The express in the form of a + bi would be 0 + 5i.
What is meant by Complex numbers?Complex numbers are those expressed as a + ib, where a, b are real numbers and 'i' is a fictitious number called a "iota." i is equal to (√-1). A pair of real and imaginary numbers combined in the form a + bi.
When a and b are real numbers, a complex number is one with the formula a + bi. The complex number has two parts: real component (a) and imaginary part (b). If both the real and imaginary components of two complex numbers are identical, only then are the two complex numbers equal.
Let the given expression be [tex]$\sqrt{-25}$$[/tex].
We have to evaluate the expression.
[tex]$$\begin{aligned}\sqrt{-25} & =\sqrt{-1 \cdot 25} \\& =\sqrt{-1} \sqrt{25} \\& =i(5) \\& =5 i\end{aligned}$$[/tex]
The express in the form of a + bi = 0 + 5i.
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In an isosceles triangle, the two equal sides are
called the
Select one:
O a. altitudes
O b. legs
O c. medians
O d. bases
Answer: B. Legs
Step-by-step explanation: The sides of the triangle are called legs because the actual name of the triangle, isosceles, comes from the greek word Iso meaning same, and the greek word Skelos, meaning leg.
Two types of stereos were on sale at a local car stereo dealer.
The J-Series model sold for $II8. The K-Series model sold for $92. During the sale, 32 stereos were sold. The receipts for these stereos totaled $3,230. How many of each type of stereo did the local dealer sell during this sale?
Answer:
11 J- series and 21 K- series
Step-by-step explanation:
create a pair of equations in 2 variables and solve simultaneously.
let x represent J- series and y the K- series , then
x + y = 32 ( subtract x from both sides )
y = 32 - x → (1)
118x + 92y = 3230 → (2)
substitute y = 32 - x into (2)
118x + 92(32 - x) = 3230
118x + 2944 - 92x = 3230
26x + 2944 = 3230 ( subtract 2944 from both sides )
26x = 286 ( divide both sides by 26 )
x = 11
substitute x = 11 into (1)
y = 32 - 11 = 21
11 of J- series and 21 of K- series models were sold
The normal price of a cooker is £540
Stan has to work out the sale price of the cooker.
Here is his working.
10% of 540 = 54
6 x 54 = 324
Sale price £324
Sale price
60% off normal price
Stan's answer is wrong.
(b) What mistake has Stan made?
Stan forgot to subtract the discount from the total price to correctly calculate the sale price.
What is the price of a cooker if it has 60% off its normal price?Regular price: £540
Now, let's calculate the 60%:
£540 / 100 = £5.4 x 60= £324
In this case, £324 represents 60% of the total price but not the sale price. To find the sale price, let's subtract the discount from the total price as shown below:
£540 - £324 = 216
Based on this, it can be concluded that Stan forgot the last step or subtracting the discount.
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Answer:
stan did not deduct the calculation with the original price hence stan is wrong
Step-by-step explanation:
two players a and b play a game rolling a fair die. if a rolls a 1, they immediately roll again, and if it is a 2, then a wins. otherwise, b rolls. if b rolls a 6, they win, otherwise a rolls again and so on. what's the probability player a wins?
The probability player a wins is [tex]\frac{1}{36}[/tex] . Probability is a measure of the likelihood of an event to occur.
Sample space for the given event is :
{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}
A sample space is the total numbers of outcomes that can happen with respect to a given single event or a combination of different event, like in this case there were two events both of rolling a dice
Player a wins if he gets (1,1) otherwise he looses. As we can see there is only one choice for the given event to happen. So his probability is less likely to happen that is 1 time in every 36 time.
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97
Use the ALEKS calculator to write as a percentage.
32
Round your answer to the nearest tenth of a percent.
The answer is 0.3% when rounded to the nearest tenth of a percent.
Solving using ALEKS calculator we have:Using the ALEKS calculator, let's divide 32 by 100 and write the result up to 2 decimal places:
= 32
100
= 0.32
Rounding to the nearest tenth of a percent., the result of the division is 0.3%.
(The second decimal place is 2, which is smaller than 5, so after rounding, the first decimal place is not changed).
