Answer:
Step-by-step explanation:
(4i)·(-8i)·(5+5i) = 160+ 160i
We take into account that (i)² = -1
1)
(4i)·(-8i) = (-32)·i² = (-32)·(-1) = 32
2)
32·(5 + 5i) = 32·5 + 32·(5i) = 160 + 160 i
Caroline leaves her house and walks north 6 blocks. She turns and heads east 8 blocks until she reaches mattie’s house. What is the shortest distance between caroline’s and mattie’s houses?.
The shortest distance between Caroline's and Mattie's houses is 10 blocks .
In the question ,
it is given that,
Caroline leaves her house and walks 6 blocks ,
let the point where she starts be A , and the point where she ends be B .
So the distance AB = 6 blocks .
then she turns east and heads to 8 blocks to reach Mattie's house ,
let the point where she stops be C ,
So, the distance BC = 8 blocks ,
the shortest distance(AC) between Caroline and Mattie house can be calculated using the Pythagoras Theorem
AB + BC = AC
6 + 8 = AC
AC = 64 + 36
AC = 100
AC = 10
Therefore , The shortest distance between Caroline's and Mattie's houses is 10 blocks .
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Giuliano is buying a new action figure. When he looks on Amazon he gets
overwhelmed and wants to buy three. He wants to buy Eddie Guerrero for $37.49.
He wants to buy Roman Reigns for $27.88. He wants to buy Kevin Owens for $23.73.
If he buys all three using $100, how much money will he have left?
Giuliano is buying a new action figure. When he looks on Amazon he gets overwhelmed and wants to buy three. The money left with Giuliano is $10.9
How to Calculate Total Cost ?
1)Sum up all fixed costs. First of all, you need to determine the fixed costs of your company.
2)Find all variable costs. The next step is to figure out the variable costs.
3)Add all fixed and variable costs to define the total cost.
4)Check the income statement to find your business's costs.
Given:
Cost of Eddie Guerrero = $37.49
Cost of Roman Reigns = $27.88
Cost of Kevin Owens = $23.73
Total amount Giuliano has = $100
Now, According to question :
Sum of all three amazon products
= (Cost of Eddie Guerrero)+(Cost of Roman Reigns)+(Cost of Kevin Owens)
= $37.49 + $27.88 + $23.73=$89.10
Thus,
amount of money left
= ($100-$89.10)
=$10.9
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In a game, players roll a number cube. the faces of the cube are numbered from 1 to 6. for the player to win a prize, the number cube must land with the top face showing the number 3. what is the probability of the complement of this event occurring?
The probability of the complement of this event occurring is 5/6.
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
The likelihood that a population parameter will be less than a given value when the null hypothesis is true is expressed as the p-value, also known as a probability value or a measure of significance, for a particular statistical model.
Sample space: {1,2,3,4,5,6}
Total number of outcomes=6
Complement of an Event: All outcomes that are NOT the event
In this case:
So, possible outcomes in the complement event:{1,2,4,5,6}
Number of possible outcomes=5
Formula:
Probability = (Number of possible outcomes)/(Total number of outcomes)
= 5/6
So, the probability of the complement of this event occurring is 5/6.
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In order to recive a B in your english class, you must earn more than 350 points of reading credits. Last week you earned 120 points. How many more points must you earn to recive a B
In order to get a B in my class, I will need at least 230 points
Ratio and ProportionsA ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.
But there's a direct way of doing that which is simply subtracting what we have from the total to get what is left.
Total points required to pass > 350Points gotten = 120 Points needed = ?The points needed = Total points required - points gotten.
Points needed = 350 - 120
Points needed = 230
I will need 230 points
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Which is true of the southern states during the early 1800’s?
A) Slave labor was needed for the economy.
B) Slavery was banned in the southern states.
C) Slave labor was not allowed in the newer states.
D) Slaves were allowed to vote.
Answer:
a) Slave labor was needed for the economy.
Step-by-step explanation:
Slave labor was needed for the economy of the southern states during the early 1800’s. Hence, the option (a) is correct.
