a) The expected annual rainfall is 15 million tons.
b) The standard deviation is the square root is 15 million tons.
c) Pgamma(4, shape = 3, scale = 5)
d) Pgamma(5, shape = 3, scale = 5) - Pgamma(2, shape = 3, scale = 5)
Gamma Distribution Probabilitiesa) The expected annual rainfall accumulated in this lake is given by the mean of the gamma distribution, which is alpha * gamma. In this case, the expected annual rainfall is 3 * 5 = 15 million tons.
b) The standard deviation of the annual amount of rainfall in this lake is given by the square root of the variance, which is the square root of alpha * gamma². In this case, the standard deviation is the square root of 3 * 5² = 15 million tons.
c) To find P(X < 4), we can use the cumulative distribution function (CDF) of the gamma distribution. In R, we can use the pgamma() function to find the CDF of the gamma distribution at a given value.
pgamma(4, shape = 3, scale = 5)
This will return the probability that X is less than 4, which is the cumulative probability.
d) To find P(2 < X < 5), we can use the cumulative distribution function (CDF) of the gamma distribution. In R, we can use the pgamma() function to find the CDF of the gamma distribution at a given value.
pgamma(5, shape = 3, scale = 5) - pgamma(2, shape = 3, scale = 5)
This will return the probability that X is between 2 and 5, which is the cumulative probability.
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How do u solve: 4x-(9-3x)=8x-1
Answer:
x=-8
Brief explanation:
Well I simplify first
4x-(9-3x)=8x-1
4x-9+3x=8x-1
then you do this operation called collecting similar terms
4x+3x-9=8x-1
7x-9=8x-1
7x-8x=-1+9
7x-8x=8
-x=8
x=-8 should be ur solution--
Answer:
[tex] \sf \: x = - 8[/tex]
Step-by-step explanation:
Given equation,
→ 4x - (9 - 3x) = 8x - 1
Now the value of x will be,
→ 4x - (9 - 3x) = 8x - 1
→ 4x - 9 + 3x = 8x - 1
→ (4x + 3x) - 9 = 8x - 1
→ 7x - 9 = 8x - 1
→ 7x - 8x = -1 + 9
→ -x = 8
→ [ x = -8 ]
Hence, the value of x is -8.
If each of these runners travels the indicated number of spaces in the same amount of time, at which numbered spot will all of the runners be next to one another?
The numbered spot at which all the runners will be next to one another is spot 19.
What is the LCM?Least Common Multiple is the meaning of the acronym LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It may also be computed using two or more real numbers.
Starting with the runner on the outside track, the provided parameters are;
The runner covered n₁ = 5 places on the outside track, which is the number of spaces.
Next, the inner runner will traverse n₂ spaces, which equals one space.
The following inner runner will cover n₃ = 3 spaces.
The subsequent runner will traverse n₄ = 2 spaces.
The Lowest Common Multiple, or LCM, of all the runners' speeds or the total number of spaces they cover in the same amount of time, determines where all the runners will be placed next to one another.
LCM(5, 1, 3, 2) = 30 is the LCM of 5, 1, 3, and 2.
Time = 30/ = 6
Consequently, when the first runner has covered 30 places, we have;
Six time units have been expended.
The runner comes to a stop at position 30- (30 -19) = Position 19.
First runner's new destination is Spot 19.
The distance covered simultaneously by runner 2 is 6 x 1 = 6.
The distance covered by two runners running simultaneously equals six spaces.
Second runner's new position: 6 spaces plus spot 13 equals spot 19.
The combined distance covered by the three runners is 6 x 3 = 18.
The distance runner 3 covers 18 spaces simultaneously.
Third runner's new position: 18 spaces + Spot 1 = 19 spaces
Runner 4 covers a distance of 6 x 2 = 12 at the same time.
Distance runner 4 journeys equals 12 spaces
Runner 4's new position is now 12 spaces Plus Spot 7 = Spot 19.
Therefore, all the runners will be next to one another is spot 19.
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The reciprocal of 10 1-2
The reciprocal of that fraction is 2/21.
What is Reciprocal?The inverse of a value or a number is how reciprocal is commonly used in mathematics. The reciprocal of n will be 1/n if n is a real number. In other words, we must change the number to be inverted. One divided by nine, or 1/9, is the reciprocal of nine, for instance. A value of one is produced when we multiply a number by its reciprocal. The term multiplicative inverse is another name for it.
reciprocal is simply defined as the inverse of a value or a number. If n is a real number, then its reciprocal will be 1/n. It means that we have to convert the number to the upside-down form.
