Answer: 7-i√3
Step-by-step explanation:
√36+ √-75+ √1-√-108
6 + √75i + 1 - √108i
7 + 5i√3 - 6i√3
7-i√3
Aiden has a collection of 63 nickels and quarters in his piggy bank. If the total value of the coins is $10.75, how many nickels does he have
The number of nickels is 25
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
The total number of nickels and quarters = 63
Total value = $10.75
20 nickels = 1 dollar
4 quarters = 1 dollar
Now,
1 nickel = $0.05
1 quarter = $0.25
Let the number of nickels = x
Let the number of quarters = y
We can make equations as,
0.05x + 0.25y = 10.75 _____(1)
x + y = 63 ______(2)
From (2) we get,
x = 63 - y
Putting in (1) we get,
0.05 (63 - y) + 0.25y = 10.75
3.15 - 0.05y + 0.25y = 10.75
3.15 + 0.20y = 10.75
0.20y = 10.75 - 3.15
0.20y = 7.6
y = 7.6/0.20
y = 38
Now,
x = 63 - y = 63 - 38 = 25
Thus,
The number of nickels is 25
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A shipment service provides uses three types of containers for shipping materials the height and width of the three container are the same the containers height is 0.15 m more than their width and volume of the smaller container is 652 m³
1) write a polynomial relating container 1 length, breadth and height with its volume?
The polynomial representing length, breadth and height of th e container is
Lw^2 + 0.15Lw - 652How to find the polynomial relating the dimensions of the containerVolume is measure in liters, cubic meters and so on
The formula for volume calculation is given by
volume = length * width * height
from the question
height is 0.15 m more than their width
width = w
height = 0.15 + w
length = L
volume = 652 m³
652 = L * w * (w + 0.15)
652 = (w^2 + 0.15w)L
652 = Lw^2 + 0.15Lw
Lw^2 + 0.15Lw - 652
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Can you remember why a perfectly competitive firm faces a perfectly elastic demand curve?.
Since they take prices rather than setting them, fully competitive enterprises must deal with a completely elastic demand curve.
What is competitive firm?
A perfectly competitive firm is a price taker, which means that it must accept the equilibrium price at which it sells goods. If a perfectly competitive firm attempts to charge even a tiny amount more than the market price, it will be unable to make any sales.
Since they take prices rather than setting them, fully competitive enterprises must deal with a completely elastic demand curve. They are so unable to alter the market selling price. In order to raise its income, a perfectly competitive firm will therefore increase output rather than pricing.
A totally competitive firm is unable to arbitrarily set its output price since it must accept the price set by the product's market demand and supply. As an alternative, the perfectly competitive firm can decide to sell any amount of output for the same price. Because customers are eager to purchase any quantity of the company's output at the market price, it follows that the firm must deal with a completely elastic demand curve for its product. The quantity that the perfectly competitive firm decides to produce, combined with the prices that are in effect on the market for inputs and outputs, will determine the firm's total revenue, total costs, and eventually the level of profits.
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-1.3 + u/4 = -7.7 solve for u
Answer:
[tex]u=-25.6[/tex]
Step-by-step explanation:
Take a look at the attachment...
Hope this helps! :)
The heat in the house is set to keep the minimum and maximum temperatures (in degrees fahrenheit) according to the equation |x – 72. 5| = 4. What are the minimum and maximum temperatures in the house? 72. 5°f and 76. 5°f 68. 5°f and 76. 5°f 70. 5°f and 74. 5°f 72. 5°f and 74. 5°f.
The indoor temperature ranges between 68.5 and 76.5 degrees Fahrenheit.
Given data;
According to the equation |x - 72. 5| = 4, the home's heating system is configured to maintain the minimum and maximum temperatures (in degrees Fahrenheit).
To find the minimum and maximum temperatures in the house,
We know that modulus is used to make a negative value into a positive;
|x - 72. 5| = 4
|A| = -A < x < A
|x - 72. 5| = 4
⇒ x - 72.5 = -4 x - 72.5 = +4
x = 72.5 - 4 x = 4 + 72.5
x = 68.5 x = 76.5
Hence, the minimum and maximum temperatures in the house are 68.5 and 76.5 Fahrenheit.
