Answer:
-4 +9i
Step-by-step explanation:
complex number in standard form.
(-2+6i)-(2-3i)=
Combine like terms
-2 -2 +6i +3i
Standard form is a+bi
-4 +9i
A quality control expert at glow tech computers wants to test their new monitors . The production manager claims that have a mean life of 93 months with the standard deviation of nine months. If the claim is true what is the probability that the mean monitor life will be greater than 91.4 months and a sample of 66 monitors? Round your answers to four decimal places
Given the following parameter:
[tex]\begin{gathered} \mu=93 \\ \sigma=9 \\ \bar{x}=91.4 \\ n=66 \end{gathered}[/tex]Using z-score formula
[tex]z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]Substitute the parameter provided in the formula above
[tex]z=\frac{91.4-93}{\frac{9}{\sqrt{66}}}[/tex][tex]z=-1.4443[/tex]The probability that the mean monitor life will be greater than 91.4 is given as
[tex]\begin{gathered} P(z>-1.4443)=P(0\leq z)+P(0-1.4443)=0.5+0.4257 \\ P(z>-1.4443)=0.9257 \end{gathered}[/tex]Hence, the probability that the mean monitor life will be greater than 91.4 months is 0.9257
which of the following is true?Blaine and Cruz made an error in picking their first steps.Cruz made and error in picking his first step All three made an error because the right side equals -1.All three chose a valid first step toward solving the equation.
Given data:
The given expression is 4/7 (7-n)=-1.
Aaron starts with multiplying 7/4 on both sides, Blaine starts with distributive property by multiplying 4/7 with 7 and -u, Cruz starts by dividiing 4/7 on both sides.
Thus, all of them are correct, correct option is last one.
Answer: d
Step-by-step explanation: yw
15. Given f (n)=3( 12), what is the value off (8) ?
We have some function f(x) and want to evaluate the function for some value of x, in this case for x=8.
Evaluate a function means replace the x for the value you want to evaluate, in this case for 8, so:
[tex]\begin{gathered} f(x)=3(1-x) \\ f(8)=f(x=8)=3(1-8) \\ f(8)=3\cdot(-7)=-21 \end{gathered}[/tex]Factor the polynomial and use the factored form to find the zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)
P(x) = x3 − 2x2 − 15x
x =
Answer:
-3, 0, 5
Step-by-step explanation:
You want the zeros of P(x) = x³ − 2x² − 15x using the factored form.
Factored formWe notice right away that x is a factor of every term. Factoring that out gives us a quadratic to factor:
P(x) = x(x² -2x -15)
To factor this, we need two factors of -15 that have a sum of -2. The factors -5 and +3 have those properties. That means our factored form is ...
P(x) = x(x +3)(x -5) . . . . factored form
ZerosThis product will be zero when any of its factors is zero. Considering them one at a time, we find the zeros of P(x) to be ...
x = 0
x +3 = 0 ⇒ x = -3
x -5 = 0 ⇒ x = 5
The zeros of P(x) are -3, 0, 5.
Which ordered pair is in the solution set fit the system of inequalities shown below?2x-y<3x+2y>-1A. (-2,-1)B. (0,1)C. (1,-2)D.(6,1)
Given the System of Inequalities:
[tex]\begin{cases}2x-y<3 \\ x+2y>-1\end{cases}[/tex]1. Take the first inequality and solve for "y":
[tex]\begin{gathered} -y<2x+3 \\ (-1)(-y)<(-2x+3)(-1) \\ y>2x-3 \\ \end{gathered}[/tex]Notice that direction of the symbol changes, because you had to multiply both sides of the inequality by a negative number.
Now you can identify that the boundary line is:
[tex]y=2x-3[/tex]Since it is written in Slope-Intercept Form, you can identify that its slope is:
[tex]m_1=2[/tex]And its y-intercept is:
[tex]b_1=-3[/tex]Notice that the symbol of the inequality is:
[tex]>[/tex]That indicates that the line is dashed and the shaded region is above the line.
Knowing all this information, you can graph the first inequality on the Coordinate Plane.