On a certain hot summer's day, 586 people used the public swimming pool. The daily prices are for children$1.75 and $2.00 for adults. The receipts for admission totaled $1,078.75 How many children and how many adults swam at the public pool that day?
Answer: 373 children and 213 adults
Step-by-step explanation:
Children can be represented by x and adults can be represented by y.
x+y=586
1.75x+2y= $1078.75
x=586-y <-- substitute into 1.75x+2y=1078.75.
1.75(586-y) +2y=1078.75
1025.5 - 1.75y+2y =1078.75
0.25y = 53.25
y=213 adults
x + 213 = 586
x= 373 children
Check:
1.75(373) +2(213)=1078.75
1078.75=1078.75
what is the number that goes in the blank
30/36 = ?/12
I NEED HELP ASAP WITH THESE
Answer:
10/12
Step-by-step explanation:
36 divided by 3 is 12 so you would have to divide 30 by 3 to make it equivalent and you would get 10/12.
Hope this helped!
HELP ASAP Question 2: Luna is riding her skateboard. She went a distance of 10 miles at a rate of 5 miles per hour. Using the distance formula, d = rt, solve for Luna's time in minutes. (1 hour = 60 minutes)
120 minutes
30 minutes
2 minutes
5 minutes
By using the distance formula, we can see that Luna's time in minutes is 120 minutes.
How to find the time in minutes?We know that she went a distance of 10 miles at a rate of 5 miles per hour.
Remember the linear relation:
distance = rate*time
Then if we define t as the time:
10 mi = (5mi/h)*t
(10 mi)/(5mi/h) = t
2 h = t
And we want the time in minutes, remember that:
1 hour = 60 min
Then:
2 hours = 2*(60 min) = 120 min
The correct option is the first one.
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I don’t understand how to do it
According to the information, it can be established that both divers will be at 181.5 feet then after 9,075 minutes.
After how long are the divers at the same depth?To find the time it took for both divers to be at the same depth, we must take into account the information provided by the question.
Distance traveled by diver A: 20 feet per minute.Distance traveled by diver B: 60 feet per minute.Diver Astart point: 0 feet.Diver B start point: 726 feet.To solve this problem we must use the following mathematical operations. We must first find the time it takes for diver A to be at 181.5 ft.
20 * 9.075 = 181.5ft
Second, we must find the time it takes for diver B to be at the same depth.
60 * 9,075 = 544.5726 - 544.5 = 181.5ftAs shown above, both divers are at 181.5 feet after 9,075 minutes.
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A brown bear can weigh 220 to 1,500 pounds. Suppose a bear traveled 65.1 miles at top speed in 3 hours. How far could the bear travel in one hour?
Answer:
21.7 mi/hr
Step-by-step explanation:
Weight of the bear is irrelevant
Unit rate = 65.1 mi / 3 hr = 21.7 mi /hr
A nutrition company is marketing a low calorie snack brownie. A serving size of the snack is 3 brownies and has a total of 50 calories.
If c represents the number of calories and b represents the number of brownies write a proportional relationship involving c and b and solve it for c.
The relationship between the variables c and b is c = [tex]\frac{50}{3}b[/tex]
What is Variation?A variation is a relation between a set of values of one variable and a set of values of other variables. Direct variation. In the equation y = mx + b, if m is a nonzero constant and b = 0, then you have the function y = mx (often written y = kx), which is called a direct variation.
if c ∝ b
Then,
c = kb where k is a constant
When c = 50, b = 3
substituting into the equation above,
50 = 3k
k = 50/3
substitute k into the equation
c = [tex]\frac{50}{3}b[/tex]
In conclusion c is related to b by the equation c = [tex]\frac{50}{3}b[/tex]
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Which table represents a direct variation function?
Input x 3 4 5
Output y 6 10 14
Input x 1 2 3
Output y 2 4 8
Input x 4 6 8
Output y 6 9 12
Input x 1 2 3
Output y 3 9 15
Option 3. The table that represents a direct variation function is Input x 4 6 8 Output y 6 9 12
What is a direct variation?Y = kx, where k is the constant proportionality, is the form of the direct variation equation. It is a two-variable linear equation. The direct variation graph is a straight line in a coordinate plane. The ratio of two directly varying quantities is a constant.
