Answer:
9018000
Step-by-step explanation:
So you need to do the exponents first because they're in the parenthesis.
10^6 = 1000000
10^4 = 10000
Now your equation should look like (9 x 1000000) + (1.8 x 10000)
Now you just simplify the equation.
(9 x 1000000) + (1.8 x 10000) = 9018000
Answer:
9,018,000
Step-by-step explanation:
point) Find two numbers differing by 42 whose product is as small as possible Enter your two numbers as a comma separated list; e.g. 2,3. Thc " tw numbers are
The numbers differing by 42 whose product is as small as possible are (- 21 + √(441 + p)) and (- 21 - √(441 + p)).
Let us suppose the numbers to be x and y.
As per the given information, we can write;
xy = p ---- (1)
We have to find two numbers differing by 42 whose product is as small as possible.
If two numbers are differing by 42; then we can say
x - y = 42 ---- (2)
From equation (2), we can say
x = y + 42
Now, substitute the value of x in equation (1), we get;
xy = p(y + 42)y² + 42y - p
= 0
Solving this quadratic equation, we will get;
∆ = 1764 + 4p
∴ y = (- 42 ± √(1764 + 4p)) / 2
Now, to find the minimum value of xy, we need to find the value of y that makes xy minimum.
Therefore, the two numbers that make xy as small as possible are;
y = (- 42 + √(1764 + 4p)) / 2
and
x = y + 42
So, the two numbers are;
y = (- 42 + √(1764 + 4p)) / 2
and
x = y + 42
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5. Suppose X 1and X 2are random variables with mean 10,20 respectively, and SDs 2, 3 respectively.
Let T=11X 1−2X2
Find the mean and SD of T when X 1and X 2are independent.
Find the mean and SD of T when X1and X 2 have correlation of
−0.76
In the case that X1and X 2 are independent, normally distributed
variables, find P(T>30)
The mean of T is -10 and the standard deviation of T is √425 when X1 and X2 are independent.
To find the mean of T, we can use the properties of expected values. Since T = 11X1 - 2X2, the mean of T can be calculated as follows: E(T) = E(11X1) - E(2X2) = 11E(X1) - 2E(X2) = 11(10) - 2(20) = -10. To find the standard deviation of T, we need to consider the variances and covariance of X1 and X2. Since X1 and X2 are independent, the covariance between them is zero. Therefore, Var(T) = Var(11X1) + Var(-2X2) = 11^2Var(X1) + (-2)^2Var(X2) = 121(2^2) + 4(3^2) = 484 + 36 = 520. Thus, the standard deviation of T is √520, which simplifies to approximately √425. When X1 and X2 have a correlation of -0.76, the mean and standard deviation of T remain the same as in the case of independent variables. To calculate the probability P(T > 30) when X1 and X2 are independent, normally distributed variables, we need to convert T into a standard normal distribution. We can do this by subtracting the mean of T from 30 and dividing by the standard deviation of T. This gives us (30 - (-10))/√425, which simplifies to approximately 6.16. We can then look up the corresponding probability from the standard normal distribution table or use statistical software to find P(T > 30). The probability will be the area under the standard normal curve to the right of 6.16.
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True or false, rectangles ABCD and WXYZ are similar.
Answer:
False
Step-by-step explanation:
These two rectangles are not similar because the corresponding sides can’t be written in proportion to each other.
1.) 5(X+6) + 11 = 25 - 3x
solve it
Answer:
x = -2
Step-by-step explanation:
Step 1: Write equation
5(x + 6) + 11 = 25 - 3x
Step 2: Solve for x
Distribute 5 on both sides: 5x + 30 + 11 = 25 - 3xCombine like terms: 5x + 41 = 25 - 3xAdd 3x to both sides: 8x + 41 = 25Subtract 41 on both sides: 8x = -16Divide both sides by 8: x = -2Step 3: Check
Plug in x to verify it's a solution.
