rate of change of the graph from x=1 to x=3, and what does this rate represent in context of the described situation?
We will have the following:
Part A:
The x-intercepts represent the prices of the goods than wen sold represent no net gain or loss.
The maximum value represents the price at which there will be a maximum profit.
Part B:
We will have that the increasing and decreasing intervals are respectively:
[tex]I_{\text{increaing}}=(-\, \infty,3)[/tex][tex]I_{\text{decreasing}}=(3,\infty)[/tex]They tells us respectively that:
Increasing: The greater the price the greater the profit.
Decreasing: The greater the price the smaller the profit.
Part C:
We determine the equation of the parabola. We can see that it's vertex is located at (3, 120), we can also see that the parabola passes by the origin (0, 0); so:
[tex]f(x)=a(x-3)^2+120\Rightarrow0=a(0-3)^2+120[/tex][tex]\Rightarrow0=9a+120\Rightarrow9a=-120\Rightarrow a=-\frac{40}{3}[/tex]So, the equation that represents the parabola is:
[tex]f(x)=-\frac{40}{3}(x-3)^2+120[/tex]Then, we will determine the average rate of change as follows:
[tex]\text{average rate of change}=\frac{f(b)-f(a)}{b-a}[/tex]So:
[tex]\text{average rate of change}=\frac{(-40/3((3)-3)^2+120)-(-40/3((1)-3)^2+120)}{3-1}[/tex][tex]\text{average rate of change}=\frac{80}{3}\Rightarrow average\text{ rate of change}\approx26.67[/tex]So, the avereage rate of change for the graph from x = 1 to x = 3 is exactly 80/3, that is approximately 26.67.
Graph the function?Can you also make a chart or like try to edit onto the graph in the picture
For x = 0 , x = 2 and x = 1, we have the following values:
[tex]\begin{gathered} f(0)=2(\frac{1}{2})^0=2\cdot1=2 \\ f(2)=2(\frac{1}{2})^2=\frac{2}{4}=\frac{1}{2} \\ f(1)=2(\frac{1}{2})^1=\frac{2}{2}=1 \end{gathered}[/tex]thus, the graph would look like this taking these point as references:
A correlation cannot have the value:A) 0.0B) 0.4C) -1.01D) -0.5E) 0.99
The possible range of values for the correlation coefficient is -1.0 to 1.0. In other words, the values cannot exceed 1.0 or be less than -1.0. A correlation of -1.0 indicates a perfect negative correlation, and a correlation of 1.0 indicates a perfect positive correlation.
Therefore, the value that is not within the range -1.0 to 1.0 is -1.01
Answer: C)
consider all of the 4 digit numbers that can be made from the digits 0 to 9 (assume that the numbers cannot start with 0) . What is the probability of choosing a random number from this group that is less than or equal to 8000? Enter a fraction or round your answer to 4 decimal places, if necessary.
First, we need to determine the total amount of numbers fulfilling the conditions:
- 4 digits
- Not starting with 0
For the first digit, we have then 9 possible numbers: 1, 2, 3, 4, 5, 6, 7, 8 and 9.
For the second, third and fourth, we have 10 possible numbers 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
Then, to determine the amount of numbers available we just need to multiply the possibilities for each digit:
[tex]9\cdot10\cdot10\cdot10=9000[/tex]Then, randomly choosing one of the given numbers, we have 9000 possible outcomes. Those will be numbers from 1000 to 9999.
Now we just need to determine how many numbers among those 9000 are lower than or equal to 8000.
As the numbers start in 1000, we have 7001 cases where the randomly selected number is lower than or equal to 8000.
We obtain 7001 since 8000 - 1000 = 7000 but we need to consider also the number 1000.
The probability will be then:
[tex]\frac{7001}{9000}\approx0.7779[/tex]Could I please get help with this. I can’t seem to figure out the answers to each of the figures after multiple tries.
Explanation:
Two figures are congruent when they have the same size and shape and two figures are similar when they have the same shape but not necessarily the same size. In similar figures, the ratio of the corresponding sides is constant.
Answer:
Then, for each pair, we get:
Solve for the missing side lengths.V1045°A. Ou = 10/2, vV =10./33B. Ou-20v2, v =1033c. Ou = 20v2, v =10D. Ou = 10v2, v = 10
We have a right triangle, where we know that one of the angles (besides the right angle) has a measure of 45°.
Then, the other angle measure can be calculated as:
[tex]\begin{gathered} \alpha+45+90=180 \\ \alpha=180-90-45 \\ \alpha=45\degree \end{gathered}[/tex]Then, as the other angle measure is equal, we have an isosceles triangle.