Y = kx is the given formula.
at that location,
y = 6
x = 4 as its value
It would provide us with
6 = 4k
4 divided
6 / 4 = 1.5
1.5 x 6 = 9
1.5 x 8 = 12
Thus, the third selection.
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How many whole groups of 25 out of 90
GIVE AN EXPLANATION PLEASE
Answer: 3
Step-by-step explanation:
25+25+25=75 90-75= 15
So 25 can only go into 90 3 times evenly.
Answer:
Step-by-step explanation:
Simple, 90 / 25 = 3.6 · 90 ÷ 25 = 3.6 · 90 over 25 = 3.6 · ⁄25 = 3.6
If you want this to be like you did not look it up and actually put work towards it then put this:
ninety divided by twenty five equals 3.6, then i checked myself by multiplying 3.6 towards 90 and it had given me 25. The amount of groups that can go in would be 3.
_________________________________
Note: in order for me to give anymore answers i will need further explanation of the question. You could send me a picture of the problem, but if not them your very welcome!
Write an equation in slope-intercept form of the line that passes through (6, 11). and
(2, 25/3).
y=2/3x+7 is equation in slope-intercept form of the line that passes through (6, 11). and (2, 25/3).
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The given two points are (6, 11) and (2, 25/3).
m=25/3-11/2-6
=-8/3/-4
=8/12=2/3
Now we have to find y intercept by considering (6,11)
y=2/3x+c
11=2/3(6)+c
11=4+c
11-4=c
7=c
The slope intercept form of line is y=2/3x+7
Hence y=2/3x+7 is equation in slope-intercept form of the line that passes through (6, 11). and (2, 25/3).
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An unstretched hanging-spring is 50 cm long. Suspending a 100-N block from it increases its length to 60 cm. Adding another 100-N block makes the spring's new length
70 cm
The new length of the unstretched hanging-spring is 70 cm.
Define the term Hooke's law?Hooke's law states that the spring's length change as a result of a compressive or tensile load is directly proportionate to the size of the force placed on the spring. Mathematically,
F = kx
Where;
K is the spring constant, while x represents the spring's length change.
As per the question-
L is the spring's uncompressed length: L = 0.5 m
Weight F1 linked to the spring: F1 = 100 N
First weight's effect on elongation x1: 60 - 50 = 10 = .01 m.
As per the Hooke's law;
F1 = Kx1
K = F1/X1
K = 100 / 0.1
K = 1000 N/m
Spring constant = 1000 N/m.
For the added 100-N block.
F = Kx2
x2 = F/K
x2 = 100 + 100 / 1000
x2 = 0.2m
x2 = 20 cm
L = 50 + 20 = 70 cm.
Thus, new length of the unstretched hanging-spring is 70 cm.
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A regular polygon has an interior angle of 157.5°. Calculate the number of sides of the polygon.
Answer:
16
Step-by-step explanation:
(n-2)*180=total of the interior angles
(n-2)*180=157.5n
180n-360=157.5n
22.5n-360=0
22.5n=360
n=16
2. Write a quadratic equation with 3 and 6 as its roots. Write the equation in the
form ax2+bx+c = 0, where a, b, and c are integers.
Answer:
x^2 - 9x + 18 = 0
Step-by-step explanation:
(x-3)(x-6) = 0
x^2 -6x - 3x + 18 = 0
x^2 - 9x + 18 = 0
Answer:
x² - 9x + 18 = 0
Step-by-step explanation:
given a quadratic with roots x = a and x = b then the factors are
(x - a) and (x - b) and the equation is the product of the factors
here roots are x = 3 and x = 6 then the factors are (x - 3) and (x - 6), then
(x - 3)(x - 6) = 0 ← expand factors using FOIL
x² - 9x + 18 = 0
The mean difference of the successive squares of the first six prime numbers is
A 24
D 33.6
B 24.2
C 33
The answer is;
62.83
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now,
The first 6 prime numbers are 2, 3, 5, 7, 11 ,13
The square of 6 prime number
4, 9 ,25, 49 , 121 , 169
The mean difference of these number is
⇒ (4 + 9 + 25 + 49 + 121 + 169) / 6
⇒ 62.83
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A 2-column table with 6 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2, 3. The second column is labeled f of x with entries negative 8, negative 3, negative 3, 4, 1, 3. What ordered pair is closest to a local minimum of the function, f(x)?.