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pls help !!! find area
The required area of the parallelogram and pentagon is 91 unit² and 75 unit².
What is surface area?The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.
A parallelogram in is shown in figure 1 with the dimensions height = 7 and base = 13,
Area of the parallelogram = 13 × 7 = 91 unit²
Now,
A pentagon is shown in figure 2,
Area of the pentagon = 5 [1/2 × height × side]
= 5 [1/2 × 5 × 6]
= 75 suqare units.
Thus, the required area of the parallelogram and pentagon is 91 unit² and 75 unit².
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Twenty-four 4 cm cube are ued to make a olid. If 2 cm cube were ued intead, how many cube would be needed?
Twenty-four 4 cm cube are used to make a solid. If 2 cm cube were used instead, 192 cube would be needed.
A cube is a solid object in three dimensions with six square faces that all have the same length sides. It is one of the five platonic solids and is also referred to as a regular hexahedron. Six square faces, eight vertices, and twelve edges make up the form. Since the 3D figure is a square with equal-length sides, the length, breadth, and height of a cube are all the same measurement.
Number of cubes = Volume of the solid / Volume of the cube
= 24 x 4x4x4 / 2x2x2
=24x64/8
=192
Number of cubes will be 192 of 2cm
The area that a cube takes up is known as its volume. Finding the cube of the cube's side length will provide the volume of the cube. There are numerous formulas that use various parameters to calculate a cube's volume.
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△ABC has vertices at A(5,1), B(−3,1), and C(−2,5).
Point D is located on the intersection of the altitude and AB¯¯¯¯¯¯¯¯, in such a way that D has coordinates at (−2,1).
What is the area of △ABC?
Answers:
16 units squared
28 units squared
18 units squared
14 units squared
The area of △ABC is 22 square units.
How to determine the area of △ABC?From the question, we have the following parameters that can be used in our computation:
△ABC has vertices at A(5,1), B(−3,1), and C(−2,5).
The area of △ABC is then calculated as
Area = |(1/2)(x1)(y2 - y3) + (x2)(y3 - y1) + (x3)(y1 - y2)|
Plugging in the given vertices for △ABC, the area can be calculated as follows:
Area = |(1/2)(5)(1 - 5) + (-3)(5 - 1) + (-2)(1 - 1)|
This gives
Area =|-22|
= 22
The area of △ABC is 22 square units.
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(0,-1)
(2,-5)
find slope
Answer: The slope between the points (0,-1) and (2,-5) is (-5 - (-1)) / (2 - 0) = -4 / 2 = -2.
Step-by-step explanation:
A urvey wa given to people who own a certain type of car. What percent of the people urveyed were completely with the car?
Using the percentage concept, it is found that 60.29% of the people surveyed were completely satisfied with the car.
A percentage is the number of desired outcomes, multiplied by 100%, and divided by the number of total outcomes and also defines a number or ratio that can be expressed as a fraction of 100.
To calculate the percentage, we have to divide the value by the total value and then multiply the resultant by 100.
In this problem, researching the internet, it is found that:
A total of 1260 + 650 + 180 = 2090 people were surveyed.
Of those, 1260 were completely satisfied.
Hence:
[tex]P=\frac{1260}{2090} *100 =60.29[/tex]
60.29% of the people surveyed were completely satisfied with the car.
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help me with this problem pls
Answer:
Heres how to do it
(i know you arent using macbook)
Step-by-step explanation:
2x-1=1+x i need help
Answer:
X = 2
2x-1+1=x+1+1
A ballet dancer whose weight is 60 kg performs a move on one foot during which she
applies a pressure of 1,500,000 Pa on the ground. Is she likely to be standing with her foot
flat on the ground, or is she on tiptoe?
It is likely that she is on tiptoe, as a pressure of 1,500,000 Pa is a high pressure for a 60 kg person to be applying with just one foot while standing flat on the ground.
How to know if the dancer is tiptoeingThe unit of pressure Pa is equivalent to Newton per square meter
A mass of 60 kg is converted to force by
= m * g
= 60 * 10
= 600 N
Pressure = Force / Area
Area = Force / Pressure
Area = 600 N / 1,500,000 Pa
Area = 0.0004 square meter
Area = 4 square centimeter
This area is much smaller than the foot hence the dancer is tiptoeing
A pressure of 1,500,000 Pa suggests that the dancer is applying a significant amount of force to a small area, which is typical of being on tiptoe.