2. Apply the same procedure to graph the second inequality. Solving for "y", you get:
[tex]\begin{gathered} 2y>-x-1 \\ \\ y>-\frac{1}{2}x-\frac{1}{2} \end{gathered}[/tex]Notice that the boundary line is:
[tex]y=-\frac{1}{2}x-\frac{1}{2}[/tex]Where:
[tex]\begin{gathered} m_2=-\frac{1}{2} \\ \\ b_2=-\frac{1}{2} \end{gathered}[/tex]Since the symbol is:
[tex]>[/tex]The line is dashed and the shaded region is above the line.
Knowing this, you can graph the second inequality.
3. Look at the graph of the System of Inequalities:
Notice that:
-The black line is the boundary line of the first inequality and the green line is the boundary line of the second inequality.
- The solution of the system is the intersection region. It is the region where the shaded region of the first inequality and the shaded region of the second inequality, intersect.
4. Plot the points given in the options on the graph of the Systems:
5. You can identify that this point is in the intersection region:
[tex](0,1)[/tex]Therefore, it is a solution.
Hence, the answer is: Option B.
Solve.(3.3 × 10³) (2 × 10²)
Here are the steps in multiplying scientific notations:
1. Multiply the coefficients first.
[tex]3.3\times2=6.6[/tex]2. Multiply the base 10 by adding their exponents.
[tex]10^3\times10^2=10^{3+2}=10^5[/tex]3. Connect the result in steps 1 and 2 by the symbol for multiplication.
[tex]6.6\times10^5[/tex]Hence, the result is 6.6 x 10⁵.
What does "equidistant” mean in relation to parallel lines?O The two lines lie in the same plane.The two lines have the same distance between them.The two lines go infinitely.The two lines have an infinite number of points.
we have that
parallel lines (lines that never intersect) are equidistant in the sense that the distance of any point on one line from the nearest point on the other line is the same for all points.
therefore
the answer is
The two lines have the same distance between them.create a model for (x + 7)(2x - 6). What is the product
Find the missing quantity with the information given. Round rates to the nearest whole percent and dollar amounts to the nearest cent
Given:
Original Price $4.50
Markdown=$1.30
[tex]\begin{gathered} \text{ \% Markdown=}\frac{1.30}{4.50}\times100 \\ \text{ \% Markdown=}28.89\text{ \%} \end{gathered}[/tex]A point is chosen at random in the square shown below. Find the probability that the point is in the shaded circular region. Each side of the square is 6in, and the radius of the circle is 3in.Use the value 3.14 for π. Round your answer to the nearest hundredth.
We will have the following:
First, we determine the area of the square and of the shaded region, that is:
[tex]\begin{gathered} A_s=6in^2\Rightarrow A_s=36in^2 \\ \\ A_c=\pi(3)^2\Rightarrow A_c=9\pi in^2 \end{gathered}[/tex]Now, we will have that the probability will be of:
[tex]P=\frac{9\pi}{36}\Rightarrow P=\frac{\pi}{4}\Rightarrow P\approx0.79[/tex]So, the probability is approximately 79%.
3. Find the value of the function h(x) = 2 when x = 10=
In order to find the value of h(x) when x=10, we replace the value of x along with the function by 10, however, since there are not any variables the function is constant for all variables
[tex]h(10)=2[/tex]x Michael uses synthetic division to divide f(x) by g(x), his last line of work 0/3is shown. How would he write his answer of f(x) divided by g(x). *7 0 24 0 0
It's important to know that synthetic division gives a polynomial as a result.
Michael obtained 7 0 24 0 0. We just need to add variables to it. As you can observe, there are 5 terms, that means the polynomial is grade 4.
[tex]7x^4+0x^3+24x^2+0x+0[/tex]Therefore, the resulting polynomial is
[tex]7x^4+24x^2[/tex]WILL GIVE BRAINLYEST 200 PO9NTS SENCE IM GIVING EXTRA
The range of the data set increased by 12 and the median of the data set is at 50.
Range of a Data SetThe Range of a data set is the difference between the lowest and highest values.
The range is the difference between the smallest and highest numbers in a list or set. To find the range, first put all the numbers in order. Then subtract (take away) the lowest number from the highest. The answer gives you the range of the list.
The given data set is;
15, 17, 19, 19, 22, 23, 25, 27, 32, 34
The range of this data set will be
range = 34 - 15 = 19.