The ordered pair which is closest to a local minimum of the function f(x) is (2,0)
Given that,
A 6-row, 2-column table. The items in the first column, x, are negative 2, negative 1, 0, 1, and 3. The second column, f of x, contains the values -8, -3, -4, 1, 3 in the entries.
The system shows a table with values of x and its correspondent in a function f(x):
x f(x)
2 -8
-1 -3
0 -3
1 4
2 1
3 3
f(x) is a local minimum of the function at x =2 and y=0 and the value of the function f(x) is -8. So, the ordered pair that lies closest to the function f(x)'s minimum is (2,0)
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todd prefers to drink mug root beer which contains 160 calories per 12 ounces. if he drinks a 44 ounce mug root beer, how many calories will he consume? round to the nearest whole number
Answer:
Step-by-step explanation:
There is a bag filled with 5 blue, 4 red and 3 green marbles. A marble is taken at random from the bag, the colour is noted and then it is replaced. Another marble is taken at random. What is the probability of getting 2 the same colour?
The probability of getting 2 the same color is 9/11.
What is probability?
According to the probability formula, the probability of an event occurring, or P(E), is equal to the proportion of positive outcomes to all outcomes. P(E) is defined mathematically as favorable outcomes divided by total outcomes. Mathematical branch known as probability deals with determining the possibility of an event occurring. Here using probability we can also calculate combination .
Here the total number of marbles are,
=>Total marbles = Blue + Red + Green
=>Total marbles = 5 + 4 + 3
=>Total marbles = 12
Then, Probability of a green = 3/12
=> Probability of not green = 1 - 3/12 = 9/12=3/4
To get exactly one green in two draws, we either get a green, not green, or a not green, green
=>First Draw Green, Second Draw Not Green
=> 1st draw: Probability of a green = 3/12
In 2nd draw: Probability of not green = 9/11 <-- 11 since we did not replace the first marble
To get the probability of the event, since each draw is independent, we multiply both probabilities
=> Probability of the event is (5/12) * (9/11) = 45/132
First Draw Not Green, Second Draw Not Green
=>1st draw: Probability of not a green = 9/12
=>2nd draw: Probability of not green = 7/11 <-- 11 since we did not replace the first marble
To get the probability of the event, since each draw is independent, we multiply both probabilities
=>Probability of the event is (9/12) * (7/11) = 63/132
To get the probability of exactly one green, we add both of the events:
First Draw Green, Second Draw Not Green + First Draw Not Green, Second Draw Not Green
=> 45/132 + 63/132 = 108/132=9/11.
Hence the probability of getting 2 the same color is 9/11.
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Greatest Common Factor (96,144)
The greatest common factor of 96 and 144 is 48
How to determine the greatest common factor of 96 and 144Information given in the question
144
96
Greatest common factor can be found by listing the factors of the numbers required and choosing the common factors, the biggest number among them is the greatest common factor
listing the factors
144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.
96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96
the common factors = 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48,
the greatest among the factors is 48
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Find measure angle ACB
i need it step by step
please help :/
Jacob bought 5. 5 pounds of jelly beans for $14. 74. How much would 7. 25 pounds of jelly beans cost, to the nearest cent?.
Answer:
$19.43
Step-by-step explanation:
when 5.5 pounds cost $14.74 then 1 pound costs $2.68
because 14.74 divided by 5.5 equals 2.68
To calculate the price of 7.25 you multiply the price for 1 pund by 7.25
7.25 * 2.68 = 19.43
Donnie has a pool and recently discovered a leak. He continues to patch the leak until someone can come out to repair it. After all the water has completely drained out of the pool due to the patch coming off, it takes him two days to fill the pool back up. It takes three days for the pool to drain completely. How long would it take to fill the pool if the patch is off while Donnie is refilling it?