Then, length v has to be equal to the side with length 10.
With the value of v we can calculate u with the Pythagorean theorem:
[tex]\begin{gathered} u^2=v^2+10^2 \\ u^2=10^2+10^2 \\ u^2=2\cdot10^2 \\ u=\sqrt[]{2}\cdot10 \\ u=10\sqrt[]{2} \end{gathered}[/tex]Answer: u = 10√2, v = 10
The box-and-whisker plot shows the ages of employees at a video store. What fraction of the employees are 20 years or older Ages of Employees + 16 + 18 + 28 + Age 14 20 22 24 26 30 32 34 About of the employees are 20 years or older.
Based on the given box-and-whisker plot. Consider that 20 years concides with the second quartile or median of the sample.
It means that one half of the employees at the video store are 20 years or older.
Hence, the fraction of such employees related to the total number of employess is 1/2.
[tex]( - 4x + 2y \leqslant 4 )(x + 4y \ \textgreater \ - 10)[/tex]how do I graph this
Given the system of inequalities
[tex]\begin{gathered} -4x+2y\leq4 \\ x+4y>-10 \end{gathered}[/tex]We start by getting the plot of one of these inequalities. Let's start on -4x + 2y ≤ 4. This equation can be rewritten as
[tex]\begin{gathered} 2y\leq4+4x \\ y\leq2+2x \end{gathered}[/tex]Initially, we consider the equation
[tex]y=2+2x[/tex]Plotting the equation, we have
Considering the values of these function at
[tex]y\leq2+2x[/tex]Let's use the same steps implemented above for the second inequality. We have
[tex]\begin{gathered} 4y>-10+x \\ y>\frac{x-10}{4} \end{gathered}[/tex]Plotting this we have,
The dashed line represents the values that are not included in the equation, as a present for inequalities with less than or greater than. The shaded region represents the solution
After plotting the two inequalities individually, we now superimpose the two graphs. We get
where the darker region represents the solution of the inequalities.
Complete the following: 1, Jabomplete the squares for each quadratic, list the center and radius, then graph each circle (a labeling its translated center: (a) r2 + 2x + y2 - 4y = 4 (c) 2x2 + 2y2 + 3x - 5y = 2 (e) r2 + y2 + 3x = 4 (g) x² + y2 + 4x = 0 (1) r² + y2 + 2mx - 2ny = 0 (b) x2 + y2 - 4x = 0 (d) x2 + y2 - 2x - 8y = 8 4x + 4y? - 16x + 24y = -27 (h) x + y? - 7y = 0 (i) x + y2 - 2ax + 2by = c Determine which of the following equations represents a circle with a real non-zero radiu a) r? + y + 10x = -30 (b) 3x2 + 3y? - 11x = -91 4x + 4y + 18-8y = -85 (d) 36x* + 36y- 36x + 48y = -16 the equation of the circle which accen 2 and is concentric
3x² + 3y² - 11x = -91
Divide through by 3
x² + y² - 11/3 x = -91/3
x² - 11/3 x + y² = -91/3
(x² - 11/3 x ) + y² = -91/3
[x² - 11/3 x +(-11/6)² ] + y² = -91/3 + (- 11/6)²
(x - 11/6)² + y² = -91/3 + 121 / 36
[tex](x-\frac{11}{6})^2+y^2=\frac{-1092+\text{ 121}}{36}[/tex][tex](x\text{ - }\frac{11}{6})^2+y^2=\frac{-971}{36}[/tex]Comparing this with (x-a)² + (y-b)² = r²
r² = -971/36
Taking the square root will give an immaginary number
The radius is NOT a real number
This equation does not have a real radius
What is an equation for each translation of y=|x|?1. 4 units up2. 7 units down
To find an equation for each translation, keep in mind this:
f(x); g(x)=f(x)+a, the function is translated a units up.
f(x); g(x)=f(x)-a, the function is translated a units down.
Use this information to find the equation for each translation.
4 units up - Add 4 units to the function:
[tex]y=\lvert x\rvert+4[/tex]7 units down - Substract 7 units to the function:
[tex]y=\lvert x\rvert-7[/tex]Those are the answers for each translation.
What is the length of the side of an equilateral triangle if the height is 9√3
An equilateral triangle is a triangle were all the sides have the same measurement, and all the angles are the same(60º).