Using the given functions to set up and simplify 1-2
10=1-2=-1
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If two lines are parallel, then
corresponding angles are congruent.
Choose the equivalent statement.
A. If two lines are parallel, then the corresponding angles are not
congruent.
B. If two lines are not parallel, then corresponding angles are
congruent.
C. If corresponding angles are not congruent, then the lines are not
parallel.
Answer:
C
Step-by-step explanation:
If two lines are parallel, then corresponding angles are congruent.
OR
If two lines are NOT parallel, then corresponding angles are NOT congruent.
So compare these 2 to the answers. Only C is right.
Complete the calculation in step 3 and drag the appropriate solute amounts to the ECF and ICF columns. Drag the appropriate labels to their respective targets.
The types of solutes and their distribution between the ICF and ECF are not the same for the appropriate solute amounts to the ECF and ICF columns.
Intracellular fluids are fluids found inside the cell's cytoplasm while extracellular fluid are fluids the flow outside the cells which consist of plasma, interstitial and trancellular fluid
The types of solutes and their distribution between the ICF and ECF are not the same because intracellular fluid of the cystosol is composed of water, dissolved ions, small molecules, and large, water-soluble molecules while extracellular fluid consist of plasma, interstitial fluid and cytosol have high potassium concentration and low sodium Concentration.
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What is the constant of proportionality in this proportional relationship?
X 2 2/1 3 3 1/2
Y 5/2 25/8 15/4 35/8
The constant of proportionality in this proportional relationship is 5/4.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x = 5 is an equation.
We have,
Let the proportional equation be y ∝ x.
y = kx
From the table,
When x = 2, y = 5/2
This means,
5/2 = 2k
k = (5/2)/2
k = 5/4
Now,
When x = 2(1/2), y = 25/8
k = y/x
k = (25/8)/(5/2)
k = 25/8 x 2/5
k = 5/4
We see that,
k = 5/4
Thus,
The constant of proportionality is 5/4.
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Of the following statements, which one or ones describe actions harmful to your credit score?
I. Owing a lot of money
II. Having many lines of credit
III. Making steady payments
Answer:
I
Step-by-step explanation:
owing a lot of money bc it hurts your credit score
do you dislike waiting in line? supermarket chain kroger has used computer simulation and information technology to reduce the average waiting time for customers at stores. using a new system called quevision, which allows kroger to better predict when shoppers will be checking out, the company was able to decrease average customer waiting time to just seconds (informationweek website). assume that waiting times at kroger are exponentially distributed.
Probability of waiting between 15 and 30 seconds and probability of waiting for more than 2 minutes are 0.2462 and 0.0099 respectively.
Given that,
Do you find lines to be tedious? The grocery store chain Kroger has reduced the average wait time for customers at 2300 locations by using computer modeling and information technology. Kroger was able to reduce the typical customer wait time to to 26 seconds thanks to a new system called QueVision that helps the retailer to better anticipate when customers would be checking out.
P(Wait between 15 and 30 seconds)
= [tex]\int{15}{30} \frac{e^{-x/26}}{26} dx[/tex]
= 0.2462
P(wait for more than 2 minutes)
= 1 - P(Wait for less than or equal to 120 seconds)
= 1 - [tex]\int{0}{120} \frac{e^{-x/26}}{26} dx[/tex]
= 0.0099
As a result, the probabilities of waiting between 15 and 30 seconds and longer than 2 minutes are, respectively, 0.2462 and 0.0099.
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the base company has assets other than investment securities, that cost $50,000. The current market value of the assets is $75 million. The assets will be recorded and reported as assets at
As the company asset other than investment securities cost $50,000 and market value of the assets is $75 million. The assets will be recorded and reported as at $75,050,000.
How are asset recorded and reported?An asset is a resource with monetary value that an individual, corporation, or country owns or controls with the expectation of future benefit. An asset is anything that can generate cash flow, reduce expenses, or increase sales in the future, whether it's manufacturing equipment or a patent.
A company's assets are reported on its balance sheet. They are divided into four categories: current, fixed, financial, and intangible. They are purchased or created in order to increase the value of a company or to benefit its operations.
The reported asset of the company will be:
= $50,000 + $75 million
= $75,050,000
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the accompanying major league baseball data provide data for one season. use the data to build a multiple regression model that predicts the number of wins. complete parts a through c.