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(2x² - 6x + 5) + (7x²-x-9)
need help finding sum or difference
Answer:
the answer is either x= 4 , or it is 9[tex]x^{2} \\[/tex] - [tex]x[/tex] - 10
Step-by-step explanation:
Sorry dude, I'm confused a little bit on what to do, but i think one of these is right.
lmk if you get it right, and which one you used
Araceli earns $85,000 per year. Now that she has paid off her credit card debt, she is ready to buy a house. Araceli has a $200 car payment, no student loans, $300 in car insurance every 6 months and she estimates that her monthly utility bills will be $250 in her new house. If her bank requires no more than a 36% debt to income ratio, what would her maximum monthly mortgage payment be?
Answer:
$2300
Step-by-step explanation:
1. Her yearly allowable debt
36% × 85000 = 30600
2. Her monthly allowable debt
30600/12 = 2550
3. Her monthly existing debt
car payment = 200
car insurance = 300/6 =50
monthly utility bill = na this is an estimation
4. allowable debt - existing debt
2550 -200-50= 2300
ps: i may be wrong
decrease 150 by 55 %
Answer:
Step-by-step explanation:
First calculate 55% of 150:
= 150 x 55/100
= 82.5 ans
Now decrease it from 150:
= 150-82.5
= 67.5 ans Hope it helps!!
What is the measure of z? X 4 Z 9 z= [?]V Give your answer in simplest form.
Answer:
3√13
Step-by-step explanation:
4 : y = y = 9
y^2 = 36
y = 6
z = [tex]\sqrt{9^2 + 6^2} = \sqrt{81 + 36} = \sqrt{117}[/tex]
117 = 3^2 * 13
[tex]\sqrt{117} = \sqrt{3^2 * 13} = 3\sqrt{13[/tex]
Please help me please
Answer:
16.53
Step-by-step explanation:
Start by finding the length of the line in the center. I will call this line a. Using the Pythagorean Theorem with 12.3 as the hypotenuse:
[tex]c^2=a^2+b^2\\a=\sqrt{c^2-b^2} \\a=\sqrt{12.3^2-5.4^2} \\a=\sqrt{122.13} \\a=11.05[/tex]
Now that this line is known, x can be found. Once again using the Pythagorean Theorem:
[tex]x^2=a^2+b^2\\x=\sqrt{a^2+b^2} \\x=\sqrt{12.3^2+11.05^2} \\x=\sqrt{273.39} \\x=16.53[/tex]
Given m/PSR = 134, find m/SQR.
The measure of the angle SQR is 68 degrees if m/PSR = 134 and Angle QPS = Angle PSQ = Angle SQP = 60 degrees.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
It is given that:
m/PSR = 134,
PQ = QS = PS
Angle QPS = Angle PSQ = Angle SQP = 60 degrees
Angle QSR = QRS
Angle SQR = 180 - (180 - 134)x2
= 180 - 112
= 68 degrees
Thus, the measure of the angle SQR is 68 degrees if m/PSR = 134 and Angle QPS = Angle PSQ = Angle SQP = 60 degrees.
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Here is an equation: 4y - 6x = 12
Is (-4, -3) a solution? Is (0, 3) a solution?
If the equation is 4y - 6x = 12, then (-4, -3) and (0, 3) are the solutions of the equation
The equation is given that
4y - 6x = 12
The first solution =(-4, -3)
The value of x = -4
The value of y = -3
Substitute the values in the equation
4(-3) - 6(-4) = 12
-12 - (-24) = 12
-12 + 24 = 12
12 = 12
Therefore (-4, -3) is the solution of the equation
Next solution is (0, 3)
The value of x = 0
The value of y = 3
Substitute the values in the equation
4(3) - 6(0) = 12
12 - 0 = 12
12 = 12
Therefore (0, 3) is the solution of the equation
Hence, if the equation is 4y - 6x = 12, then (-4, -3) and (0, 3) are the solutions of the equation
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the eigenvectors of the covariance matrix show the direction in which the data has the highest correlation. true or false
It is true that the eigenvectors of the covariance matrix are equal to the principal components. Concretely, the first principal component (i.e. the largest eigenvector and associated largest eigenvalue) gives you the direction of the maximum variability in your data
The covariance matrix's eigenvectors are identical to its major components, which is a well-known fact. In more concrete terms, the direction of the most variability in your data is provided by the first principal component, which is represented by the largest eigenvector and related largest eigenvalue. After that, each primary component provides you decreasingly variable output. The fact that each primary component is orthogonal to the others is also important to note.
The above picture was taken from the Principal Component Analysis article on Wikipedia, which I previously referred to. This is a scatter plot of samples having a bivariate Gaussian distribution with a center at (1,3), a standard deviation of 3 roughly in the (0.878, 0.478) direction, and a standard deviation of 1 roughly in the orthogonal direction. The first principal component is the one with a standard deviation of 3, and the second is the orthogonal component. The shown vectors are the eigenvectors of the covariance matrix scaled by the relevant eigenvalue's square root and moved to place their tails at the mean.