The height of an equilateral triangle divides the triangle into two equal right triangles. The height represents the oposite side of the angle of 60º, and the hypotenuse has the length of the side of the equilateral triangle, if we find the hypotenuse we have our answer.
Using trigonometric relations on the right triangle, we can find the value for the hypotenuse. The ratio between the opposite side to an angle and the hypotenuse is equal to the sine of this angle. If we call the hypotenuse as h, we have the following relation
[tex]\sin (60^o)=\frac{9\sqrt[]{3}}{h}[/tex]The sine of 60º is a known value
[tex]\sin (60^o)=\frac{\sqrt[]{3}}{2}[/tex]Then, combining both expressions, we have
[tex]\frac{9\sqrt[]{3}}{h}=\frac{\sqrt[]{3}}{2}[/tex]Solving for h
[tex]\begin{gathered} \frac{9\sqrt[]{3}}{h}=\frac{\sqrt[]{3}}{2} \\ \frac{9}{h}=\frac{1}{2} \\ \frac{h}{9}=2 \\ h=18 \end{gathered}[/tex]The length of the side of an equilateral triangle if the height is 9√3 is equal to 18.
Graph the function. Label the vertex and axis of symmetry. 1. f(x)=(x-2)^2
We have the following:
Two trees are leaning on each other in the forest. One tree is 19 feet long and makes a 32° angle with the ground. The second tree is 16 feet long.What is the approximate angle, x, that the second tree makes with the ground?
39º
1) Considering what's been given we can sketch this out:
From these trees leaning on each other, we can visualize a triangle (in black).
2) So now, since we need to find the other angle, then we need to apply the Law of Sines to find out the missing angle:
[tex]\begin{gathered} \frac{a}{\sin(A)}=\frac{b}{\sin (B)} \\ \frac{16}{\sin(32)}=\frac{19}{\sin (X)} \\ 16\cdot\sin (x)=19\cdot\sin (32) \\ \frac{16\sin(X)}{16}=\frac{19\sin (32)}{16} \\ \sin (X)=\frac{19\sin(32)}{16} \\ \end{gathered}[/tex]As we need the measure of the angle, (not any leg) then we need to use the arcsine of that quotient:
[tex]\begin{gathered} X=\sin ^{-1}(\frac{19\cdot\sin (32)}{16}) \\ X=38.996\approx39 \end{gathered}[/tex]3) Hence, the approximate measure of that angle X is 39º
The diameter of a bicycle wheel is 26 inches. What is its circumference? (Round to the nearest inch.)
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Bicycle wheel:
diameter = 26 in
circumference = ?
Step 02:
Circumference
C = π d
C = π * (26 in) = 81.68 in
The answer is:
C = 82 in
Answer:
82 inches.
Step-by-step explanation:
diameter = 26 inches
radius = 13 inches
circumference = 2πr
π = 22÷7 or 3.142
... 2 × 22÷7 × 13 = 81.714
(to nearest inch) = 82inches.
How many men and women should the sample include. What were the steps you took to solve?
We are asked to determine the sample size to determine the difference in the proportion of men and women who own smartphones with a confidence of 99% and an error of no more than 0.03. If we assume that both samples are equal then we can use the following formula:
[tex]n=\frac{Z^2_{\frac{\alpha}{2}}}{2E^2}[/tex]Where Z is the confidence and E is the error. Replacing the values we get:
[tex]n=\frac{(0.99)^2}{2(0.03)^2}[/tex]Solving the operations we get:
[tex]n=544.5\cong545[/tex]Therefore, each sample of men and women should be of 545.
Write the slope of the line in slope-intercept form using y=mx+b
In order to find the equation for this line in the slope-intercept form, let's use two points of the line in the equation.
Using the points (-3, 3) and (0, -3), we have:
[tex]\begin{gathered} y=mx+b \\ (0,-3)\colon \\ -3=0\cdot m+b \\ b=-3 \\ \\ (-3,3)\colon \\ 3=-3m-3 \\ -3m=6 \\ m=-2 \end{gathered}[/tex]So the slope of this line is m = -2, the y-intercept is b = -3 and the equation is y = -2x - 3.
I struggle with word problems please helpYou are ordering a new home theater system that consists of a TV, surround sound system, and DVD player. You can choose from 6 different TVs, 8 types of surround sound systems, and 20 types of DVD players. How many different home theater systems can you build?
We are given the following :
• Number of different Tvs = 6
,• Number of different surround system = 8
,• Number of different Dvds = 20
In order to determine How many different home theater systems you can build: just multiply the items as follows :
=6*8*20 = 960 You can build 960 home theater systems.