Considering the data we have been provided, we can build a multiple regression model as follows.
a.) In MS Excel, we enter the data set and utilize the "Correlation" option under Data > Data Analysis to create the correlation matrix and answer the question. The correlation matrix may be seen below.
[Fig. 1]
Correlation coefficients for at least one of the independent variables are larger than 0.7.
b.) We must look at the column labeled "Won" in the correlation matrix. The variables are Runs, Hits, Earned Run Average (ERA) and Walks if the criteria are 0.4.
c.) In MS Excel, we enter the data set and utilize the "Regression" option under Data > Data Analysis to create the regression model and answer the question. The result is shown below.
[Fig. 2,3,4]
Runs, ERA, and SO are all significant, with p-values less than 0.05. As a result, we recreate the regression model with these three independent variables.
[Fig. 5,6,7]
The right answer is Won = 80.321 + (0.101) X1 + (-14.276) X3 + (-0.011) X4.
The R2 value of the model is 0.948. This suggests that these factors can predict 94.8% of the number of victories. This model does not make use of the same variables as the previous one (b).
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The store owner put 10 Tshirts on clearance. The Tshirts were originally priced at $22.00 each. The owner marked down the price of the Tshirts by 40%.
How much money did the store owner receive for selling all 10 Tshirts?
Answer:
$132
Step-by-step explanation:
Looks like $22.00 was the price at 100%
The owner marks the price down by 40%, making the total price 60% of $22 because 100%-40% is 60%
We can set up a ratio
60%. X
-------. =. ------
100%. $22
Cross multiplying makes it (100)(x) = (60)(22)
100x = 1,320
Dividing both by 100 to get X alone
x = 13.2
Each shirt is now $13.20
Last, but not least, we multiply by 10 because he sold 10 shirts
= $132
In the pattern below, the cat moves clockwise through the four squares, and the mouse moves counterclockwise through the eight exterior segments of the four squares.
If the pattern is continued, where would the cat and mouse be after the 247th move?
Only setup A places the mouse on the bottom right square and the cat there.
The pattern is continued, so we have to define where the cat and mouse would be after the 247th move.
Divide the issue into two parts: the location of the mouse and the location of the cat after the 247th move.
Every cycle, which consists of four different positions for the cat, is repeated once every four movements. When 247 is divided by 4, the remainder is 3. This matches the bottom right corner, where the cat is located after the third move.
Similar to the mouse, which repeats every eight moves, the mouse has eight possible places in a single cycle. When 247 is divided by 8, the remainder is 7. This matches the rat's bottom left corner position after the seventh motion.
The only configuration with the cat in the bottom right square and the mouse in that position is A.
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The complete question is given below:
Helio in Jersey live down the street from each other 1500 m apart they leave their homes at the same time walking towards each other Julia travels at a rate of 2000 m an hour and Josie travels at a rate of 4000 m an hour how far they apart after they walk for 15 minutes
After 15 minutes of walking, Julia and Josie are facing each other at the same point (in distance).
How are their positions determined?Distance between Julia and Josie = 1,500 m
Julia's traveling rate (speed) per hour = 2,000 mph
Josie's traveling rate (speed) per hour = 4,000 mph
Walking time = 15 minutes
Distance formula = time x speed.
In 15 minutes, Julia's distance traveled = 500 m (2,000/60 x 15)
In 15 minutes, Josie's distance traveled = 1,000 m (4,000/60 x 15)
Thus, in 15 minutes, Julia and Josie have covered the 1,500 m distance separating them and will be at the same point.
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Simplify. Need ASAP. show work
The solutions to the simplification of the following surds are:[tex]-12\sqrt[3]{3}+4\sqrt[3]{2}[/tex] and [tex]-5x^2 y^2\sqrt[3]{3x^2y^2}[/tex]
Simplification of surd forms:A number without a root is simply referred to as a surd. These surds illustration comprises fractions as powers if presented in exponential form. There are three main forms of surds, according to the definition of surds.
