Let's denote the width of the rug by x.
The dimensions of the rug to the nearest tenth of a foot are:
Width ≈ 6.7 feet
Length ≈ 11.7 feet
Since the rug is 5 feet longer than it is wide, its length can be expressed as (x+5).
We know that the diagonal of the rug is 12 feet. We can use the Pythagorean theorem to set up an equation relating the length, width, and diagonal:
(diagonal)^2 = (length)^2 + (width)^2
Substituting the values we know, we get:
12^2 = (x+5)^2 + x^2
Simplifying this equation gives:
144 = 2x^2 + 10x + 25
2x^2 + 10x - 119 = 0
Using the quadratic formula, we can solve for x (the width of the rug):
x = (-10 ± √(10^2 - 4(2)(-119))) / (2(2))
x ≈ 6.7 feet (rounded to the nearest tenth)
Now we can use the expression we found for the length (x+5) to find the length of the rug:
length ≈ 11.7 feet (rounded to the nearest tenth)
The rug measures 6.7 feet wide by 11.7 feet long, to the nearest tenth of a foot.
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14. Cheyenne took a train to visit her aunt. The train traveled at a constant speed of 60 miles per hour. Complete the table, and then write an equation to find the total distance, d, traveled after t hours.
The equation to find the total distance would be 60t.
What is total distance?
Whole distance refers to the actual distance between the origin and destination locations of the substance.
The distance traveled is equal to the speed multiplied by the time traveled, which gives the formula:
d = 60t
where d is the total distance traveled in miles, and t is the time traveled in hours.
Therefore, The equation to find the total distance would be 60t.
The table is below:
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f(x) = -3x + 2 f(7) =
The value of the function is -19.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = -3x + 2
Substitute x = 7.
f(7) = -3 x 7 + 2
f(7) = -21 + 2
f(-7) = -19
Thus,
-19 is the value.
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Benjamin considers purchasing a car for $35,000. He has been approved for a 6-
year loan for $30,000 with an interest rate of 5.25%. He also has the option to lease the car for $600 per month for 6 years with a $2,500 down payment.
Using the loan amortization formula, how much money does Benjamin save over the 6 years if he purchases the car? Do not consider the future value of the car in your answer.
Answer: Benjamin would save $11,720.48 over 6 years if he purchases the car instead of leasing it.
Step-by-step explanation:
To calculate the cost of the car if Benjamin purchases it, we can use the loan amortization formula. The formula for calculating the monthly payment of a loan is:
P = (r * A) / (1 - (1 + r)^(-n))
Where:
P = the monthly payment
r = the monthly interest rate (which is the annual interest rate divided by 12)
A = the loan amount
n = the total number of payments
For Benjamin's loan, the loan amount is $30,000, the interest rate is 5.25%, and the loan is for 6 years, or 72 months. Plugging these values into the formula, we get:
r = 0.0525 / 12 = 0.004375
A = $30,000
n = 72
P = (0.004375 * $30,000) / (1 - (1 + 0.004375)^(-72)) = $484.64
Therefore, Benjamin's monthly payment for the car loan is $484.64.
If Benjamin chooses to lease the car instead, he will pay $600 per month for 72 months, plus a $2,500 down payment. Therefore, the total cost of leasing the car is:
Total cost = ($600 * 72) + $2,500 = $45,700
To calculate how much money Benjamin saves by purchasing the car instead of leasing it, we can subtract the total cost of the car loan from the total cost of the lease:
Savings = Total cost of lease - Total cost of car loan
Savings = $45,700 - ($484.64 * 72)
Savings = $11,720.48
1. Which of the following is not a variable cost?
A. wages paid to labor
B. seeds and fertilizers for paddy farmers
C. rent on land
D. electricity bills
Answer:
b
Step-by-step explanation:
b seeds snd fertilizer
Phyllis invested $11,000, a portion earning a simple interest rate of
2 1/2% per year and the rest earning a rate of 2% per year. After one year the total interest earned on these investments was $255.00. How much money did she invest at each rate?