Assuming we add another age of 46, the range will become
range = 46 - 15 = 31
This will impact the range of the data by 31 - 19 = 12.
The range will be impacted by an increase with 12.
Median of a Data SetThe median is the value that's exactly in the middle of a dataset when it is ordered. It's a measure of central tendency that separates the lowest 50% from the highest 50% of values. The steps for finding the median differ depending on whether you have an odd or an even number of data points.
The data set given is
48, 63, 75, 40, 32, 52, 35, 68, 83, 40
We have to rearrange the data points first before finding the median;
32, 35, 40, 40, 48, 52, 63, 68, 75, 83.
The median of the data set will be the average between 48 and 52 which is 50.
the median of the data is 50.
Learn more on range and median of a data set here;
https://brainly.com/question/3514929
#SPJ1
Jelani filled an aquarium with blocks that were each one cubic foot in size. He filled the bottom layer of the aquarium with 21 blocks. He then stacked three more blocks on top of the bottom layer. The partially filled aquarium is shown below. What is the total volume, in cubic feet, of the aquarium?
Answer:
The total volume of the aquarium is;
[tex]84\text{ }ft^3[/tex]Explanation:
Given the figure in the attached image.
The bottom of the aquarium was covered with 21 blocks with 1 cubic foot each.
Each face of the cubic blocks will have a surface area of 1 square foot each.
So, the surface area of the base of the aquarium will be;
[tex]\begin{gathered} A=21\times1ft^2 \\ A=21\text{ }ft^2 \end{gathered}[/tex]Recall that volume equals base area multiply by the height of the aquarium;
[tex]V=A\times h[/tex]From the figure, the height of the aquarium requires 4 blocks, which makes the height 4 ft;
[tex]h=4ft[/tex]So, we can now substitute the values of the height and the base area to calculate the total volume of the aquarium;
[tex]\begin{gathered} V=A\times h \\ V=21ft^2\times4ft \\ V=84\text{ }ft^3 \end{gathered}[/tex]Therefore, the total volume of the aquarium is;
[tex]84\text{ }ft^3[/tex]Nikolas bought a Falcon's ticket for $80. The sales tax on the ticket is 7%. How much was the tax?
ok
100% ---------------------------- $80
7% ---------------------------- x
x = (80 x 7)/100
x = 560/100
x = 5.6
The tax was of $5.6
quick!! will give brainliest!! Given g(x) = -x + 3, solve for a when g(2) = -1
We have the following:
[tex]g(x)=-x+3[/tex]replacing when x is 2:
[tex]g(2)=-2+3=1[/tex]which statement is true
We have to analyze the given options to solve this problem.
Option 1.
The absolute value of -12 is larger than the absolute value of 12.
The absolute value is always a positive number:
[tex]undefined[/tex]7.5 is 15% of what number?
Let the number be x. So equation for x is,
[tex]\begin{gathered} \frac{15}{100}\cdot x=7.5 \\ x=\frac{7.5\cdot100}{15} \\ =\frac{750}{15} \\ =50 \end{gathered}[/tex]The number is 50.
Figure 2 is a scaled copy of Figure 1.B.Figure 1AsADMYColJFigure 2MYHKProIdentify the side in Figure 2 that corresponds to side BC in Figure 1.
Figure 1 was enlarged to figure 2
Hence the side |AB| is corresspounding to the side |PQ|
Nathan loved learning about earthquakes in science class. He told his brother that up until a 7.8-magnitude earthquake hit Nepal in 2015, Mount Everest had been moving northeast at a rate of 7.7×10^-6 centimeters per minute. What would be the most appropriate unit for Nathan to use instead of centimeters per minute?
The most appropriate unit for Nathan to use instead of centimeters per minute is centimeters per year.
What is an earthquake?An earthquake simply means a rapid motion of the solid layer of the Earth.
In this case, Nathan told his brother that up until a 7.8-magnitude earthquake hit Nepal in 2015, Mount Everest had been moving northeast at a rate of 7.7×10^-6 centimeters per minute.
Since the year is being discussed, the unit should be based on the year.