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use the median income 27 and 29 years old to write an equation in slope intercept from of the line of fit
Answer: ?
Step-by-step explanation:
that's how you do it.
Maryanne invests $500 into an account that earns 4% annual interest compounded quarterly.
What is her account balance after 5 years if she makes no withdrawals or deposits?
Enter your answer in the box.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$500\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &5 \end{cases} \\\\\\ A=500\left(1+\frac{0.04}{4}\right)^{4\cdot 5} \implies A=500(1.01)^{20}\implies A \approx 610.10[/tex]
A _____________ t-test evaluates data from dependent samples in which the two treatments are applied to the same individual.
A Paired t-test evaluates data from dependent samples in which the two
treatments are applied to the same individual.
T-test is a statistical statistics mainly use when population variance is
unknown and sample size is small.
In Paired t-test , we compare means of two dependent samples. It gives
hypothesis examination on difference between of mean.
It uses same items or people in both sample that's why they are also known as dependent t-test or Paired t-test also increases the statistical power of our analysis.
Formula of paired t-test :
t = m / S / n
with (n-1) degree
where , m --> mean difference
S ---> standard deviation difference
n --> sample size
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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=530(1.04)x
The given exponential function will grow at rate of 4%
Given, the following exponential function,
y = 530(1.04)ˣ
we are asked to identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
we have:
y = 530(1.04)ˣ
The equation represents exponential growth because the growth factor is greater than 1.
The general form equation is:
y(x) = a(1-r)ˣ
⇒ 1+r = 1.04
⇒ r = 0.04
⇒ r = 4%
Hence the given exponential function will grow at 4%.
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9^3 in standard form
Answer:
729! Hope this helps :)
Step-by-step explanation:
Answer:
9^3 in standard form
Step-by-step explanation:
9 × 9 × 9
81 × 9
729
pls help urgent!
Solve for the roots in simplest form using the quadratic formula:
x²-16x = -100
Answer:
x has no real solution/roots
Step-by-step explanation:
please see the attached image:
write the equation using function notation
x - y = -4
A) f(x) = x - 4
B) f(x) = x + 4
C) f(x) = -x + 4
D) f(x) = -x - 4
Answer:
B
Step-by-step explanation:
[tex]x-y=-4 \\ \\ x-f(x)=-4 \\ \\ f(x)-x=4 \\ \\ f(x)=x+4[/tex]
When testing the difference between two population means, the sample variances are pooled to estimate the population variance when ________________.
The population means are known
The population variances are assumed equal but unknown
The population variances are known and equal
The population variances are assumed unequal and unknown
When testing the difference between two population means, the sample variances are pooled to estimate the population variance when The population variances are assumed equal but unknown.
Population Mean:
The population mean can be calculated by the sum of all values in the given data/population divided by a total number of values in the given data/population.
In testing for the differences between the means of two independent populations where the variances in each population are unknown but assumed equal, the degrees of freedom are: n1 + n2 - 2.
population variance:
Population variance is a measure of how spread out a group of data points is. Specifically, it quantifies the average squared deviation from the mean.
Therefore When testing the difference between two population means, the sample variances are pooled to estimate the population variance when The population variances are assumed equal but unknown.
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A bowling alley and a skating rink both offer birthday party rentals. The bowling alley costs $5 per person plus a $15 room rental fee. The skating rink costs $3 per person plus a $20 room rental fee. You have $50. If you want to invite as many people as possible, which location should you choose?
Follow the steps to decide on the party location.
1. Write an expression for the amount you would spend on a birthday party at the bowling alley. Let x represent the number of people you invite. (2 points)
2. Write an expression for the amount you would spend on a birthday party at the skating rink. (2 points)
3. How many people could you invite to the bowling alley? Show how you found your answer. (2 points)
4. How many people could you invite to the skating rink? Show your work. (2 points)
5. To which location could you afford to invite more people? (2 points)
Answer:
I'll try my best B r u h ....
Step-by-step explanation:
Bowling:
15+5x where x is the number of people
Skating:
20+3x
We have 50 dollars so the amount must be less than or equal to 50
Bowling
15+5x≤50
Subtract 15 from each side
15-15+5x≤50-15
5x ≤35
Divide each side by 5
5x/5 ≤35/5
x ≤7
She can have 7 or less people
Skating
We have 50 dollars so the amount must be less than or equal to 50
20+3x ≤50
Subtract 20 from each side
20-20+3x ≤50-20
3x ≤30
Divide each side by 3
3x/3 ≤30/3
x ≤10
She can have up to 10 people
She can invite more people skating
Hope this helped.
999Find the sum.
10+30+50+...+(20n-10)
Answer:
10
Step-by-step explanation:
tbh i am confused
please if you see this, i am really trying my best and you guys gave me the hardest question i ever had. sincerely apologize
I need help with this
A rectangular-shaped object has a mass of 120 grams. It is 5cm long, 2cm wide, and 3cm high. Solve the following:
V-
Hint: Make sure to use your units in your answer!!!
D-
Blank 1:
Blank 2:
Answers:
V = 30 cubic cm
D = 4 grams per cubic cm
=========================================================
Explanation:
The volume of a rectangular solid (aka block or brick) is equal to its length times width times height
V = length*width*height
V = 5*2*3
V = 10*3
V = 30 cubic cm
-------------
You haven't mentioned it, but the "D" probably refers to the density. This is a measure how much stuff occupies a certain volume of space. The higher the density, the more stuff in that space. Think of it like cramming more packing peanuts in a box.
To find the density, we divide the mass over the volume
density = mass/volume
density = (120 grams)/(30 cubic cm)
density = 4 grams per cubic cm
In each cubic centimeter of space, there are 4 grams of mass.
Please do the one you are able to do anything is helpful!
Answer:
9. train a = 8.33 hours
train b = 5 hours
time of coincidence = 3.33 hours
Step-by-step explanation:
I'm not sure about this but I think it's correct.
you and your friends went to dinner together and ordered 4 hamburgers at $5.95 each, 3 baskets of fries at $4.25 each, and 4 sodas at $1.75 each. how much was the total for all of the food and drink?
Using the concepts of unitary method, we got that $42.83 was the total for all of the food and drink. if me and my friend went to dinner together and ordered 4 hamburgers at $5.95 each, 3 baskets of fries at $4.25 each, and 4 sodas at $1.75 each
Since, we are given that cost price of one hamburger is $5.95,
so total cost of 4 hamburgers is =4×5.95=$23.08
Similarly, we are given that cost price of one baskets of fries which is $4.25,
so total cost of three baskets of fries is =3×4.25=$12.75
Similarly, we are given that cost price of one soda which is $1.75,
so total cost of 4 soda is =4×1.75=$7.00
So, Total cost of my order is= 4 hamburger cost+3 baskets of fries cost +4 sodas cost =23.08+12.75+7.00=$42.83
Hence, if me and my friends went to dinner together and ordered 4 hamburgers at $5.95 each, 3 baskets of fries at $4.25 each, and 4 sodas at $1.75 each, the total for all of the food and drink was $42.83
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write (-4x^2ya^3)^2 as a monomial in standard form
^ means exponent and the number after is the exponent
PLS HELP
Answer:
[tex]16x^4y^2 a^6[/tex]
Step-by-step explanation:
[tex](-4x^2ya^3)^2=(-4)^2(x^2)^2(y)^2(a^3)^2 \\ \\ =16x^4y^2 a^6[/tex]
A helicopter hovers 60 m above the ocean's surface. A submarine is resting 30 m
underwater, directly below the helicopter. What is the difference between the positions of these two objects?
Answer:
90 m
Step-by-step explanation:
because the helicopter is 60 m up and the submarine is 30 m under so combining the two helps us identify the difference between the two objects
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is placed. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Use the rules of exponents to evaluate or simplify. Write without negative exponents.
(bm)⁻³
The expression can be written without negative exponents as 1/(bm)³
Simplification of ExponentsExponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself. For example, 6 is multiplied by itself 4 times, i.e. 6 × 6 × 6 × 6. This can be written as 6⁴. Here, 4 is the exponent and 6 is the base.
Simplifying exponents is a method of simplifying the algebraic expressions involving exponents into a simpler form such that they cannot further be simplified. There are rules in algebra for simplifying exponents with different and same bases that we can use.
Steps to removing exponents are;
Step 1
remove parentheses by multiplying factors.
Step 2
use exponent rules to remove parentheses in terms with exponents.
Step 3
combine like terms by adding coefficients.
Step 4
combine the constants.
In this case, we have an expression;
(bm)⁻³ which can be rewritten using cube.
(bm)⁻³ = 1/ (bm)³
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