Pure surds, which are surds that include just one irrational number. Surd that comprises both rational and irrational numbers is called Mixed surds. Compound surds are two surds combined into one.The simplification of the given surds is carried out as follows:
[tex]-2\sqrt[3]{81} +2\sqrt[3]{16}-2\sqrt[3]{81}[/tex]
Factor 27 out of 81
[tex]-2\sqrt[3]{27*3} +2\sqrt[3]{16}-2\sqrt[3]{27*3}[/tex]
Rewrite it as 3³*3
[tex]-2\sqrt[3]{3^3*3} +2\sqrt[3]{16}-2\sqrt[3]{3^3*3}[/tex]
Rearrange and simplify
[tex]-2\sqrt[3]{3^3*3} -2\sqrt[3]{3^3*3}+2\sqrt[3]{16}[/tex]
Pull term out from the radical
[tex]-2*3\sqrt[3]{3} -2*3\sqrt[3]{3}+2\sqrt[3]{16}[/tex]
[tex]-6\sqrt[3]{3} -6\sqrt[3]{3}+2\sqrt[3]{16}[/tex]
Rewrite 16 as 2³*2
[tex]-6\sqrt[3]{3} -6\sqrt[3]{3}+2\sqrt[3]{2^3*2}[/tex]
Pull term out of the radical
[tex]-6\sqrt[3]{3} -6\sqrt[3]{3}+2*2\sqrt[3]{2}[/tex]
[tex]-6\sqrt[3]{3} -6\sqrt[3]{3}+4\sqrt[3]{2}[/tex]
Simplify altogether;
[tex]-12\sqrt[3]{3}+4\sqrt[3]{2}[/tex]
In [tex]\sqrt[3]{-375x^8y^8}[/tex]; simplify the radical by breaking the radicand up into a product of known factors, assuming real numbers.
[tex]\sqrt[3]{(-5) ^3(x^2)^3 (y^2)^3*3x^2y^2}[/tex]
[tex]\sqrt[3]{(-5x^2y^2) ^3*3(x^2y^2)}[/tex]
[tex]-5x^2 y^2\sqrt[3]{3x^2y^2}[/tex]
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Helpppppppppppppppppppppppppppppppp
Answer:
Step-by-step explanation:
Its the second one
Answer: -1/3 > -2/5
Step-by-step explanation:
If we put them as common denominators we can solve this. To do that look at this:
-1/3 = -5/15
-2/5 = -6/15
So we can see that -2/5 is smaller
I hope this was able to help you :D
Given that z is a standard normal random variable, compute the following probabilities (to 4 decimals).
P(z ? -1.0)
P(z ? -1.0)
P(z ? -1.5)
P(z ? -2.5)
P(-3 < z ? 0)
Computed the probabilities P(z < -1.0)=0.1587, P(z > -1.0)=0.8413, P(z < -1.5)=0.0668, P(z < -2.5)=0.0062, P(-3 < z < 0)=0.4987.
What is deviation ?
Deviation refers to how far a value or set of values is from the mean or average. In statistics, the standard deviation is a measure of the spread of a dataset, calculated as the square root of the variance. It represents the average distance of each data point from the mean. A low standard deviation indicates that the data points tend to be close to the mean.
To compute the probabilities for a standard normal random variable, we can use a standard normal table or a calculator with standard normal distribution functions.
P(z ? -1.0) = P(z < -1.0) = 0.1587
P(z ? -1.0) = P(z > -1.0) = 1 - 0.1587 = 0.8413
P(z ? -1.5) = P(z < -1.5) = 0.0668
P(z ? -2.5) = P(z < -2.5) = 0.0062
P(-3 < z ? 0) = P(-3 < z < 0) = P(z < 0) - P(z < -3) = 0.5 - 0.0013 = 0.4987,
Computed the probabilities P(z < -1.0)=0.1587, P(z > -1.0)=0.8413, P(z < -1.5)=0.0668, P(z < -2.5)=0.0062, P(-3 < z < 0)=0.4987.
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Alessandra is having a dinner party she calculates that each meal will cost 13.00$ a person she has an 85 dollar budget for her party which inequality represents the number of people she can invite without going over her 85$ budget
She can only invite a total of six individuals, and the inequality that best captures the circumstance is 13x ≤ 85.
What is inequality?In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Given, Alessandra is having a dinner party she calculates that each meal will cost 13.00$ a person she has an 85 dollar budget
Let "x" be the number of people she can invite to the party
Thus,
The total cost required for the party = 13x
Since her budget is $85.
Maximum people she can invite:
13x ≤ 85
x ≤ 85/13
x ≤ 6.53
therefore, she can maximum invite 6 people and the inequality that represents the given situation is 13x ≤ 85.
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The floor of a rectangular room is to be covered with tiles 1-foot sides. The floor of the room is 18 feet long and 12 feet wide. How much would it cost at $4 a tile?
The cost for the flooring of the rectangular room is $864.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
Given that,
Dimension of each time = 1 foot
Length of the room = 18 feet
Width of the room = 12 feet
Number of tiles needed for the room = 18 × 12 = 216
Cost of one tile = $4
Total cost for the tile = 216 × $4 = $864
Hence the total cost for the tiles is $864.