She invest money at each rate
First = 1000
Second = 10,000
What is simple interest?Simple interest is a method of calculating the interest charge. The interest can be calculated as the product of principal amount, rate and time peroid.
We are given that Phyllis invested $11,000, a portion earning a simple interest rate of 2 1/2% per year and the rest earning a rate of 2% per year.
Given the following :
Amount invested = $11,000
A portion earns 2 and 1/2 % interest per year
The rest earns a rate of 2% per year
The Total Interst earned after a year = $255
Amount invested at each rate;
Let amount invested at 2 1/2% = a
Amount invested at 2% is; 11,000 - a
Simple interest = principal x rate x time
First investment :
a x 5/2% x 1
Second :
(11000 - a) x 2%
Firat investment + second = $225
a x 0.025 + (11000 - a) x 0.02 = 225
0.025a + 220 - 0.02a = 225
0.005a = 225 - 220
0.005a = 5
a = 5 / 0.005
a = 1000
Amount in first investment = 1000
Second investment = 11000 - 1000 = 10,000
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In a transshipment problem, which of the following statements is a correct representation of the balance-of-flow rule if Total supply < total demand
Inflow-Outflow >= S or D
I + O >= S or D
I - O <= S or D
I + O <= S or D
In a transshipment problem (c) I - O <= S or D. here s is supply and D is demand,
A model that falls within the category of transportation issues is the transshipment model. Transshipment issues come in two different flavors.
Using transient (i.e. intermediate) nodes as sources and destinations
between the sources and the destination with a few temporary nodes
In a transportation issue, the shipment may move from S1 to D1, S1 to D2, S1 to D3, S2 to D1, S2 to D2, and so forth, from one specific source to another specific destination.
In this approach, the shipment travels via one or more intermediary nodes before arriving at the final location. With this technique, the shipment can move back and forth between sources and destinations before arriving at the intended location.
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The heights of a certain type of tree are approximately normally distributed with a mean height Mu = 5 ft and a standard deviation Sigma = 0.4 ft. Which statement must be true?
A tree with a height of 6.2 ft exists 3 standard deviations above the mean.
What is meant by normally distributed?The normal distribution represents a symmetrical display of data around its mean value, with the standard deviation serving as the determinant of the curve's breadth. The "bell curve" is used to visually represent it.
The normal distribution, sometimes referred to as the Gaussian distribution, is a probability distribution that is symmetric about the mean and demonstrates that data that exists closer to the mean exists more likely to even than data that exists farther from the mean. The normal distribution is depicted graphically as a "bell curve."
The majority of data points in a continuous probability distribution known as a "normal distribution" cluster around the middle of the range, while the remaining data points taper off symmetrically toward either extreme. The mean of the distribution is another name for the center of the range.
It exists said that an X value exists found Z standard deviations from the mean if:
[tex]$\frac{X-\mu}{\sigma}=Z$$[/tex]
Given:
[tex]$$\begin{aligned}& \mu=5 \mathrm{ft} \\& \sigma=0.4 \mathrm{ft}\end{aligned}$$[/tex]
We have four different values of X and we must calculate the Z-score for each
For X = 5.4 ft
[tex]$& Z=\frac{X-\mu}{\sigma} \\[/tex]
substitute the values in the above equation, we get
[tex]$ Z=\frac{5.4-5}{0.4}=1\end{aligned}$$[/tex]
A tree with a height of 5.4 ft exists 1 standard deviation above the mean
First Option: False
For X = 4.6 ft
[tex]$Z=\frac{4.6-5}{0.4}=-1\end{aligned}$$[/tex]
A tree with a height of 4.6ft exists 1 standard deviation below the mean
Second Option: False
For X = 5.8 ft
[tex]$Z=\frac{5.8-5}{0.4}=2\end{aligned}$$[/tex]
A tree with a height of 5.8 ft exists 2 standard deviation above the mean
Third Option: False
For X = 6.2 ft
[tex]$ Z=\frac{6.2-5}{0.4}=3\end{aligned}$$[/tex]
A tree with a height of 6.2 ft exists 3 standard deviations above the mean.
Therefore, the correct answer is option d) A tree with a height of 6.2 ft is 3 standard deviations above the mean.
The complete question is;
The heights of a certain type of tree are approximately normally distributed with a mean height y = 5 ft and a standard deviation = 0.4 ft. Which statement must be true?
a) A tree with a height of 5.4 ft is 1 standard deviation below the mean
b) A tree with a height of 4.6 ft is 1 standard deviation above the mean.
c) A tree with a height of 5.8 ft is 2.5 standard deviations above the mean
d) A tree with a height of 6.2 ft is 3 standard deviations above the mean.
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By conversion of the markup formula, solve the following.
Note: Round your answer to the nearest whole percent.
Percent markup on cost: ?
Percent markup on selling price: 25%
Markup on cost price is 75%
Percent markup on selling price: 25%
Percent markup on cost: ?
Markup is the total profit on a particular commodity or service. It is represented as a percentage over a cost price.
Percent markup on selling price is 25% which means that a product is sold out with 25% profit,
Percent markup on cost price =100-markup on selling price
= 100-25
=75
Hence, markup on cost price is 75%
The value of Percent markup on cost nearest to the whole number is,
⇒ 75%.
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
The value of Percent markup on selling price is,
⇒ 25%
Hence, The value of Percent markup on cost is,
⇒ 100% - selling price
⇒ 100% - 25%
⇒ 75%
Thus, We get;
The value of Percent markup on cost is,
⇒ 75%
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Compute the probability of randomly drawing six cards from a standard deck of cards and getting four aces and two kings. Give your answer accurate to at least eight decimal places. Compute the probability that a five-card poker hand is dealt to you that contains all hearts. Give your answer accurate to at least six decimal places.
The probability of being dealt a five-card poker hand that contains all hearts is approximately 0.000495, or 0.0495%.
Probability is the measure of the likelihood of an event happening, and it is expressed as a number between 0 and 1. The closer the number is to 0, the less likely the event is to occur, and the closer it is to 1, the more likely it is to occur.
Now, let's look at the first question: what is the probability of drawing six cards from a standard deck of cards and getting four aces and two kings?
So, the number of combinations of six cards from a deck of 52 cards is:
52C6 = 52!/6!(52-6)! = 20,358,520
Next, we need to find out how many ways we can draw four aces and two kings from the deck. There are 4 aces and 4 kings in a standard deck of cards, so the number of ways to draw four aces and two kings is:
4C4 x 4C2 = 1 x 6 = 6
The first factor, 4C4, represents the number of ways to draw all 4 aces, and the second factor, 4C2, represents the number of ways to draw 2 kings from the remaining 4 kings.
Finally, we can calculate the probability of getting four aces and two kings by dividing the number of ways to draw four aces and two kings by the number of combinations of six cards from the deck:
P(four aces and two kings) = 6/20,358,520 = 0.000000294
So, the probability of randomly drawing six cards from a standard deck of cards and getting four aces and two kings is approximately 0.00000029, or 0.0000294%.
Now, let's move on to the second question: what is the probability that a five-card poker hand is dealt to you that contains all hearts?
In a standard deck of cards, there are 13 hearts and 52 cards in total, so the probability of drawing one heart from the deck is 13/52, or 1/4. The probability of drawing five hearts in a row is the product of the probabilities of drawing each heart, since each card is drawn without replacement:
P(five hearts) = (13/52) x (12/51) x (11/50) x (10/49) x (9/48) = 0.000495
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Nancy collected 7 times as many bags of can if her friend collected 5/6 of a bag how many bags did Nancy collect
Nancy collected 5 5/6 cans of bags which is 7 times more than her friend.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, Nancy collected 7 times as many bags of can and her friend collected 5/6 of a bag.
Therefore, The amount of bags of cans Nancy collected can be obtained by multiplying 7 by the number of bags of can collected by her friend which is,
= (5/6)×7 bags.
= 35/6 bags.
= 5 5/6 can of bags.
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Government saving equals
Select one:
a.
taxes less government expenditures.
b.
government purchases of goods and services less taxes.
c.
taxes.
d.
government purchases of goods and services plus transfer payments less taxes.
e.
transfer payments.
Government saving equals: a. taxes less government expenditures.
What is government expenditure?Government expenditure can be defined as those expenses that government has incurred and this occur when government spent on goods and services.
Government saving tend to equals taxes less government expenditure which is option A was the correct option.
Therefore we can conclude that the correct option is A.
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Enrique can spend at most $2240 to renovate his home. One roll of wallpaper costs $32, and one can of paint costs $28. He needs at least 30 rolls of wallpaper and at least 20 cans of paint. Identify the graph that shows all possible combinations of wallpaper and paint that he can buy. Also, identify two possible combinations.
The possible combinations made by Enrique are mentioned below:
What is the combination?In mathematics, Combination is a term which tells us how many ways there are for the selection of a few things without considering their order.
Formula for selection of a objects from the n objects,
N = ⁿCₐ
The graph shows a scatter plot of points and does not have the feasible region shaded to show the combinations of wallpaper and paint that Enrique can buy.
In order to graph the feasible region, the budget constraint and minimum requirements constraint need to be plotted as lines on the same graph, and the feasible region would be the region that lies between these lines and below them.
Two possible combinations that Enrique can buy are (30, 100) and (40, 80).
These points represent 30 rolls of wallpaper and 100 cans of paint, or 40 rolls of wallpaper and 80 cans of paint, respectively.
These points lie on the feasible region and satisfy both the budget constraint and the minimum requirements constraint.
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Which of the following are sources of sampling error and which are sources of nonsampling error? Explain your answers.
a. The subject lies about past illegal drug use.
b. A typing error is made in recording the data.
c. Data are gathered by asking people to go to a website and answer questions online.
a. The subject lies about past illegal drug use: This is a source of nonsampling error, as it is not related to the process of selecting a sample from a population. Rather, it is an error that arises from the behavior or characteristics of the individual being sampled.
b. A typing error is made in recording the data: This is a source of nonsampling error, as it is a mistake that occurs during the process of recording or processing the data, and is not related to the sample selection process.
c. Data are gathered by asking people to go to a website and answer questions online: This is a source of sampling error, as it can potentially lead to a biased sample. Only people who have access to the internet and are willing to answer questions online will be included in the sample, which may not be representative of the population as a whole. This type of bias is known as "self-selection bias" and is a common problem with online surveys.
a cyclist is riding their bicycle on flat terrain at a speed of 22 miles per hour. the wheels on the bike have a diameter of 26 inches.
The angular speed in radians per minute of the cyclist riding a bike with wheels of diameter 26 inches at a speed of 22 miles per hour is approximately 1124.65 radians per minute.
The formula for the angular speed is:
angular speed = linear speed / radius
where the radius is half the diameter of the wheel. We need to convert the units to be consistent, so let's convert the speed from miles per hour to inches per minute and the diameter from inches to feet:
22 miles per hour = 22 * 5280 feet per hour / 60 minutes per hour
≈ 2437.3 inches per minute
26 inches = 26/12 feet = 2.1667 feet
Now we can calculate the angular speed:
angular speed = 2437.3 / 2.1667 ≈ 1124.65 radians per minute
Your question is incomplete, most likely it was:
A cyclist is riding their bicycle on flat terrain at a speed of 22 miles per hour. the wheels on the bike have a diameter of 26 inches.
Find the angular speed in radians per minute.
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A group of friends’ dinner bill is $82.95 They want to leave a 15% tip. What is their total dinner bill, including tip?
The total dinner cost, including the tip, comes at $92.40.
What is the percentage of a number explained?The definition of percentage is "out of 100." In mathematics, percentages are used to represent parts of a whole, much as fractions and decimals.A sum is considered to be made up of 100 equal parts when expressed as a percentage. Use the symbol% to denote percentages in numbers.A lunch for a few friends will set you back $82.95
They want to leave a 15% tip.
So,
Amount of tip:
15 % of 82.95 = 15*82.95 / 100
15 % of 82.95 = 12.4425
Total cost = 82.95 + 12.4425
Total cost = 95.3925
Total cost = $92.40
Thus, the total dinner cost, including the tip, comes at $92.40.
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In 2016 the average NBA ticket for the finals was $1444. In 2017, the price increased by 20%. If this trend continues, what will be the price in 2020? Round to the nearest dollar
Answer:
Step-by-step explanation:
To find the price of the NBA ticket in 2017, we need to add 20% to the 2016 price:
Price in 2017 = $1444 + 0.20 x $1444 = $1732.80
To find the price of the NBA ticket in 2020, we need to increase the 2017 price by 20%:
Price in 2020 = $1732.80 + 0.20 x $1732.80 = $2079.36
Rounding this to the nearest dollar, we get:
Price in 2020 = $2079
A jug contained314 pints of milk at the start of a baking class. At the end of the class, only 3 fluid ounces were left.
How many fluid ounces of milk were used during the class?
Responses
10 fl oz
10 fl oz
23 fl oz
23 fl oz
49 fl oz
49 fl oz
101 fl oz
Answer:
311 fl oz only were used, that is what I got for your answer..
The answer is 49 fl oz
Write the equation of the line in fully simplified slope-intercept form.
-12-11-10-9-8-7-6-5-4-3-2
298 165 +3
12
11
10
2
3
-8
-9
-10
-11
-12
1 2 3 4 5 6 7 8 9 10 11 12
An equation of the line in fully simplified slope-intercept form is y = -13x - 22.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.At data points (-2, 4), a linear equation of this line can be calculated by using the point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 4 = (10 - (-3))/(-3 - (-2))(x - (-2))
y - 4 = -13(x + 2)
y = -13x - 26 + 4
y = -13x - 22
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95. A basketball team has won 60 games out of 80 played. It has 40 games still to play. How many of these must the team win to make its record for the season 80%?
F) 20
G) 22
H) 25
J) 30
K). none of these
Help 30 points !!!
Answer:
K. none of these (36 wins needed)
Step-by-step explanation:
1st way
80 + 40 = 120
80% of 120 = 96
96 - 60 = 36
2nd way
80 played + 40 left = 120 total
80% season record times 120 total =
12 times 8 is 96 = 80% win record
60 won 20 lost out of 80 total
120 total - 96 wins = 24 losses
96 wins 24 losses 120 total
96 wins - 60 wins = 36 wins out of 40 total
For each function x given below, find a single expression for x (i.e., an expression that does not involve multiple cases). Group similar unit-step function terms together in the expression for x. (c) x(t) = 4t +4 -1 St<-Ź 412 -
Thus, a single expression for x(t) that does not involve multiple cases is:
x(t) = 4t + 4 - u(t-2) - 2u(t-4) + 12u(t-12)
Using the properties of the unit step function,
we can write:
x(t) = 4t + 4 - u(t-2) - 2u(t-4) + 12u(t-12)
Breaking it down:
For t < 2, the unit step function u(t-2) is 0,
so it does not affect the expression for x(t).
For 2 ≤ t < 4, u(t-2) = 1 and u(t-4) = 0,
so the expression becomes:
x(t) = 4t + 4 - 1 = 4t + 3
For 4 ≤ t < 12, u(t-2) = u(t-4) = 1,
so the expression becomes:
x(t) = 4t + 4 - 2 = 4t + 2
For t ≥ 12, u(t-2) = u(t-4) = 1, and u(t-12) = 1,
so the expression becomes:
x(t) = 4t + 4 - 1 - 2 + 12 = 4t + 13
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Solve the inequalities
Answer:
m ≥ 6
Step-by-step explanation:
The question asks us to solve the following inequality:
[tex]8m - 8 \geq 40[/tex].
To solve it, we need to make m the subject of the inequality:
[tex]8m - 8 \geq 40[/tex]
⇒ [tex]8m - 8 + 8 \geq 40 + 8[/tex] [Adding 8 to both sides of inequality]
⇒ [tex]8m \geq 48[/tex]
⇒ [tex]\frac{8}{8}m \geq \frac{48}{8}[/tex] [Dividing both sides of inequality by 8]
⇒ [tex]m \geq \bf 6[/tex]
Therefore, the solution to the inequality is m ≥ 6.
Determine whether the set S spans R3. If the set does not span R3, then give a geometric description of the subspace that it does span.
S = {(1, −2, 0), (0, 0, 1), (−1, 2, 0)}
The set S spans R₃ if and only if for any vector (a, b, c) in R₃, there exist scalars x, y, and z such that z is not zero and z/2 is nonzero. This is true for all vectors in R₃, so we conclude that S spans R₃.
To determine if the set S spans R₃, we need to see if any vector in R₃ can be written as a linear combination of the vectors in S.
Let (a, b, c) be an arbitrary vector in R₃. Then we want to see if there exist scalars x, y, and z such that:
x(1, -2, 0) + y(0, 0, 1) + z(-1, 2, 0) = (a, b, c)
This is equivalent to the system of equations:
x - z = a
-2x + 2z = b
y = c
Solving for x, y, and z, we get:
x = (a - z)/2
y = c
z = (b + 2x)/2 = (b + a - z)/2
Substituting these values into the equation for the linear combination, we get:
[(a - z)/2](1, -2, 0) + c(0, 0, 1) + [(b + a - z)/2](-1, 2, 0)
= ((a - z)/2 - (b + a - z)/2, -2(a - z)/2 + 2(b + a - z)/2, 0)
= (-b/2, (3a - b)/2, z/2)
Geometrically, the set S consists of two nonparallel vectors and a vector orthogonal to the xy-plane. Thus, the subspace spanned by S is a plane in R₃ passing through the origin.
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Hi. Please help. each container will be made from material that costs $0.0015 per square inch. Explain how to determine the costs of each container. Then find the cost of container B. Round to the nearest cent.
PICTURES OF CONTAINER B:
The cost of each container is $0.18.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
from the given figure we get,
container's length = 6in
width = 2.5in
height = 8in
volume of the container =120 in^3
each container will be made from material that costs $0.0015 per cubic inch.
so, the costs of each container = $0.0015* 120
= $0.18
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59.05 as a fraction of an hour
The given decimal in fraction as 1181/20.
What is conversion of decimal number to fraction?Steps for conversion:
Identify the place value of the digits after the decimal, in the number.Use that to determine what the denominator of the fraction would be.Remove the decimal point. Re-write in the fraction form and simplify itExpress in terms of the lowest equivalent fraction.The given decimal number is 59.05
Here, multiply 100 to both the numerator and denominator of the decimal, that is
59.05/1 ×100/100
= 5905/100
= 1181/20
Therefore, the fraction is 1181/20.
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(15x²+x²+7)-(6x² - 2x³)-7x²
Answer:
= 3x² + 7 +2x³.
Step-by-step explanation:
Here is my solution to my answer.
in a scientific study there are 10 guinea pigs,4 of which are pregnant. if are selected at random without replacement, find the probability that all are pregnant. enter your answer as a fraction or a decimal rounded to decimal places.
The probability that all the guinea pigs selected randomly are pregnant is 1/30 or 0.033
Given, we have 10 guinea pigs out of which 4 are pregnant. We know that probability of an event ⇒ P(E) = (No of favorable outcomes)/(No of all outcomes) . So, The probability of selecting pigs that are pregnant is :
⇒ 4/10
Now, 3 selections are made randomly. The probability that the 1st selected guinea pig will be pregnant = 4/10
The probability that the 2nd selected guinea pig will be pregnant = 3/9
The probability that the 3rd selected guinea pig will be pregnant = 2/8
Therefore, the probability of all the 3 selected guinea pigs being pregnant will be :
⇒ (4/10) x (3/9) x (2/8)
⇒ 1/30
Therefore, The probability of all the selections of pigs being pregnant without replacement rounded to 3 decimal places is 0.033 or 1/30
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The complete question will be :
In a scientific study there are 10 guinea pigs,4 of which are pregnant. if 3are selected at random without replacement, find the probability that all are pregnant. enter your answer as a fraction or a decimal rounded to 3 decimal places.
Definition: If r and s are statements, r unless s means if ∼s then r. Consider the following statement. This door will not open unless a security code is entered. Which of the following expresses the statement in if-then form? If a security code is entered, then the door will not open. If the door will not open, then a security code was entered. If a security code is not entered, then the door will open. If the door will open, then a security code was not entered. If a security code is not entered, then the door will not open.
The statement "This door will not open unless a security code is entered" can be expressed in if-then form as "If a security code is not entered, then the door will not open."
This is because the statement "unless" indicates a necessary condition. In other words, the security code must be entered in order for the door to open, and if the security code is not entered, then the door will not open. Therefore, the correct option is: If a security code is not entered, then the door will not open.
The capacity to use numerical data to recognise patterns, solve problems without a pre-existing formula, understand graphs, and reach reasonable conclusions when faced with numerical evidence is known as mathematical reasoning.
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Suppose A is nxn and the equation Ax-b has a solution for each b in R" Explain why A must be invertible. [Hint Is A row equivalent to n] Choose the correct answer below. O A. If the equation Ax-b has a solution for each b in R, then A has one pivot pasition It fallows that A is row equivalent ton Therefore, A is invertible O B f the equation Ax-b has a solution for each b ın Rn nen A has a prot position n each row. Srce 4 s s ae he p os mus be on e da ona of A t o lo s hat s :There re s nven ble O C. If the equation Ax-b has a solution for each b in R" then A has a pivot position in each row Since A is square, the pivots must be on the diagonal of A. It follows that A is row equivalent to In Therefore, A is invertble O D. the equation Ax -b has a solution for each b in IR", then A does not have a pivot position in each row Since A is square, and In is square, A is row equvalent to In Therefore, A is invertible
The right response is C. A has a pivot location in each row if the equation Ax-b has a solution for each b in [tex]R^n[/tex].
The pivots must be on A's diagonal since A is square. Hence, A is a row that is identical to In. A is hence invertible.
If there is an answer to the equation Ax-b for each b in [tex]R^n[/tex], then there is an answer to the equation Ax = b for each b. This indicates that A has complete rank since the column space of A is all of [tex]R^n[/tex].
A must-have n pivot points (one in each row), and the pivots must be on the diagonal of A since A is a square matrix with complete rank.
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What is the value of a?
[tex]k=\sqrt{f+f}\\f=a^2\\a=?[/tex]
In linear equation, √2a² is the value of a .
What are examples of linear equations?
Ax+By=C represents a two-variable linear equation in its standard form. As an illustration, the conventional form of the linear equation 2x+3y=5 It is rather simple to locate both intercepts when an equation is stated in this way (x and y).
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
k = √f + f
f = a²
k = √a² + a²
= √2a²
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Brett's fish tank can hold up to 10.5 gallons of water before it overflows. Brett has poured 9 gallons of water into his fish tank so far.
Let x represent how many more gallons of water Brett can pour into his fish tank. Which inequality describes the problem?
Solve the inequality. Then, complete the sentence to describe the solution.
Brett can pour at most
more gallons of water into his fish tank.
Answer:
x ≤ 1.5
Step-by-step explanation:
Brett can pour at most 1.5 more gallons of water into his fish tank. This is because the fish tank can only hold 10.5 gallons of water and Brett has already poured 9 gallons into the tank. So, the maximum amount of water he can pour is the remaining 1.5 gallons.