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All monkeys are good chess players. All wookies are monkeys. All wookies are good chess players. what is the conclusion?
The average conclusion is that since they are monkeys, all wookies are good chess players.
Two premises form the basis for the conclusion. All monkeys are skilled chess players, according to the first postulate. The idea that all Wookies are monkeys is the second premise. The first assumption indicates that all monkeys are brilliant chess players, and since the second premise states that all wookies are monkeys, it follows that all wookies must likewise be good chess players. The conclusion is that since they are monkeys, all wookies are good chess players. This conclusion comes logically from the two supplied premises. The conclusion is also presumptively true because the premises are believed to be true.
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The slope Ab is 3. The slope of A’B is A’B through the point O
The slope will remain constant, thus it will still be 3.
What is dilation?Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.
Given AB is dilated by a scale factor of 3 to form A'B',
and Point O, which lies on AB, is the center of dilation,
AB has expanded due to the scaling factor, to form A'B'
The image is thus consistent with the preimage according to the laws of dilation.
This suggests that other than the size, the image won't change in any way.
Therefore, the slope will stay the same, the slope of A'B' is 3.
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The complete question is,
AB is dilated by a scale factor of 3 to form A'B'. Point O, which lies on AB , is the center of dilation. The slope of AB is 3. The slope of A'B' is . through point O.
Based on these formulas, which scenario would not have been possible?
Following the volumes a cone formula, one can determine a cone's volume given the necessary inputs. When the basis radius or even the see that, height, and slanted height of the cone are determined, the further stages can be carried out.
What is the cone's volume formula?V=1/3hπr²
Cone volume is calculated using the method V=1/3hr2. Learn how to solve a sample problem using this formula.
Step 1: Write down the given parameters, "r" denoting the radius of the cone's base, "d" denoting its diameter, "L" denoting its slant height, and "h" denoting its height.
Step 2: Apply the calculation to determine the cone's volume.
Cone volume using the base radius: V = 1/(r2h) or 1/(r2) (L2 - r2)
Cone volume using the formula V = (1/12)d2h = (1/12)d2 (L2 - r2)
Determine the volume of the a cone with a 3 inch radius and a 7 inch height. (Use π = 22/7).
Solution: We are aware of the volume
As we already know, the cone's volume is (1/3)r2h.
Taking into account that r = 3 inches, h = 7 inches, and = 22/7
So, the volume of the cone is V = (1/3)r2h V = (1/3) × (22/7) × (3)2 × (7) = 22 × 3 = 66 in3
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A construction company completes two projects. The first project has $3,000 in labor expenses for 60 hours worked, while the second project has $2,100 in labor expenses for 42 hours worked. The relationship between the company’s labor expenses and hours worked is linear. Which of the following would correctly calculate the y-intercept of the linear equation? Select all that apply. 3,000 = 50(60) + b 3,000 = 0.02(60) + b 60 = 50(3,000) + b 2,100 = 0.02(42) + b 2,100 = 50(42) + b 42 = 50(2,100) + b
The equation that correctly calculate the y-intercept of the linear equation would be;
3,000 = 50(60) + b
2,100 = 50(42) + b
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
Given that The first project has $3,000 in labor expenses for 60 hours worked, while the second project has $2,100 in labor expenses for 42 hours worked.
Then the relationship between the company’s labor expenses and hours worked is linear.
So, the required equation are;
3,000 = 50(60) + b
2,100 = 50(42) + b
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How do you determine the equation of a circle in center-radius form whose center is (4,-3) and passes through the point (6,0)?
Using the formula (x - a) 2 + (y - b) 2 = r 2 and knowing the circle's radius and center, you can determine the circle's equation. Here, stands for the circle's center, and is the radius.
How to Find the equation of a circle using the centre and radius?A circle's center and radius can be used to get its equation. The discriminant can identify the type of intersections between two circles or a circle and a line to demonstrate tangency.
Utilize the equation (x - a2 + (y - b)2 = r 2 to determine a circle's equation when you are aware of its radius and center. Here, (a,b) stands for the circle's center and is its radius.