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Find each percent of increase.round to the nearest percent 60 to 70
The percent of increase from 60 to 70 rounded to the nearest percent is 17%.
What is the percent of increase?Percent increase is simply the amount of increase from the initial value to the new value in terms of 100 parts of the initial value.
It is expressed as;
C = ((x₂ - x₁) / x₁)100%
Where x₁ is initial value and x₂ is new value
Given that;
Initial value x₁ = 60New value x₂ = 70Percentage increase C = ?Plug in the given values and solve for C.
C = ((x₂ - x₁) / x₁)100%
C = ((70 - 60) / 60) × 100%
C = ( 10 / 60) × 100%
C = 1/6 × 100%
C = 17%
Therefore, the percentage increase is 17%.
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◄) Convert:
5 gal 13 c =с
13 c is equal to 48.775 L.
What is equality?Equality in math is a concept that states that two expressions, equations, or values are equal to each other. Equality is symbolized by the equals sign “=.” Equality is a fundamental law of mathematics, and it is used in a variety of contexts and equations. Equality can be used to compare two different objects, or to set a value for a single object. Equality can also be used to determine if two equations are equivalent. Equality is an important concept in mathematics, as it allows us to find solutions to difficult problems.
5 gallons (gal) is equal to 18.925 liters (L). Therefore, 13 c is equal to 48.775 L.
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Need help with question (3)
Answer:
The statement "The series converges by the Integral Test" is true. The Integral Test is a method used to determine the convergence or divergence of a series. The test states that if the series is of the form:
∑(f(n))
where f(n) is a positive and continuous function defined for n ≥ 1 and is decreasing for n ≥ 1, then if the integral of f(n) from 1 to infinity converges, the series also converges. If the integral diverges, the series diverges.
It is important to note that the Integral Test is only one method of determining the convergence or divergence of a series and that it has some limitations such as it only works when the function f(n) is positive and decreasing. Also, the test is only inconclusive if the necessary conditions are not met, so statement 4 and 5 are not true.
Answer:
Step-by-step explanation:You should notice because you're in the class you should notice because the teachers are obviously teaching this because they wouldn't just give you something that they didn't cheat so if you sleep in class or like not paying attention speak into a friend or like something like doing something in my pay attention you ain't getting no you ain't getting nothing.
Which of the values make 4x<45 true?
A 12
B. 11
C. 13.5
D. 16
Answer: B - 11
Step-by-step explanation: Hello! How you can do this is by substituting A, B, C, and D for x.
D:
4(16)<45
64<45
64 is not less than 45, so this is false. D is not the answer.
C:
4(13.5)<45
54<45
54 is not less than 45, so this is false. C is not the answer.
A:
4(12)<45
48<45
48 is not less than 45, so this is false. A is not the answer.
B:
4(11)<45
44<45
44 is less than 45 so this is true.
The answer is B - 11.
13.) 5x − 2 – (8x − 1) =
14.) 1-(2-x) =
15.) 2x + 1 + (x + 3) =
16.) -1(3 + 2x) =
An equation is said to be linear if each term has a maximum of one degree.The system of linear equations is solved by (2,6).
What is a linear equation?An equation is said to be linear if each term has a maximum of one degree.
It is possible to formulate linear equations in the form y=mx+c.
A straight line results from a linear equation with two variables when its axes are plotted on the cartesian plane.
When the second equation for x is solved,
x + 5y = 32
x = 32 - 5y
Add the value of x to the first equation now,
2(32 - 5y) + 5y = 34
64 - 10y + 5y = 34
-5y = -30
y = 6
the value of y should be replaced in any one of the equations,
x + 5y = 32
x + 5(6) = 32
x = 2
Consequently, the system of linear equations' solution is (2,6).
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a white cylindrical silo has a diameter of $30$ feet and a height of $80$ feet. a red stripe with a horizontal width of $3$ feet is painted on the silo, as shown, making two complete revolutions around it. what is the area of the stripe in square feet?
So, the area of the stripe is 394.25= 282.75 square feet.
Silo Stripe Area CalculationThe stripe is a rectangle, with a width of 3 feet and a length that is the circumference of the cylinder. The diameter of the cylinder is 30 feet, so the circumference is 30pi=94.25 feet. So, the area of the stripe is 394.25= 282.75 square feet.
The white cylindrical silo has a red stripe painted on it, which makes two complete revolutions around the silo. The stripe is a horizontal rectangle with a width of 3 feet and a length equal to the circumference of the cylinder, which is calculated by multiplying the diameter of 30 feet by pi. The area of the stripe is the width of 3 feet multiplied by the length of 94.25 feet, which equals 282.75 square feet.
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The label on a car's antifreeze container claims to protect the car at temperatures greater than −40°C and less than 140°C. To convert Celsius temperature to Fahrenheit temperature, the formula is C equals five ninths times the quantity F minus thirty two.. Write a compound inequality to determine the Fahrenheit temperature range at which the antifreeze protects the car
Answer:
-40F to 284F
Step-by-step explanation:
C = 5/9F -32
so F = 32+9/5*C
so the range is
F= 32+9/5*(-40) = 32-72 = -40F
F= 32+9/5*(140) = 32+252 = 284F
if Kis the smallest positive integer such that(2k)(5200) has 303digits. Find the sum of the digits of that number when expanded.
The sum of the digits of the number 10302k, when k = 151, is 157.
The smallest positive integer such that (2k)(5200) has 303 digits is k = 151. In order to calculate the sum of the digits of this number, we will first expand the expression (2k)(5200). This expression can be expanded to 10302k. The sum of the digits of this number is equal to 1 + 0 + 3 + 0 + 2 + k. Since k = 151, the sum of the digits of this number is equal to 1 + 0 + 3 + 0 + 2 + 151 = 157. Therefore, the sum of the digits of the number 10302k, when k = 151, is 157.
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Suppose that y varies directly with x, and y=4 when x=20. (a) Write a direct variation equation that relates and y Equation: (b) Find y when x=9. y=
Answer:
(a) Since y varies directly with x, hence, y = kx, where k is a constant.
(b) When x = 20, y = 4
20k = 4
∴ k = 0.2
∴ When x = 9,
y = 9(0.2)
y = 1.8
pls help me with this 4(x−2+y)
Answer: 4x + 4y - 8
Step-by-step explanation:
4(x−2+y)
4x -8 +4y
4x + 4y - 8
Maleri Designs sells cartons of cloth face masks ($12) and cartons of hand-sanitizer ($6) on eBay. One of their customers, Mod World, purchased 22 cartons for $216. How many of cartons of each did Mod World purchase? Check your answer. Hint: Let F = Face masks.
The customer purchased 14 face masks and 8 hand sanitizers.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Given that, Maleri Designs sells cartons of cloth face masks ($12) and cartons of hand-sanitizer ($6) on eBay.
Let the number of face masks be f an the number of hand-sanitizers be h.
One of their customers, Mod World, purchased 22 cartons for $216.
Now, f+h=22 --------(I) and
12f+6h=216 --------(II)
f=22-h
Substitute f=22-h in equation (II), we get
12(22-h)+6h=216
264-12h+6h=216
264-216=6h
6h=48
h=8
Substitute h=8 in equation (I), we get
f+8=22
f=14
Hence, the customer purchased 14 face masks and 8 hand sanitizers.
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Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0
An equation 6(2x+4)²=(2x+4)+2 has degree 2, so it is quadratic equation. Therefore, option D is the correct answer.
What is a quadratic function in standard form?The standard form of a quadratic equation is given as:
ax² + bx + c = 0 where a, b, c are real numbers and a ≠ 0.
Quadratics are the polynomial equation which has highest degree of 2.
A) x⁴-6x²-27=0
Here, the highest degree is 4 so, it is biquadratic equation.
B) 3x⁴=2x
3x³=2
Here, the highest degree is 3 so, it is cubic equation.
C) 2(x + 5)⁴+2x²+5=0
Here, the highest degree is 4 so, it is biquadratic equation.
D) 6(2x+4)²=(2x+4)+2
6(4x²+16x+16)=(2x+4)+2
24x²+96x+96=2x+4+2
24x²+94x+90=0
Here, the highest degree is 2 so, it is quadratic equation.
E) 6x⁴= -x²+5
6x⁴+x²+5=0
Here, the highest degree is 4 so, it is biquadratic equation.
F) 8x⁴+2x²-4x=0
Here, the highest degree is 4 so, it is biquadratic equation.
Therefore, option D is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
Select all of the following equation(s) that are quadratic in form.
a) x⁴-6x²-27=0
b) 3x⁴=2x
c) 2(x + 5)⁴+2x²+5=0
d) 6(2x+4)²=(2x+4)+2
e) 6x⁴= -x²+5
f) 8x⁴+2x²-4x=0