Learn more about earthquake on:
brainly.com/question/248561
#SPJ1
Write the coordinates of the vertices after a reflection over the line y=-x
The coordinates of the vertices after a reflection over the line y=-x are (y, -x)
How to determine the coordinates?From the question, the transformation rule is given as
Reflection over the line y=-x
There are four types of transformation,
These transformations are
DilationRotationReflectionTranslationEach of these transformations have their rule, and they are represented as
Reflection: reflection across linesDilation: k(x, y)Rotation: rotation by anglesTranslation: (x + h, y + k)So, we have
Reflection over the line y=-x
When represented as a coordinate, the coordinate is
(x, y) = (y, -x)
Hence, the coordinates are (y, -x)
Read more about transformation at
https://brainly.com/question/27224272
#SPJ1
The Oldest rocks on Earth are about 4 x 10^9 years old. For which of these ages could this be an approximation?
A. 3,862,100,000 years
B. 3.849999999x10^9 years
C. 0.000000004 years
D.4,149,000,000 years
E.3.45x10^9 years
ax-5y = -2
3x+4y = b
Consider the angle shown below with an initial ray pointing in the 3-o'clock direction that measures θ radians (where 0≤θ<2π). The circle's radius is 2 units long and the terminal point is (−1.79,−0.89).The terminal point is how many radius lenghts to the right of the circle's center?h= radii Then, cos−1(h)=Does the number we get in part (b) give us the correct value of θ? Therefore, θ=
Given the terminal point ( -1.79 , -0.89 )
So, the x- coordintes = -1.79
[tex]\begin{gathered} \theta=\cos ^{-1}h \\ \\ h=-\frac{1.79}{2} \\ \\ \theta=\cos ^{-1}(-\frac{1.79}{2})=206.5^o \end{gathered}[/tex]
In circle F with mZEFG = 30 and EF = 4 units, find the length of arc EG.. 4Round to the nearest hundredth.
The arc length can be found through the formula:
[tex]s=2\ast\pi\ast r\ast\frac{\theta}{360}[/tex]then, we can say that r is equal to 4 and the angle is 30°
[tex]\begin{gathered} s=2\ast\pi\ast4\ast\frac{30}{360} \\ s\approx2.09 \end{gathered}[/tex]Answer:
The arc length is approximately equal to 2.09
Solve the system of equation by the elimination method {1/3x+1/2y=1/2{1/6x-1/3y=5/6(x,y)=(_, _)
Solution
- The solution steps to solve the system of equations by elimination is given below:
[tex]\begin{gathered} \frac{x}{3}+\frac{y}{2}=\frac{1}{2}\text{ \lparen Equation 1\rparen} \\ \\ \frac{x}{6}-\frac{y}{3}=\frac{5}{6}\text{ \lparen Equation 2\rparen} \\ \\ \text{ Multiply Equation 2 by 2} \\ 2\times(\frac{x}{6}-\frac{y}{3})=\frac{5}{6}\times2 \\ \\ \frac{x}{3}-\frac{2y}{3}=\frac{5}{3}\text{ \lparen Equation 3\rparen} \\ \\ \\ \text{ Now, }\frac{x}{3}\text{ is common to both Equations 1 and 3.} \\ \\ \text{ We can therefore subtract both equations to eliminate }x. \\ \text{ We have:} \\ \text{ Equation 1 }-\text{ Equation 3} \\ \\ \frac{x}{3}+\frac{y}{2}-(\frac{x}{3}-\frac{2y}{3})=\frac{1}{2}-\frac{5}{3} \\ \\ \frac{x}{3}-\frac{x}{3}+\frac{y}{2}+\frac{2y}{3}=\frac{1}{2}-\frac{5}{3}=\frac{3}{6}-\frac{10}{6} \\ \\ \frac{y}{2}+\frac{2y}{3}=-\frac{7}{6} \\ \\ \frac{3y}{6}+\frac{4y}{6}=-\frac{7}{6} \\ \\ \frac{7y}{6}=-\frac{7}{6} \\ \\ \therefore y=-1 \\ \\ \text{ Substitute the value of }y\text{ into any of the equations, we have:} \\ \frac{1}{3}x+\frac{1}{2}y=\frac{1}{2} \\ \frac{1}{3}x+\frac{1}{2}(-1)=\frac{1}{2} \\ \\ \frac{1}{3}x=\frac{1}{2}+\frac{1}{2} \\ \\ \frac{1}{3}x=1 \\ \\ \therefore x=3 \end{gathered}[/tex]Final Answer
The answer is:
[tex]\begin{gathered} x=3,y=-1 \\ \\ \therefore(x,y)=(3,-1) \end{gathered}[/tex]Is this correct?