5(-2 + 6) + 11 = 25 - 3(-2)
5(4) + 11 = 25 + 6
20 + 11 = 25 + 6
31 = 31
Answer:
x=-8
Step-by-step explanation:
5x+30+11=
5x +41= 25-3x
5x+ 41-25= 25-25-3x
5x+16=3x
5x-5x= 3x-5x
16=-2x
16/-2=x
-8=x
...........................
Answer:
....................... What's the question?
How many 8 in pieces of ribbon can you cut from a 12 ft roll of ribbon?
Answer:
1 1/2
Step-by-step explanation:
12 divided by 8 = 1.5
Answer:
18
Step-by-step explanation:
first convert 12 ft to in. there are 12 inches in 1 ft so 12*12=144
then dived 144/8=18
Which equation is linear?
a
xy = 60
b
y + 1 = x
c
3x – 2y = 5
Answer:
equation B is linear. A linear equation will not contain exponents.
Step-by-step explanation:
Answer:
b and c
Step-by-step explanation:
They both follow the formula of a linear function: y = mx + c, where m is the gradient and c is the y-intercept.
When you rearrange:
a. y = 60/x (this is a reciprocal function)
b. y = x - 1 (says that this linear function has a gradient of 1 and cuts the y-intercept at (0,-1))
c. y = 3x/2 -5/2 (says that this linear function has a gradient of 3/2 and cuts the y-intercept at (0, 5/2))
please help me. this is due today.
Answer:
...
let me c
Step-by-step explanation:
Answers:
It's the last one in the chart
(-3-2i -2(24)=8 -51-6i)
There are 35students 2 out of 5 students are boys how many boys are there
Answer:
21 boys
its simple math
Answer:
14 boys
Step-by-step explanation:
In order for the answer to be 14, you need to know the times tables of 5 and 7. 5 times 7 is 35, and 2 times 7 is 14. Your answer is 14.
Jeanette makes and sells greeting cards. She uses 18 square inches of paper for each card. How many square feet of paper does she need to make 150 card?
Answer:
Step-by-step explanation:
We are told that Jeanette uses 18 square inches of paper for each card, for us to get the number of square inches she will need to make 150 cards, we will use the equality operation;
18 in² = 1 card
x in² = 150 cards
cross multiply
x * 1 = 18*150
x = 2700 in²
Convert 2700 in² to feet²
Since 1in² = 0.00694444ft²
2700in² = x
cross multiply
x = 2700 * 0.00694444
x = 18.749988ft²
Hence she will] need 18.749988ft² to make 150 cards
1. A company borrows $100,000 today at 12% nominal annual interest. The monthly payment of a 5-year loan is most nearly?
2. A tractor cost $7,500. After 10 years it has a salvage value of $5000. Maintenance costs are $500 per year. If the interet rate is 10%, the equivalant uniform annual cost is most nearly?
1. The monthly payment of the 5-year loan is approximately $2,225.77.
2. The equivalent uniform annual cost for the tractor is approximately $5,572.50.
1. To calculate the monthly payment of a loan, we can use the formula for an amortizing loan. The formula is:
PMT = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
PMT = Monthly payment
P = Principal amount (loan amount)
r = Monthly interest rate (annual interest rate divided by 12)
n = Total number of payments (number of years multiplied by 12)
In this case, the principal amount (P) is $100,000, the annual interest rate is 12%, and the loan duration is 5 years.
r = 12% / 12 = 1% per month
n = 5 years * 12 months/year = 60 months
PMT = 100,000 * (0.01 * (1 + 0.01)^60) / ((1 + 0.01)^60 - 1)
PMT ≈ $2,225.77
Therefore, the monthly payment of the 5-year loan is approximately $2,225.77.
2. To calculate the equivalent uniform annual cost, we need to consider the initial cost of the tractor, salvage value, maintenance costs, and the interest rate.
The equivalent uniform annual cost (EUAC) can be calculated using the formula:
EUAC = (Initial cost - Salvage value) + (Annual maintenance cost * Present worth factor)
The present worth factor can be calculated using the formula:
Present worth factor = (1 - (1 + r)^-n) / r
Where:
r = Interest rate (10%)
n = Number of years (10 years)
EUAC = ($7,500 - $5,000) + ($500 * ((1 - (1 + 0.10)^-10) / 0.10))
EUAC = $2,500 + ($500 * ((1 - 0.3855) / 0.10))
EUAC ≈ $2,500 + ($500 * 6.145)
EUAC ≈ $2,500 + $3,072.50
EUAC ≈ $5,572.50
Therefore, the equivalent uniform annual cost for the tractor is approximately $5,572.50.