It's merely spelled differently, but this equation is the same as the basic equation of a circle.
Example
A circle with a center at (2,-3) and a radius of √7 has an equation that you must find.
(x - 2 )² + (y - (-3))² = (√7)²
(x - 2 )² + (y + 3 )² = 7
You can add more to this if it's necessary for more labor to provide:
x² - 4x + 4 + y² + 6y + 9 - 7 = 0
x² + y² -4x + 6y + 6 =0.
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you are told you will have to wait 5 hours in a line with a group of other people determine if you know the number of minutes you have to wait
Answer:
Below
Step-by-step explanation:
There are 60 min / hr
5 hr * 60 min/hr = 300 min
A carnival game charges each contestant $ 10 to spin a wheel with 6 equally likely spaces: 3 spaces result in the contestant winning nothing. 2 spaces result in the contestant winning a prize whose value is $ 5. 11 space results in the contestant winning a prize whose value is $ 20 .
Based on the information above, the probability of winning the $20 prize is 0.16.
How to find the probability that the contestant wins $20?To find the probability that the contestant wins $20 we must carry out the following mathematical procedure:
1 / 6 = 0.160.16 * 1 = 0.16Based on this result, we can infer that the probability that the contestant wins the $20 is 0.16. Additionally, you have a 0.5 chance of winning nothing and a 0.33 chance of winning $5.
0.16 * 3 = 0.50.16 * 2 = 0.33Note: This question is incomplete because there is some information missing. Here is the complete information:
Tasks
Find the probability that the contestant will win the $20 prize.
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for which equation would x = 24 not be a solution
x/6=5
x/4=6
x/3=8
x/12=2
Answer:
x/6=5, False
Step-by-step explanation:
For which equation would x = 24 not be a solution
x/6=5 = 24/6 FALSE
x/4=6 = 24/4 TRUE
x/3=8 = 24/3 TRUE
x/12=2 = 24/12 TRUE
Give a geometric description of the set of points in space whose coordinates satisfy the given pairs of inequalities.
y\leqx2 , z\leq0
x\geqz2 , -5\leqy\leq0
The set of points is a pyramid-shaped region in space with a base of the xz-plane between x = z2 and x = 0, extending to a height of y = 0 at its peak. The region is bounded by the planes y = x2, z = 0, and y = -5.
The set of points is bounded by the four planes: y = x2, z = 0, x = z2, and y = -5. The two inequalities, y <= x2 and z <= 0, imply that the region is limited to the space below the plane y = x2 and behind the plane z = 0. The other two inequalities, x >= z2 and -5 <= y <= 0, indicate that the region is limited to the space in front of the plane x = z2 and between the planes y = -5 and y = 0. This forms a pyramid-shaped region with a base at the xz-plane between x = z2 and x = 0, extending to a height of y = 0 at its peak.
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sam estimates that if he leaves his car parked outside his office all day on a weekday, the chance that he will get a parking ticket is 13%. if sam leaves his car parked outside his office all day next tuesday, what is the chance that he will not get a parking ticket?
The chance that Sam will not get a parking ticket is 87%.
No Parking Ticket ChanceTo find the chance of not getting a parking ticket, subtract the chance of getting a ticket from 100%.
Step 1: Take the chance of getting a ticket, which is 13%
Step 2: Subtract it from 100%
100% - 13% = 87%
So, the chance that he will not get a parking ticket is 87% if Sam want to leaves his car parked outside his office all day next tuesday.
This question is about the probability of Sam getting a parking ticket if he leaves his car parked outside his office on a weekday. Sam estimates that the chance of getting a ticket is 13%. To find the chance of not getting a ticket, the probability of getting a ticket (13%) was subtracted from 100%. The result, 87%, represents the chance that Sam will not get a parking ticket.
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I deal myself 5 cards from a standard 52-card deck. Find the probabilities of each of the following events: (a) 2 of a kind: (b) 3 of a kind: (c) 2 pair (e.g., 2 eights and 2 queens): (d) a flush (65 cards all of the same suit): (e) a full house (3 of one kind and 2 of another kind): (f) a straight (5 cards in consecutive order).
the probabilities of each of the following events are a) 9.23×10⁻⁶ and b) 0.00144
Since we have given that
Number of cards = 52
a) Probability that we draw 3 aces and 2 kings.
As we know that
Number of aces = 4
Number of kings = 4
Number of cards drawn = 5
So, the probability becomes,
9.23×10⁻⁶
(b) a "full house" (3 cards of one kind, 2 cards of another kind)
Since there are 13 sets of each type and we have to select and 2 kinds of it, so, it becomes
So, it becomes,
Hence, a) 9.23×10⁻⁶ and b) 0.00144
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a researcher chooses 100 random samples for an experiment, and for each sample he obtains a 95% confidence interval for an unknown parameter. approximately how many of those confidence intervals will not contain the value of the unknown parameter?
5 samples will not contain the value of the confidence interval of the unknown parameter. The rest will have the confidence interval.
x% confidence interval implies that the mean of x% is in the interval, also x% in the sample space will have the value of unknown parameter.
Here 95% of confidence interval is present and the sample space is 100. So, 100%- 95% = 5%. Thus only 5% of the sample space will not contain the confidence level of the unknown parameter.
5% of 100 = [tex]\frac{5}{100}[/tex] × [tex]100[/tex] = 0.5 × 100 = 5
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four $12$-sided dice are rolled. what is the probability that the number of dice showing a two digit number is equal to the number of dice showing a one digit number? express your answer as a common fraction. (assume that the numbers on the $12$ sides are the numbers from $1$ to $12$ expressed in decimal.)
27/128 is the probability that the number of dice showing a two-digit number is equal to the number of dice showing a one-digit number.
Probability means Possibility. It states how likely an event is about to happen.
The probability of an event can exist only between 0 and 1 where 0 indicates that the event is not going to happen i.e. Impossibility and 1 indicates that it is going to happen for sure i.e. Certainty.
I'll take a stab at this one. if the number of dice showing a two-digit number = the number of dice showing a one-digit number, then 2 must show a two-digit number and 2 must show a one-digit number
There are 3 two-digit numbers and 9 one-digit numbers on each die
So....the probability is
C(4,2) (3/12)^2 (9/12)^2
C(4,2) (1/4)^2 (3/4)^2
=27/128.
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Why is a rhombus not a square?
The primary distinction between a square and a rhombus is that whereas the angles in a square are all 90 degrees, the angles in a rhombus are not.
How do you prove a rhombus is not a square?Since a rectangle need not have equal sides, it is not square. Every square is a rectangle and a rhombus. Due to the fact that every square has an equal number of sides, they are all rhombuses. Due of the 90-degree interior angles, all squares are also rectangles.
The main difference between a square and a rhombus is that whereas a square's angles are all 90 degrees, a rhombus's angles are not. However, both shapes have equal sides on every side.
Both a square and a rhombus have equal-length sides. But while a rhombus only has its opposite angles equal, a square only has angles that are all 90 degrees.
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Jan spends part of her year as a member of a gym. She then finds a better deal at another gym, so she
cancels her membership with the first gym and spends the rest of the year with the second gym. The
membership to the first gym costs $80 per month, while the membership for the second gym costs $45 per
month. If she ends up spending a total of $645 over the course of the year, how much time did she spend at
each gym?
Answer:
Jan spent $240 at the first gym and $405 at the second gym.
I need help with this question please and thank you .
Step 1: [tex]6.3^2+x^2=15.4^2[/tex]
Step 2: [tex]x^2=15.4^2-6.3^2[/tex]
Step 3: [tex]x=\sqrt{15.4^2-(6.3)^2}[/tex]
Step 4: [tex]x=14.05[/tex]
Dexter thinks of a number, x. He subtracts 4 from his number and multiplies the answer by his original number. His answer is 60 a) Use this information to form a quadratic equation of the form x² + ax + b = 0
Answer:
Let y = x - 4, then xy = 60.
Expanding the product on the right side, we have x(x-4) = 60.
Expanding the left side, we have x² - 4x = 60.
Adding 4x to both sides, we have x² = 60 + 4x.
Re-arranging the equation, we have x² - 4x - 60 = 0.
Thus, the quadratic equation is x² - 4x - 60 = 0.