Or please provide an explanation.
Answer:
The answer selected is correct
Step-by-step explanation:
When talking about balance, having -X (being X in the negative) , means owing X.
Dylan owes $19.25
Elise owes $42.75
Francesca owes $23
Jamaal owes $35.50
So naturally, Dylan owes the least.
please try to answer quickly my brainly app keeps crashing
From the figure, the radius of the sphere is:
[tex]r=1\text{ in}[/tex]The volume of the sphere is given by the formula:
[tex]V=\frac{4}{3}\pi r³[/tex]Using the value of the radius:
[tex]\begin{gathered} V=\frac{4}{3}\pi(1)³ \\ \\ \therefore V=\frac{4\pi}{3}\text{ in^^b3} \end{gathered}[/tex]Approximating to the nearest cubic inch:
[tex]\therefore V\approx4\text{ in^^b3}[/tex]ther
How many terms do you have in the expression 7x - 2y + 8?
Answer:
3 terms we have constant ,Y and X terms
The numbers of regular season wins for 10 football teams in a given season are given below. Determine the range, mean, variance, and standard deviation of the population data set.2, 10, 15, 4. 14. 7. 14, 8, 2, 10The range is(Simplify your answer.)The population mean is(Simplify your answer. Round to the nearest tenth as needed.)The population variance is I(Simplify your answer. Round to the nearest tenth as needed.)The population standard deviation is(Simplify your answer. Round to the nearest tenth as needed)Enter your answer in each of the answer boxes.
The numbers of regular-season wins for 10 football teams in a given season are given below
[tex]2,10,15,4,14,7,14,8,2,10[/tex]We are asked to find the range, mean, variance, and standard deviation of the population data set.
Range:
The range is the difference between the maximum value and the minimum value in a data set.
From the given data set,
Maximum value = 15
Minimum value = 2
[tex]\begin{gathered} \text{Range}=\text{maximum}-\text{minimum} \\ \text{Range}=15-2 \\ \text{Range}=13 \end{gathered}[/tex]Therefore, the range is 13
Mean:
The population mean is given by
[tex]\mu=\frac{\sum^{}_{}X}{N}[/tex]Where X is the terms in the data set and N is the number of terms in the data set.
[tex]\begin{gathered} \mu=\frac{2+10+15+4+14+7+14+8+2+10}{10} \\ \mu=\frac{86}{10} \\ \mu=8.6 \end{gathered}[/tex]Therefore, the population mean is 8.6
Variance:
The population variance is given by
[tex]\sigma^2=\frac{\sum^{}_{}(X-\mu)^2}{N}[/tex]Where X is the terms in the data set, μ is the mean, and N is the number of terms in the data set.
[tex]\begin{gathered} \sigma^2=\frac{\sum^{}_{}(X-\mu)^2}{N} \\ \sigma^2=\frac{(2-8.6)^2+(10-8.6)^2+(15-8.6)^2+(4-8.6)^2+(14-8.6)^2+(7-8.6)^2+(14-8.6)^2+(8-8.6)^2++(2-8.6)^2++(10-8.6)^2}{10} \\ \sigma^2=\frac{214.4}{10} \\ \sigma^2=21.4 \end{gathered}[/tex]Therefore, the population variance is 21.4
Standard deviation:
The population standard deviation is given by
[tex]\begin{gathered} \sigma^{}=\sqrt[]{\frac{\sum^{}_{}(X-\mu)^2}{N}} \\ \sigma=\sqrt[]{\sigma^2} \end{gathered}[/tex]Since we have already find the population variance, we can simply find take the square root of variance.
[tex]\begin{gathered} \sigma=\sqrt[]{\sigma^2} \\ \sigma=\sqrt[]{21.4} \\ \sigma=4.6 \end{gathered}[/tex]Therefore, the population standard deviation is 4.6