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Q6. (5+2.5+2.5 Marks) A. Use double integral and polar coordinates to calculate the size of a tower bounded by the plane z = 0 and the paraboloid z = 1 - x² - y²
A. The size of the tower bounded by the plane z = 0 and the paraboloid z = 1 - x² - y² can be calculated using a double integral in polar coordinates. B. Differential equation models can be 1. free-falling stone, 2. spring vertical displacement C. The rate of change of temperature at the origin in the direction of the unit vector u = (3,-5) can be determined by T = r² + s².
A. To calculate the size of the tower bounded by the plane z = 0 and the paraboloid z = 1 - x² - y², we can use a double integral in polar coordinates. By expressing the paraboloid equation in polar coordinates, we can set up the integral and evaluate it to find the size of the tower.
B. Differential equation models are mathematical representations used to describe various real-life phenomena. For the given examples:
The free-falling stone can be modeled using Newton's second law and the concept of acceleration due to gravity.
The vertical displacement of a spring can be described using Hooke's law and the properties of springs.
Kirchhoff's Second Law, also known as the voltage law, can be used to model the behavior of electrical circuits.
Newton's Law of Cooling is a differential equation that describes the rate of change of temperature of an object as it loses heat to its surroundings.
Growth and decay phenomena, such as population growth or radioactive decay, can be modeled using exponential or logarithmic functions.
C. To calculate the rate of change of temperature at the origin in the direction of the unit vector u = (3,-5), we need to find the gradient of the temperature function T = r² + s². The gradient represents the direction of the steepest increase in a function. By computing the gradient at the origin and taking the dot product with the unit vector u, we can determine the rate of change of temperature in the desired direction.
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(5+2.5+2.5 Marks) A. Use double integral and polar coordinates to calculate the size of a tower bounded by the plane z = 0 and the paraboloid z = 1 - x² - y² B. Design a differential equation model for the following real-life phenomena: 1. free-falling stone, 2. spring vertical displacement, 3. Kirchoff's Second Law for the circuit, 4. Newton's Law of Cooling, and 5. Growth and Decay. C. The external body temperature in the r-s plane is T = r² +s². Calculate the rate of change of temperature at the origin in the direction of the unit vector u = (3,-5).
The
of a light wave is how fast it goes up and down -
Wavelength
O period
O amplitude
O frequency
O velocity
Answer:
frequency
Step-by-step explanation:
frequency is the amount of waves in a certain period of time
The light wave is how fast it goes up and down wavelength will be "frequency"
What is wavelength?The separation between such a wave motion's crests and troughs would be known as the wavelength of a particular light.
What is frequency?The frequency of a repeated event would be its number of instances per unit of time. Frequency in the context of light would be the count of wavelength repetitions per second.
Therefore, the light wave is how fast it goes up and down wavelength will be "frequency"
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i need help!! i don’t know how to graph it
View this :
I think this is your answer.
A 2-column table with 4 rows titled Drama Club Revenue. Column 1 has entries a percent, a percent, a percent, a percent. Column 2 has entries b dollars, b dollars, b dollars, b dollars.
A drama club made $3,200 from a school play. Seventy-five percent of that amount came from ticket sales. Identify the values of the variables in the model. Then use the model to find the amount of ticket sales.
a =
b =
The amount of ticket sales is $
.
Answer:
A: 25
B: 800
C: 2,400
Step-by-step explanation:
Hopes this helps. :) ( Unless you have already solved ) Just have a good day.
Answer:
A: 25
B: 800
C: 2,400
Step-by-step explanation:
Which answers are equal to the expression in the box? Check all
that apply.
16 • 25
Answer:
i dont understand what you're trying to say but 16 * 25 = 400
Rick's Phone Service charges $20.79 for an activation fee plus $4 for every gigabyte (g) used.