The time it will take to fill the pool if the patch is off while Donnie is filling it, found using the combined filling rate is 6 days.
What is a flow rate?A flow rate is the fluid volume that passes a specified area within a unit of time.
The number days it takes to fill the pool = 2 days
The number of days it takes for the pool to drain = 3 days
The rate at which the pool fills = [tex]\dfrac{1}{2}[/tex] per day
The rate at which the pool drains = [tex]\dfrac{1}{3}[/tex] per day
The number of days it will take the pool to fill while the patch is off is found from the combined filling rate as follows;
The combined filling rate is [tex]\dfrac{1}{2} -\dfrac{1}{3} = \dfrac{3-2}{6} = \dfrac{1}{6}[/tex]
The combined filling rate can be taken as a combined flow rate.
The combined filling rate for filling the pool while the patch is off is [tex]\dfrac{1}{6}[/tex], which is a 6th of the pool is filled per day, therefore, it takes 6 days to fill the pool while the patch is off.
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Please help! A, B, C, D
Screenshot inserted below :)
A graph that matches this linear equation is: graph D.
How to interpret the linear equation?Mathematically, the slope-intercept form of a line can be calculated by using this equation:
y = mx + c
Where:
m represents the slope.x and y are the points.c represents the y-intercept.In Mathematics, the y-intercept of any graph such as a linear equation occurs at the point where the value of "x" is equal to zero (0). Next, we would describe the parameters contained in the given linear equation:
y = mx + c ≡ y = -8x
Slope, m is equal to -8.
y-intercept, c is equal to 0.
In this context, we can reasonably and logically deduce that the graph of this linear equation would pass through the origin (0) and slopes downward towards the negative values on the y-coordinate.
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Find '?' in the following series:
1, 4, 10, ?, 46, 94
answers: (a) 20 (b) 16 (c) 15 (d) 22 (e) 94
please put the correct one if you are going to answer
Answer:
(d) 22
Step-by-step explanation:
1 to 4 difference is 3
4 to 10 difference is 6
10 to 22 difference is 12
22 to 46 difference is 24
46 to 94 difference is 48
so, you can see that the difference multiplies by 2 (3x2 = 6, 6x2 = 12, etc.)
thus the answer is d. 22
9 ÷ 2 = ?
show solution, ty!
Answer:
4.5
Step-by-step explanation:
4.5 + 4.5 = 9
OR
4.5 x 2 = 9
Alex leaves home, travels 5 miles east, and arrives at the library. He leaves the library and travels 3 miles north to a friend's house. This trip can be plotted on the coordinate plane, where home is the point (0,0). Alex wants to find out how far his house is from his friend's house and uses the distance formula. Which other formula can he use?.
Alex uses the Pythagorean distance method to calculate the distance between his home and his friend's home.
5² (a) + 3² (β). Can use any other formulas
Given
After leaving his house, Alex drives five miles to the east to reach the library. He leaves the library and drives three miles to a friend's home in the north.
Home would be, followed by the library and the homes of your friends.
By the Pythagoras theorem, we now have points a, b, and c.
House a2 plus library b2 equals friend's house c2.
He must utilize this formula to resolve the issue. √5² + 3².
√5² + 3².
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a coffee machine dispenses coffee into 16-ounce cups. tests show that the actual amount of coffee dispensed is normally distributed, with a mean of 15.2 ounces and a standard deviation of 0.9 ounces. what percent of cups will receive greater than 15.2 ounces of coffee?
The coffee machine dispenses 50% of the cups with more than 15.2 ounces of coffee
Here it is given that amount of coffee dispensed follows a Normal distribution with mean = 1.2 ounces and a Standard deviation of 0.9 ounces.
In a normal distribution, the mean is also the median and the mode. Since the mean is the median, it divides the distribution into 2 equal halves, hence, 50% of the frequency lies on the right of the mean and 50% on the left.
Here we are required to find the percent of cups greater than 15.2 ounces, which is the median.
Therefore, 50% of cups receive coffee of more than 15.2 ounces.
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