Answer:
Are you asking how much per $ gigabyte, if so, it's $24.79
Step-by-step explanation:
Sketch the graph of the line x - y = 4
the answer is in the photo
which of the following data sets would most likely have a negative association and a correlation coefficient between 0 and -1? a.) average seasonal temperature in the united states; air-conditioning costs for homes in the united states b.) number of miles driven by paul; number of gallons of gas used by paul's car c.) swimsuit sales throughout the year; sunscreen sales throughout the year d.) steepness of the appalachian trail; john's speed while hiking the appalachian trail
The correct option is c.) swimsuit sales throughout the year; sunscreen sales throughout the year.
Correlation coefficient is a measure of the strength and direction of a relationship between two variables. The correlation coefficient varies from -1 to +1. A correlation of -1 means that a negative association between two variables is perfect, while a correlation of +1 means that there is a positive association between two variables that is perfect. The closer the correlation coefficient is to 0, the weaker the association between two variables is. A correlation coefficient of 0 means that there is no relationship between two variables.From the given options, the data set that is most likely to have a negative association and a correlation coefficient between 0 and -1 is (c) swimsuit sales throughout the year and sunscreen sales throughout the year.The reason behind this is that when it's summer or a hot season, people tend to buy more swimsuits than sunscreen. And when it's winter or a cold season, people tend to buy more sunscreen than swimsuits. Hence, the correlation coefficient between swimsuit sales throughout the year and sunscreen sales throughout the year is most likely to be between 0 and -1 because there is an inverse relationship between these two variables.
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Answer:Steepness of Appalachian Trail; John’s Speed while hiking the Appalachian Trail
Step-by-step explanation:
you have a drawer that has an infinite number of gloves, what is the expected number of attempts at taking out gloves individually from the drawer till you find both sides (left hand and right hand) of gloves?
The expected number of attempts at taking out gloves individually from the drawer till you find both sides (left hand and right hand) of gloves is n.
To find the expected number of attempts at taking out gloves individually from the drawer till you find both sides (left hand and right hand) of gloves we can use the principle of geometric distribution. The geometric distribution is a probability distribution that represents the number of trials required to obtain the first success in repeated Bernoulli trials where each trial has a constant probability of success.To find the expected number of attempts at taking out gloves individually from the drawer till you find both sides (left hand and right hand) of gloves we have to first determine the probability of finding the first glove. Since the drawer has an infinite number of gloves, the probability of finding a left glove or a right glove is 1/2. Thus, the probability of finding the first glove is 1. Now, we have to find the probability of finding the matching glove of the first glove. The probability of this is 1/n, where n is the total number of gloves in the drawer. Thus, the probability of finding both the left glove and the right glove is given by the product of the probability of finding the first glove and the probability of finding the matching glove. This is given by 1 x 1/n or 1/n. Therefore, the expected number of attempts at taking out gloves individually from the drawer till you find both sides (left hand and right hand) of gloves is given by the formula E(X) = 1/p, where p is the probability of finding both the left glove and the right glove. Thus, E(X) = 1/(1/n) = n.
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what’s the domain and range
Answer:
Domain {-1, 2, 8}
Range {3}
Step-by-step explanation:
This relation is displayed as a mapping diagram.
The inputs (domain) are in the left circle and the outputs (range) are in the right circle.
The domain is {-1, 2, 8}. They are on the left side of the two circles.
The range is {3}. It is on the right side of the two circles.
Hope this helps.
You want to buy a new Apple Watch. It costs $279.00, but you have to pay 6% sales tax. How much will the watch cost you with tax?
Answer:
279.06
Step-by-step explanation:
You are 5 dollars in debt. You borrow 12 dollars more. What is the total amount of your debt?
Answer:
17
Step-by-step explanation:
You already owe 5 dollars and if you borrow 12 more, you have to pay that back later. You just add 5 and 12 and get 17.
The total debt is $17.
What is addition?Combining items and counting them as a single, large group is done through addition.
Given that, the debt amount is $5.
Now, you borrowed $12 more, therefore, the total debt is:
5 + 12
= 17
Hence, the total debt is $17.
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Write an equation using "x" as the variable: Bill
won 48 super bouncy balls playing the bean
bag toss at the county fair. At school he gave
two to every student in his math class. He only
had 4 balls remaining.
Answer: 48 = 2x + 4
Step-by-step explanation:
x = number of students Bill gave bouncy balls to
The + 4 is there because he had 4 remaining bouncy balls.
48 is what it equals because that is his total number of bouncy balls that he won.
Hope this helps!
graph the libne with a Y intercept of -2 and slope of -1/3 what is the X intercept of the line
Answer:
y = -1/3x -2
x-intercept = -6
Step-by-step explanation:
Slope = -1/3
y-intercept = -2
Substitute values into slope intercept form ;
y =mx +b
Where ; m = slope
b =y-intercept
Equation =
[tex]y = -\frac{1}{3} x -2[/tex]
Now graph the equation
x-intercept = ?
[tex]y = -\frac{1}{3} x -2[/tex]
Arrange in standard form and Let y = 0
[tex]y = -\frac{1}{3} x -2\\\\\frac{1}{3} x +y =-2\\\\\frac{1}{3} x +0=-2\\\\\frac{1}{3} x =-2[/tex]
Cross Multiply
[tex]x \times 1 = 3\times -2\\\\x = -6\\\\=(-6,0)[/tex]
So , (-6,-2)
y-2x=14
Solve the literal equation for y
Answer:
y =2x+14
Step-by-step explanation:
y - 2x= 14
Add 2x to each side
y -2x+2x = 2x+14
y =2x+14
Simplify the expression: 22
.
5 + (20 + 4)
(6 - 2)
19.
a. Given the formula A= (1/2)bh , solve for b.
Only answer if you know the question please
Answer: b = 2A/h
Step-by-step explanation:
1/2 bh = A
2 ⋅ 1/2 bh = 2A
bh = 2A
bh/h = 2A/h
b = 2A/h
An airplane is flying overhead at a constant elevation of 5000 ft. A man is viewing the plane from a position 12000 ft from the base of a radio tower. The airplane is flying horizontally away from the man. If the plane is flying at the rate of 520 ft/sec, at what rate is the distance between the man and the plane increasing when the plane passes over the radio tower?
The rate at which the distance between the man and the plane is increasing when the plane passes over the radio tower is approximately 519.92 ft/sec.
Let's denote the distance between the man and the plane as x and the time elapsed since the plane passes over the radio tower as t. We are given that the plane is flying horizontally away from the man, so the height of the plane remains constant at 5000 ft.
We can set up a proportion based on the similar triangles formed by the man, the plane, and the tower:
x / 12000 = 5000 / t
Cross-multiplying, we have:
xt = 12000 * 5000
xt = 60,000,000
Now, we can differentiate both sides of the equation with respect to time t:
d(xt)/dt = d(60,000,000)/dt
dx/dt * t + x * dt/dt = 0
dx/dt * t + x * 1 = 0
dx/dt = -x/t
We are given that the plane is flying at a rate of 520 ft/sec, so dx/dt = 520 ft/sec.
At the moment the plane passes over the radio tower, the distance x is 12000 ft. We can substitute these values into the equation to find the rate at which the distance between the man and the plane is increasing:
520 = -12000 / t
Solving for t:
t = -12000 / 520 = -23.08 sec (approximately)
Since time cannot be negative, we discard the negative value and take the positive value of t.
Now, we can substitute the value of t into the equation to find dx/dt:
dx/dt = -x / t = -12000 / (-23.08) = 519.92 ft/sec (approximately)
Therefore, the rate at which the distance between the man and the plane is increasing when the plane passes over the radio tower is approximately 519.92 ft/sec.
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why are the solutions to the proportions 50/x = 10/20 and 10/50 = 20/× the same?
Answer:
because both result in the equation 10x=1000
Step-by-step explanation:
beacuse of cross multiplication, your gonna find that they are the same
Answer:
D
Step-by-step explanation:
